Mian–Chowla sequence: Difference between revisions

Revision as of 19:10, 20 April 2013

A cell membrane defines a boundary between the living cell and its environment. The primary constituent of a membrane is a phospholipid bilayer that forms in a water-based environment due to the hydrophilic nature of the lipid head and the hydrophobic nature of the two tails. In addition there may be other lipids and proteins in the membrane, the latter typically in the form of isolated rafts.

Of the numerous models that have been developed to describe the deformation of cell membranes, a widely accepted model is the fluid mosaic model proposed by Singer and Nicolson in 1972. ^[1] In this model, the cell membrane surface is modeled as a two-dimensional fluid-like lipid bilayer where the lipid molecules can move freely. The proteins are partially or fully embedded in the lipid bilayer. Fully embedded proteins are called integral membrane proteins because they traverse the entire thickness of the lipid bilayer. These communicate information and matter between the interior and the exterior of the cell. Proteins that are only partially embedded in the bilayer are called peripheral membrane proteins. The membrane skeleton is a network of proteins below the bilayer that links with the proteins in the lipid membrane.

Elasticity of closed lipid vesicles

The simplest component of a membrane is the lipid bilayer which has a thickness that is much smaller than the length scale of the cell. Therefore the lipid bilayer can be represented by a two-dimensional mathematical surface. In 1973, based on similarities between lipid bilayers and nematic liquid crystals, Helfrich ^[2] proposed the following expression for the curvature energy per unit area of the closed lipid bilayer Template:NumBlk where $k_{c},{\bar {k}}$ are bending rigidities, $c_{0}$ is the spontaneous curvature of the membrane, and $H$ and $K$ are the mean and Gaussian curvature of the membrane surface, respectively.

The free energy of a closed bilayer under the osmotic pressure $\Delta p$ (the outer pressure minus the inner one) as: Template:NumBlk where dA and dV are the area element of the membrane and the volume element enclosed by the closed bilayer, respectively, and λ is the surface tension of the bilayer. By taking the first order variation of above free energy, Ou-Yang and Helfrich ^[3] derived an equation to describe the equilibrium shape of the bilayer as: Template:NumBlk

They also obtained that the threshold pressure for the instability of a spherical bilayer was Template:NumBlk where $R$ being the radius of the spherical bilayer.

Using the shape equation (3) of closed vesicles, Ou-Yang predicted that there was a lipid torus with the ratio of two generated radii being exactly ${\sqrt {2}}$ . ^[4] His prediction was soon confirmed by the experiment ^[5] Additionally, researchers obtained an analytical solution ^[6] to (3) which explained the classical problem, the biconcave discoidal shape of normal red cells.

Elasticity of open lipid membranes

The opening-up process of lipid bilayers by talin was observed by Saitoh et al. ^[7] arose the interest of studying the equilibrium shape equation and boundary conditions of lipid bilayers with free exposed edges. Capovilla et al., ^[8] Tu and Ou-Yang ^[9] carefully studied this problem. The free energy of a lipid membrane with an edge $C$ is written as Template:NumBlk where $ds$ and $\gamma$ represent the arclength element and the line tension of the edge, respectively. The first order variation gives the shape equation and boundary conditions of the lipid membrane: Template:NumBlk Template:NumBlk Template:NumBlk Template:NumBlk

where $k_{n}$ , $k_{g}$ , and $\tau _{g}$ are normal curvature, geodesic curvature, and geodesic torsion of the boundary curve, respectively. $\mathbf {e} _{2}$ is the unit vector perpendicular to the tangent vector of the curve and the normal vector of the membrane.

Elasticity of cell membranes

A cell membrane is simplified as lipid bilayer plus membrane skeleton. The skeleton is a cross-linking protein network and joints to the bilayer at some points. Assume that each proteins in the membrane skeleton have similar length which is much smaller than the whole size of the cell membrane, and that the membrane is locally 2-dimensional uniform and homogenous. Thus the free energy density can be expressed as the invariant form of $2H$ , $K$ , $\mathrm {tr} (\varepsilon )$ and $\det(\varepsilon )$ : Template:NumBlk where $\varepsilon$ is the in-plane strain of the membrane skeleton. Under the assumption of small deformations, and invariant between $\mathrm {tr} \varepsilon$ and $-\mathrm {tr} \varepsilon$ , (10) can be expanded up to second order terms as: Template:NumBlk where $k_{d}$ and $\mu$ are two elastic constants. In fact, the first two terms in (11) are the bending energy of the cell membrane which contributes mainly from the lipid bilayer. The last two terms come from the entropic elasticity of the membrane skeleton.

