Sublinear function: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older edit
en>Liuzhe821
m Provided an alternative name for the subject.
en>Quietbritishjim
m Change f' to g to avoid confusion with derivative
 
Line 1: Line 1:
{{refimprove|date=March 2010}}
SINGAPORE – A residential website at Yishun Avenue 9 obtained only 5 bids at the close of the tender yesterday, indicating tempering demand in a traditionally well-liked district, although some analysts famous the relatively excessive offer by EL Improvement.<br><br>In addition, HDB will pilot a brand new kind of Three-Era (3 Gen) flats to cater to multi-technology households dwelling under one roof. These 3Gen flats will characteristic 4 bedrooms and three bogs (two en-suites), with an inner ground area of about one hundred fifteen square metres. To be eligible for 3Gen flats, applicants should form a multi-technology household comprising at least a married/courting couple and their guardian(s). To ensure that these goal-built 3 Gen flats serve the goal group, subletting of room(s) will not be allowed through the 5-yr Minimum Occupation Period (MOP). After fulfilling the MOP, these 3Gen flats can solely be resold in the open market to other eligible multi-generation families. Application for Jan 2014 BTO Train<br><br>HDB's newest BTO launch consists of a wide range of flats, from studio apartments to five-roomers. In complete, 3,861 flats are up on the market underneath the July 2013 BTO exercise. At the first sale launch during SERS (2006/07), a 4-room flat value a median of $250k (inclusive of compensation). At the 2nd sale launch in the course of the Balance of Sale balloting exercise (2009), a 4-room flat was going at a mean of $450k. The 3-room flats additionally had an 80% raise in value. c) SSD at 5% if the property is sold within the third 12 months of buy, i.e. the property is held for more than two years and up to three years from the date of buy. Value of 2 bedder from New Launch $950,000 (For example Riverbay in Bendemeer area) 5% cash is $ 47,500 Sale of The Rainforest Executive Rental<br><br>The combined elements of a secure government, foreign capital inflows, rising Singapore Greenback, land scarcity, detailed land use planning and confidence within the government to deliver on its commitments have made buying a HDB flat a horny investment choice. So what are these changes? First, stamp duty will probably be raised to 5% when everlasting residents purchase their first property irregardless if it is an HDB flat or personal property. Everlasting residents are now not allowed to sub-let their HDB flat and after they have bought a personal residential property, they have to let go and promote their HDB flat as nicely. Ministry of Finance, Ministry of National Improvement, Monetary Authority of Singapore and Ministry of Trade & Business a DBSS flat from a developer;<br><br>Residences and condominium are strata-subdivided housing units, with the common areas owned and property for sale singapore ([http://Mixedandmatchedonline.com/index.php?m=member_profile&id=170880 visit this site right here]) managed by a Administration Company. Hybrid housing forms comparable to townhouses, cluster housing and strata-bungalows additionally come underneath the strata-subdivision association. There are clearly-defined planning tips governing every of these property varieties. The Government is introducing Seller's Stamp Obligation (SSD) on industrial property to discourage short-term speculative activity which could distort the underlying prices of business properties and raise prices for businesses. If you need to know more about how this can give you the results you want and re-construction your property portfolio in a protected & low-risk way, please name me at 90228919 for a no-obligation chat! 2011 one hundred eighty.3<br><br>The Government has subsequently determined to implement an extra set of measures to cool the non-public and public housing markets. These measures are calibrated to be tighter on property possession for funding, as well as on foreign patrons. To discourage over-borrowing, financing conditions for housing have additionally been tightened. As well as, structural measures have been implemented to strengthen the policy intent of public housing and government condominiums.<br><br>You are liable to pay a resale levy of $55,000 whenever you buy a second subsidised flat from HDB or take over possession of a subsidised HDB flat after selling The Rainforest EC if you purchased it underneath the CPF Housing Grant Scheme (after assembly the 5-yr Minimal Occupation Interval (MOP) and the 30-month interval). The primary mission with about 80 models of 3Gen flats will be launched in Yishun in the Sep 2013 BTO exercise. HDB will monitor the response and calibrate the availability of 3Gen flats accordingly. Can the 80% raise in HDB pricing for residences direct from HDB be justified when the flats are in the identical estate, have identical development price and are handed over at the similar time? That is the primary tranche of the 24,300 BTO flats that HDB has deliberate for 2014.
In [[statistical mechanics]], '''universality''' is the observation that there are properties for a large class of systems that are independent of the [[mechanics|dynamical]] details of the system. Systems display universality in a scaling limit, when a large number of interacting parts come together. The modern meaning of the term was introduced by [[Leo Kadanoff]] in the 1960s {{citation needed|date=April 2013}}, but a simpler version of the concept was already implicit in the [[van der Waals equation]] and in the earlier Landau theory of phase transitions, which did not incorporate scaling correctly {{citation needed|date=April 2013}}.
 