References

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Bibliography

Reviews on configurations of lipid vesicles

[1] R. Lipowsky, The Conformation of Membranes, Nature 349 (1991) 475-481.

[2] U. Seifert, Configurations of Fluid Membranes and Vesicles, Adv. Phys. 46 (1997) 13-137.

[3] Z. C. Ou-Yang, J. X. Liu and Y. Z. Xie, Geometric Methods in the Elastic Theory of Membranes in Liquid Crystal Phases (World Scientific, Singapore, 1999).

Research papers on closed vesicles

[1] W. Helfrich, Elastic Properties of Lipid Bilayers—Theory and Possible Experiments, Z. Naturforsch. C 28 (1973) 693-703.

[2] O.-Y. Zhong-Can and W. Helfrich, Instability and Deformation of a Spherical Vesicle by Pressure, Phys. Rev. Lett. 59 (1987) 2486-2488.

[3] O.-Y. Zhong-Can, Anchor Ring-Vesicle Membranes, Phys. Rev. A 41 (1990) 4517-4520.

[4] H. Naito, M. Okuda, and O.-Y. Zhong-Can, Counterexample to Some Shape Equations for Axisymmetric Vesicles, Phys. Rev. E 48 (1993) 2304-2307.

[5] U. Seifert, Vesicles of toroidal topology, Phys. Rev. Lett. 66 (1991) 2404-2407.

[6] U. Seifert, K. Berndl, and R. Lipowsky, Shape transformations of vesicles: Phase diagram for spontaneous- curvature and bilayer-coupling models, Phys. Rev. A 44 (1991) 1182-1202.

[7] L. Miao etal., Budding transitions of fluid-bilayer vesicles: The effect of area-difference elasticity, Phys. Rev. E 49 (1994) 5389-5407.

Research papers on open membranes

[1] A. Saitoh, K. Takiguchi, Y. Tanaka, and H. Hotani, Opening-up of liposomal membranes by talin, Proc. Natl. Acad. Sci. 95 (1998) 1026-1031.

[2] R. Capovilla, J. Guven, and J.A. Santiago, Lipid membranes with an edge, Phys. Rev. E 66 (2002) 021607.

[3] R. Capovilla and J. Guven, Stresses in lipid membranes, J. Phys. A 35 (2002) 6233-6247.

[4] Z. C. Tu and Z. C. Ou-Yang, Lipid membranes with free edges, Phys. Rev. E 68, (2003) 061915.

[5] T. Umeda, Y. Suezaki, K. Takiguchi, and H. Hotani, Theoretical analysis of opening-up vesicles with single and two holes, Phys. Rev. E 71 (2005) 011913.

Numerical solutions on lipid membranes

[1] J. Yan, Q. H. Liu, J. X. Liu and Z. C. Ou-Yang, Numerical observation of nonaxisymmetric vesicles in fluid membranes, Phys. Rev. E 58 (1998) 4730-4736.

[2] J. J. Zhou, Y. Zhang, X. Zhou, Z. C. Ou-Yang, Large Deformation of Spherical Vesicle Studied by Perturbation Theory and Surface Evolver, Int J Mod Phys B 15 (2001) 2977-2991.

[3] Y. Zhang, X. Zhou, J. J. Zhou and Z. C. Ou-Yang, Triconcave Solution to the Helfrich Variation Problem for the Shape of Lipid Bilayer Vesicles is Found by Surface Evolver, In. J. Mod. Phys. B 16 (2002) 511-517.

[4] Q. Du, C. Liu and X. Wang, Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions, J. Comput. Phys. 212 (2006) 757.

[5] X. Wang and Q. Du, physics/0605095.

Selected papers on cell membranes

[1] Y. C. Fung and P. Tong, Theory of the Sphering of Red Blood Cells, Biophys. J. 8 (1968) 175-198.

[2] S. K. Boey, D. H. Boal, and D. E. Discher, Simulations of the Erythrocyte Cytoskeleton at Large Deformation. I. Microscopic Models, Biophys. J. 75 (1998) 1573-1583.

[3] D. E. Discher, D. H. Boal, and S. K. Boey, Simulations of the Erythrocyte Cytoskeleton at Large Deformation. II. Micropipette Aspiration, Biophys. J. 75 (1998) 1584-1597.

[4] E. Sackmann, A.R. Bausch and L. Vonna, Physics of Composite Cell Membrane and Actin Based Cytoskeleton, in Physics of bio-molecules and cells, Edited by H. Flyvbjerg, F. Julicher, P. Ormos And F. David (Springer, Berlin, 2002).

[5] G. Lim, M. Wortis, and R. Mukhopadhyay, Stomatocyte–discocyte–echinocyte sequence of the human red blood cell: Evidence for the bilayer–couple hypothesis from membrane mechanics, Proc. Natl. Acad. Sci. 99 (2002) 16766-16769.

[6] Z. C. Tu and Z. C. Ou-Yang, A Geometric Theory on the Elasticity of Bio-membranes, J. Phys. A: Math. Gen. 37 (2004) 11407-11429.

[7] Z. C. Tu and Z. C. Ou-Yang, Elastic theory of low-dimensional continua and its applications in bio- and nano-structures,arxiv:0706.0001.

↑ Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

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Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
↑ Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
↑ Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
↑ Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
↑ Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
↑ Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
↑ Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
↑ Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
↑ Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010

[1] Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010

[2] Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010

[3] Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010

[4] Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010

[5] Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010

[6] Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010

[7] Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010

[8] Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010

[9] Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010

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+A [[cell membrane]] defines a boundary between the living cell and its environment.  The primary constituent of a membrane is a [[phospholipid]] bilayer that forms in a water-based environment due to the [[hydrophilic]] nature of the lipid head and the [[hydrophobic]] nature of the two tails.  In addition there may be other [[lipid]]s and [[protein]]s in the membrane, the latter typically in the form of isolated rafts.
+Of the numerous models that have been developed to describe the deformation of cell membranes, a widely accepted model  is the [[fluid mosaic model]] proposed by Singer and Nicolson in 1972. <ref>{{Citation|last1=Singer|first1= S. Jonathan|first2= Garth L.|last2= Nicolson|title=The fluid mosaic model of the structure of cell membranes|journal= Science|volume= 175|number= 23|year=1972|pages= 720-731.}}</ref> In this model, the [[cell membrane]] surface is modeled as a two-dimensional [[fluid]]-like [[lipid bilayer]] where the lipid molecules can move freely.  The proteins are partially or fully embedded in the lipid bilayer.  Fully embedded proteins are called [[integral membrane protein]]s because they traverse the entire thickness of the lipid bilayer.  These communicate information and matter between the interior and the exterior of the cell.  Proteins that are only partially embedded in the bilayer are called [[peripheral membrane protein]]s. The [[membrane skeleton]] is a network of proteins below the bilayer that links with the proteins in the lipid membrane.
+==Elasticity of closed lipid vesicles==
+The simplest component of a membrane is the lipid bilayer which has a thickness that is much smaller than the length scale of the cell.  Therefore the lipid bilayer can be represented by a two-dimensional mathematical surface. In 1973, based on similarities between lipid bilayers and [[nematic]] [[liquid crystal]]s, Helfrich <ref>{{Citation|last=Helfrich|first= Wolfgang|title=Elastic properties of lipid bilayers: theory and possible experiments|journal=Zeitschrift für Naturforschung. Teil C: Biochemie, Biophysik, Biologie, Virologie|volume= 28|number=11 |year=1973|pages= 693.}}</ref>  proposed the following expression for the curvature energy per unit area of the closed lipid bilayer