The term is slowly gaining a broader usage in several fields of mathematics, including [[combinatorics]] and [[probability theory]], whenever the quantitative features of a structure (such as asymptotic behaviour) can be deduced from a few global parameters appearing in the definition, without requiring knowledge of the details of the system.
 
The [[renormalization group]] explains universality. It classifies operators in a statistical field theory into relevant and irrelevant. Relevant operators are those responsible for perturbations to the free energy, the imaginary time Lagrangian, that will affect the continuum limit, and can be seen at long distances. Irrelevant operators are those that only change the short-distance details. The collection of scale-invariant statistical theories define the [[universality classes]], and the finite dimensional list of coefficients of relevant operators parametrize the near critical behavior.
 
==Universality in statistical mechanics==
The notion of universality originated in the study of [[phase transition]]s in statistical mechanics {{citation needed|date=April 2013}}. A phase transition occurs when a material changes its properties in a dramatic way: water, as it is heated boils and turns into vapor; or a magnet, when heated, loses its magnetism. Phase transitions are characterized by an [[order parameter]], such as the density or the magnetization, that changes as a function of a parameter of the system, such as the temperature. The special value of the parameter at which the system changes its phase is the system's [[critical point (thermodynamics)|critical point]]. For systems that exhibit universality, the closer the parameter is to its [[critical value]], the less sensitively the order parameter depends on the details of the system.
 
If the parameter β is critical at the value β<sub>c</sub>, then the order parameter ''a'' will be well approximated by {{citation needed|date=April 2013}}
 
:<math>a=a_0 \left\vert \beta-\beta_c \right\vert^\alpha.\,</math>
 
The exponent α is a [[critical exponent]] of the system. The remarkable discovery made in the second half of the twentieth century was that very different systems had the same critical exponents {{citation needed|date=April 2013}}.
 
In 1976, [[Mitchell Feigenbaum]] discovered universality in iterated maps.<ref>Mitchell J. Feigenbaum, Universal behavior in nonlinear systems, Physica D: Nonlinear Phenomena, Volume 7, Issues 1–3, May 1983, Pages 16-39, ISSN 0167-2789, http://dx.doi.org/10.1016/0167-2789(83)90112-4.
(http://www.sciencedirect.com/science/article/pii/0167278983901124)</ref><ref>Mitchell Feigenbaum, Universality in complex Discrete dynamics, http://chaosbook.org/extras/mjf/LA-6816-PR.pdf</ref><ref>Mitchell J. Feigenbaum, Universal behavior in nonlinear systems, http://www.fas.org/sgp/othergov/doe/lanl/pubs/00818090.pdf</ref>
 
==Examples==
Universality gets its name because it is seen in a large variety of physical systems. Examples of universality include:
 
* [[Avalanche]]s in piles of sand. The likelihood of an avalanche is in power-law proportion to the size of the avalanche, and avalanches are seen to occur at all size scales. This is termed "[[self-organized criticality]]" {{citation needed|date=April 2013}}.
* The formation and propagation of cracks and tears in materials ranging from steel (e.g., scissors) to rock to paper. The variations of the direction of the tear, or the roughness of a fractured surface, are in power-law proportion to the size scale {{citation needed|date=April 2013}}.
* The [[electrical breakdown]] of [[dielectric]]s, which resemble cracks and tears.
* The [[percolation]] of fluids through disordered media, such as [[petroleum]] through fractured rock beds, or water through filter paper, such as in [[chromatography]]. Power-law scaling connects the rate of flow to the distribution of fractures {{citation needed|date=April 2013}}.
* The [[diffusion]] of [[molecule]]s in [[solution]], and the phenomenon of [[diffusion-limited aggregation]].
* The distribution of rocks of different sizes in an aggregate mixture that is being shaken (with gravity acting on the rocks) {{citation needed|date=April 2013}}.
* The appearance of [[critical opalescence]] in fluids near a [[phase transition]] {{citation needed|date=April 2013}}.
 