+{{NumBlk|:|
+<math>
+  f_c = \frac{k_c}{2}(2H-c_0)^2+\bar{k}\,K
+</math>
+|{{EquationRef|1}}}}
+where <math>k_c,\bar{k}</math> are [[bending rigidity|bending rigidities]], <math>c_0</math> is the spontaneous curvature of the membrane, and <math>H</math> and <math>K</math> are the [[Mean curvature|mean]] and [[Gaussian curvature]] of the membrane surface, respectively.
+The [[Thermodynamic free energy|free energy]] of a closed bilayer under the osmotic pressure <math>\Delta p</math> (the outer pressure minus the inner one) as:
+{{NumBlk|:|
+<math>
+  F_H=\int (f_c+\lambda)\, dA+\Delta p\int dV
+</math>
+|{{EquationRef|2}}}}
+where ''dA'' and ''dV'' are the area element of the membrane and the volume element enclosed by the closed bilayer, respectively, and ''λ'' is the [[surface tension]] of the bilayer. By taking the first order variation of above free energy, Ou-Yang and Helfrich <ref>{{Citation|last1=Zhong-Can|first1= Ou-Yang|first2= Wolfgang |last2=Helfrich|title=Instability and deformation of a spherical vesicle by pressure|journal= Physical Review Letters |volume=59|number=21|year=1987|pages= 2486.}}</ref> derived an equation to describe the equilibrium shape of the bilayer as:
+{{NumBlk|:|
+<math>
+  \Delta p-2\lambda H+k_c(2H+c_0)(2H^2-c_0H-2K)+2k_c\nabla^2 H=0
+</math>
+|{{EquationRef|3}}}}
+They also obtained that the threshold pressure for the instability of a spherical bilayer was
+{{NumBlk|:|
+<math>
+  \Delta p_{c}\propto k_c/R^3
+</math>
+|{{EquationRef|4}}}}
+where <math>R</math> being the radius of the spherical bilayer.
+Using the shape equation (3) of closed vesicles, Ou-Yang predicted that there was a lipid torus with the ratio of two generated radii being exactly <math>\sqrt{2}</math>. <ref>{{Citation|last=Zhong-Can|first= Ou-Yang|title=Anchor ring-vesicle membranes|journal=Physical Review A|volume= 41|number=8|year=1990|pages= 4517.}}</ref> His prediction was soon confirmed by the experiment <ref>{{Citation|last1=Mutz|first1= M.|first2=D.|last2=Bensimon|title=Observation of toroidal vesicles|journal=Physical Review A|volume=43|number=8|year=1991|pages=4525.}}</ref> Additionally, researchers obtained an analytical solution <ref>{{Citation|last1=Naito|first1= Hiroyoshi|first2= Masahiro |last2=Okuda|first3=Ou-Yang |last3=Zhong-Can|title=Counterexample to some shape equations for axisymmetric vesicles|journal=Physical Review E|volume= 48 |year=1993|pages= 2304-2307.}}</ref> to (3) which explained the classical problem, the biconcave discoidal shape of normal red cells.
+==Elasticity of open lipid membranes==
+The opening-up process of lipid bilayers by [[talin]] was observed by Saitoh et al. <ref>{{Citation|last1=Saitoh|first1= Akihiko|first2=Kingo|last2=Takiguchi|first3=Yohko|last3=Tanaka|first4=Hirokazu|last4=Hotani|title=Opening-up of liposomal membranes by talin|journal= Proceedings of the National Academy of Sciences |volume=95|number=3 |year=1998|pages= 1026-1031.}}</ref> arose the interest of studying the equilibrium shape equation and boundary conditions of lipid bilayers with free exposed edges. Capovilla et al., <ref>{{Citation|last1=Capovilla|first1= R.|first2=J. |last2=Guven|first3= J. A. |last3=Santiago|title=Lipid membranes with an edge|journal= Physical Review E |volume=66|number= 2 |year=2002|pages= 021607.}}</ref> Tu and Ou-Yang <ref>{{Citation|last1=Tu|first1=Z. C.|first2=Ou-Yang|last2=Z. C.|year=2003|title= Lipid membranes with free edges|journal= Physical Review E|volume= 68|number=6|pages= 061915.}}</ref> carefully studied this problem. The free energy of a lipid membrane with an edge <math>C</math> is written as
+{{NumBlk|:|
+<math>
+  F_o=\int (f_c+\lambda) dA+\gamma\oint_C ds
+</math>
+|{{EquationRef|5}}}}
+where <math>ds</math> and <math>\gamma</math> represent the arclength element and the line tension of the edge, respectively. The first order [[variational calculus|variation]] gives the shape equation and boundary conditions of the lipid membrane:
+{{NumBlk|:|
+<math>
+   k_{c}(2H+c_{0})(2H^{2}-c_{0}H-2K)-2\lambda H+k_{c}\nabla^{2}(2H)=0
+</math>
+|{{EquationRef|6}}}}
+{{NumBlk|:|
+<math>
+  \left. \left[ k_{c}(2H+c_{0})+\bar{k}k_n\right]\right\vert _{C}=0
+</math>
+|{{EquationRef|7}}}}
+{{NumBlk|:|
+<math>
+  \left. \left[ -2k_{c}\frac{\partial H}{\partial\mathbf{e}_2}+\gamma k_n+\bar{k}\frac{d\tau_g}{ds}\right]\right\vert _{C}=0
+</math>
+|{{EquationRef|8}}}}
+{{NumBlk|:|
+<math>
+  \left. \left[ \frac{k_{c}}{2}(2H+c_{0})^{2}+\bar{k}K+\lambda+\gamma k_{g}\right]\right\vert _{C}=0
+</math>
+|{{EquationRef|9}}}}
+where <math>k_n</math>, <math>k_g</math>, and <math>\tau_g</math> are normal curvature, [[geodesic curvature]], and [[geodesic torsion]] of the boundary curve, respectively. <math>\mathbf{e}_2</math> is the unit vector perpendicular to the tangent vector of the curve and the normal vector of the membrane.
+==Elasticity of cell membranes==
+A cell membrane is simplified as lipid bilayer plus membrane skeleton. The skeleton is a cross-linking protein network and joints to the bilayer at some points. Assume that each proteins in the membrane skeleton have similar length which is much smaller than the whole size of the cell membrane, and that the membrane is locally 2-dimensional uniform and homogenous. Thus the free energy density can be expressed as the invariant form of <math>2H</math>, <math>K</math>, <math>\mathrm{tr}(\varepsilon)</math> and <math>\det(\varepsilon)</math>:
+{{NumBlk|:|
+<math>
+  f_{cm}=f(2H,K,\mathrm{tr}(\varepsilon),\det(\varepsilon))
+</math>
+|{{EquationRef|10}}}}
+where <math>\varepsilon</math> is the in-plane [[infinitesimal strain theory|strain]] of the membrane skeleton. Under the assumption of small deformations, and invariant between <math>\mathrm{tr}\varepsilon</math> and <math>-\mathrm{tr}\varepsilon</math>, (10) can be expanded up to second order terms as:
+{{NumBlk|:|
+<math>
+  f_{cm}=\frac{k_c}{2}(2H-c_0)^2+\bar{k}K+\lambda+\frac{k_d}{2}(\mathrm{tr}\varepsilon)^2-2\mu (\det\varepsilon)
+</math>
+|{{EquationRef|11}}}}
+where <math>k_d</math> and <math>\mu</math> are two elastic constants. In fact, the first two terms in (11) are the bending energy of the cell membrane which contributes mainly from the lipid bilayer. The last two terms come from the [[rubber elasticity|entropic elasticity]] of the membrane skeleton.
+== References ==
+{{reflist|2}}
+== Bibliography ==
+===Reviews on configurations of lipid vesicles===
+[1] R. Lipowsky, The Conformation of Membranes, Nature 349 (1991) 475-481.
+[2] U. Seifert, Configurations of Fluid Membranes and Vesicles, Adv. Phys. 46 (1997) 13-137.
+[3] Z. C. Ou-Yang, J. X. Liu and Y. Z. Xie, Geometric Methods in the Elastic Theory of Membranes in Liquid Crystal Phases (World Scientific, Singapore, 1999).
+===Research papers on closed vesicles===
+[1] W. Helfrich, Elastic Properties of Lipid Bilayers—Theory and Possible Experiments, Z. Naturforsch. C 28 (1973) 693-703.
+[2] O.-Y. Zhong-Can and W. Helfrich, Instability and Deformation of a Spherical Vesicle by Pressure, Phys. Rev. Lett. 59 (1987) 2486-2488.
+[3] O.-Y. Zhong-Can, Anchor Ring-Vesicle Membranes, Phys. Rev. A 41 (1990) 4517-4520.
+[4] H. Naito, M. Okuda, and O.-Y. Zhong-Can, Counterexample to Some Shape Equations for Axisymmetric Vesicles, Phys. Rev. E 48 (1993) 2304-2307.
+[5] U. Seifert, Vesicles of toroidal topology, Phys. Rev. Lett. 66 (1991) 2404-2407.