==Theoretical overview==
 
One of the important developments in [[materials science]] in the 1970s and the 1980s was the realization that statistical field theory, similar to quantum field theory, could be used to provide a microscopic theory of universality {{citation needed|date=April 2013}}. The core observation was that, for all of the different systems, the behaviour at a [[phase transition]] is described by a continuum field, and that the same statistical field theory will describe different systems. The scaling exponents in all of these systems can be derived from the field theory alone, and are known as [[critical exponents]].
 
The key observation is that near a phase transition or [[critical point (thermodynamics)|critical point]], disturbances occur at all size scales, and thus one should look for an explicitly [[scale-invariant theory]] to describe the phenomena, as seems to have been put in a formal theoretical framework first by [[Valery Pokrovsky|Pokrovsky]] and Patashinsky in 1965 {{citation needed|date=April 2013}}. Universality is a by-product of the fact that there are relatively few scale-invariant theories. For any one specific physical system, the detailed description may have many scale-dependent parameters and aspects. However, as the phase transition is approached, the scale-dependent parameters play less and less of an important role, and the scale-invariant parts of the physical description dominate. Thus, a simplified, and often [[exactly solvable]], model can be used to approximate the behaviour of these systems near the critical point.
 
Percolation may be modeled by a random [[electrical resistor]] network, with electricity flowing from one side of the network to the other. The overall resistance of the network is seen to be described by the average connectivity of the resistors in the network {{citation needed|date=April 2013}}.
 
The formation of tears and cracks may be modeled by a random network of [[electrical fuse]]s. As the electric current flow through the network is increased, some fuses may pop, but on the whole, the current is shunted around the problem areas, and uniformly distributed. However, at a certain point (at the phase transition) a [[cascade failure]] may occur, where the excess current from one popped fuse overloads the next fuse in turn, until the two sides of the net are completely disconnected and no more current flows {{citation needed|date=April 2013}}.
 
To perform the analysis of such random-network systems, one considers the stochastic space of all possible networks (that is, the [[canonical ensemble]]), and performs a summation (integration) over all possible network configurations. As in the previous discussion, each given random configuration is understood to be drawn from the pool of all configurations with some given probability distribution; the role of temperature in the distribution is typically replaced by the average connectivity of the network {{citation needed|date=April 2013}}.
 
The expectation values of operators, such as the rate of flow, the [[heat capacity]], and so on, are obtained by integrating over all possible configurations. This act of integration over all possible configurations is the point of commonality between systems in [[statistical mechanics]] and [[quantum field theory]]. In particular, the language of the [[renormalization group]] may be applied to the discussion of the random network models. In the 1990s and 2000s, stronger connections between the statistical models and [[conformal field theory]] were uncovered. The study of universality remains a vital area of research.
 
==Applications to other fields==
 
Like other concepts from [[statistical mechanics]] (such as [[entropy]] and [[master equation]]s), universality has proven a useful construct for characterizing distributed systems at a higher level, such as [[multi-agent systems]]. The term has been applied<ref name="Paru04">{{citation
| first1 = H.V.D.
| last1 = Parunak
| first2 = W.
| last2 = Brueckner
| first3 = R.
| last3 = Savit
| title = Universality in Multi-Agent Systems
| conference = Third International Joint Conference on Autonomous Agents and Multi-Agent Systems (AAMAS 2004)
| year = 2004
| pages = 930–937
| url = http://www.jacobstechnology.com/vrc/pdf/AAMAS04Universality.pdf }}</ref> to multi-agent simulations, where the system-level behavior exhibited by the system is independent of the degree of complexity of the individual agents, being driven almost entirely by the nature of the constraints governing their interactions.
 