+[6] U. Seifert, K. Berndl, and R. Lipowsky, Shape transformations of vesicles: Phase diagram for spontaneous- curvature and bilayer-coupling models, Phys. Rev. A 44 (1991) 1182-1202.
+[7] L. Miao etal., Budding transitions of fluid-bilayer vesicles: The effect of area-difference elasticity, Phys. Rev. E 49 (1994) 5389-5407.
+===Research papers on open membranes===
+[1] A. Saitoh, K. Takiguchi, Y. Tanaka, and H. Hotani, Opening-up of liposomal membranes by talin, Proc. Natl. Acad. Sci. 95 (1998) 1026-1031.
+[2] R. Capovilla, J. Guven, and J.A. Santiago, Lipid membranes with an edge, Phys. Rev. E 66 (2002) 021607.
+[3] R. Capovilla and J. Guven, Stresses in lipid membranes, J. Phys. A 35 (2002) 6233-6247.
+[4] Z. C. Tu and Z. C. Ou-Yang, Lipid membranes with free edges, Phys. Rev. E 68,  (2003) 061915.
+[5] T. Umeda, Y. Suezaki, K. Takiguchi, and H. Hotani, Theoretical analysis of opening-up vesicles with single and two holes, Phys. Rev. E 71 (2005) 011913.
+===Numerical solutions on lipid membranes===
+[1] J. Yan, Q. H. Liu, J. X. Liu and Z. C. Ou-Yang, Numerical observation of nonaxisymmetric vesicles in fluid membranes, Phys. Rev. E 58 (1998) 4730-4736.
+[2] J. J. Zhou, Y. Zhang, X. Zhou, Z. C. Ou-Yang, Large Deformation of Spherical Vesicle Studied by Perturbation Theory and Surface Evolver, Int J Mod Phys B 15 (2001) 2977-2991.
+[3] Y. Zhang, X. Zhou, J. J. Zhou and Z. C. Ou-Yang, Triconcave Solution to the Helfrich Variation Problem for the Shape of Lipid Bilayer Vesicles is Found by Surface Evolver, In. J. Mod. Phys. B 16 (2002) 511-517.
+[4] Q. Du, C. Liu and X. Wang, Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions, J. Comput. Phys. 212 (2006) 757.
+[5] X. Wang and Q. Du, physics/0605095.
+===Selected papers on cell membranes===
+[1] Y. C. Fung and P. Tong, Theory of the Sphering of Red Blood Cells, Biophys. J. 8 (1968) 175-198.
+[2] S. K. Boey, D. H. Boal, and D. E. Discher, Simulations of the Erythrocyte Cytoskeleton at Large Deformation. I. Microscopic Models, Biophys. J. 75 (1998) 1573-1583.
+[3] D. E. Discher, D. H. Boal, and S. K. Boey, Simulations of the Erythrocyte Cytoskeleton at Large Deformation. II. Micropipette Aspiration, Biophys. J. 75 (1998) 1584-1597.
+[4] E. Sackmann, A.R. Bausch and L. Vonna, Physics of Composite Cell Membrane and Actin Based Cytoskeleton, in Physics of bio-molecules and cells, Edited by H. Flyvbjerg, F. Julicher, P. Ormos And F. David (Springer, Berlin, 2002).
+[5] G. Lim, M. Wortis, and R. Mukhopadhyay, Stomatocyte–discocyte–echinocyte sequence of the human red blood cell: Evidence for the bilayer–couple hypothesis from membrane mechanics, Proc. Natl. Acad. Sci. 99 (2002) 16766-16769.
+[6] Z. C. Tu and Z. C. Ou-Yang, A Geometric Theory on the Elasticity of Bio-membranes, J. Phys. A: Math. Gen. 37 (2004) 11407-11429.
+[7] Z. C. Tu and Z. C. Ou-Yang, Elastic theory of low-dimensional continua and its applications in bio- and nano-structures,[http://arxiv.org/abs/0706.0001 arxiv:0706.0001].
+[[Category:Cell anatomy]]
+[[Category:Membrane biology]]
+[[Category:Cell mechanics]]

Mian–Chowla sequence: Difference between revisions

Revision as of 19:10, 20 April 2013

Contents

Elasticity of closed lipid vesicles

Elasticity of open lipid membranes

Elasticity of cell membranes

References

Bibliography

Reviews on configurations of lipid vesicles

Research papers on closed vesicles

Research papers on open membranes

Numerical solutions on lipid membranes

Selected papers on cell membranes

Navigation menu

Mian–Chowla sequence: Difference between revisions

Revision as of 19:10, 20 April 2013

Elasticity of closed lipid vesicles

Elasticity of open lipid membranes

Elasticity of cell membranes

References

Bibliography

Reviews on configurations of lipid vesicles

Research papers on closed vesicles

Research papers on open membranes

Numerical solutions on lipid membranes

Selected papers on cell membranes

Navigation menu

Search