== References ==
{{reflist}}
 
[[Category:Dynamical systems]]
[[Category:Critical phenomena]]

Latest revision as of 13:45, 19 August 2014

SINGAPORE – A residential website at Yishun Avenue 9 obtained only 5 bids at the close of the tender yesterday, indicating tempering demand in a traditionally well-liked district, although some analysts famous the relatively excessive offer by EL Improvement.

In addition, HDB will pilot a brand new kind of Three-Era (3 Gen) flats to cater to multi-technology households dwelling under one roof. These 3Gen flats will characteristic 4 bedrooms and three bogs (two en-suites), with an inner ground area of about one hundred fifteen square metres. To be eligible for 3Gen flats, applicants should form a multi-technology household comprising at least a married/courting couple and their guardian(s). To ensure that these goal-built 3 Gen flats serve the goal group, subletting of room(s) will not be allowed through the 5-yr Minimum Occupation Period (MOP). After fulfilling the MOP, these 3Gen flats can solely be resold in the open market to other eligible multi-generation families. Application for Jan 2014 BTO Train

HDB's newest BTO launch consists of a wide range of flats, from studio apartments to five-roomers. In complete, 3,861 flats are up on the market underneath the July 2013 BTO exercise. At the first sale launch during SERS (2006/07), a 4-room flat value a median of $250k (inclusive of compensation). At the 2nd sale launch in the course of the Balance of Sale balloting exercise (2009), a 4-room flat was going at a mean of $450k. The 3-room flats additionally had an 80% raise in value. c) SSD at 5% if the property is sold within the third 12 months of buy, i.e. the property is held for more than two years and up to three years from the date of buy. Value of 2 bedder from New Launch $950,000 (For example Riverbay in Bendemeer area) 5% cash is $ 47,500 Sale of The Rainforest Executive Rental

The combined elements of a secure government, foreign capital inflows, rising Singapore Greenback, land scarcity, detailed land use planning and confidence within the government to deliver on its commitments have made buying a HDB flat a horny investment choice. So what are these changes? First, stamp duty will probably be raised to 5% when everlasting residents purchase their first property irregardless if it is an HDB flat or personal property. Everlasting residents are now not allowed to sub-let their HDB flat and after they have bought a personal residential property, they have to let go and promote their HDB flat as nicely. Ministry of Finance, Ministry of National Improvement, Monetary Authority of Singapore and Ministry of Trade & Business a DBSS flat from a developer;

Residences and condominium are strata-subdivided housing units, with the common areas owned and property for sale singapore (visit this site right here) managed by a Administration Company. Hybrid housing forms comparable to townhouses, cluster housing and strata-bungalows additionally come underneath the strata-subdivision association. There are clearly-defined planning tips governing every of these property varieties. The Government is introducing Seller's Stamp Obligation (SSD) on industrial property to discourage short-term speculative activity which could distort the underlying prices of business properties and raise prices for businesses. If you need to know more about how this can give you the results you want and re-construction your property portfolio in a protected & low-risk way, please name me at 90228919 for a no-obligation chat! 2011 one hundred eighty.3

The Government has subsequently determined to implement an extra set of measures to cool the non-public and public housing markets. These measures are calibrated to be tighter on property possession for funding, as well as on foreign patrons. To discourage over-borrowing, financing conditions for housing have additionally been tightened. As well as, structural measures have been implemented to strengthen the policy intent of public housing and government condominiums.

You are liable to pay a resale levy of $55,000 whenever you buy a second subsidised flat from HDB or take over possession of a subsidised HDB flat after selling The Rainforest EC if you purchased it underneath the CPF Housing Grant Scheme (after assembly the 5-yr Minimal Occupation Interval (MOP) and the 30-month interval). The primary mission with about 80 models of 3Gen flats will be launched in Yishun in the Sep 2013 BTO exercise. HDB will monitor the response and calibrate the availability of 3Gen flats accordingly. Can the 80% raise in HDB pricing for residences direct from HDB be justified when the flats are in the identical estate, have identical development price and are handed over at the similar time? That is the primary tranche of the 24,300 BTO flats that HDB has deliberate for 2014.

Retrieved from "https://en.formulasearchengine.com/index.php?title=Sublinear_function&oldid=239746"