Non-negative matrix factorization: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older editNewer edit →
en>Qwertyus
months shouldn't show in refs to scientific works, (2): remove the month fields
en>RomanSpa
Line 1: Line 1:
The '''Sauerbrey equation''' was developed by G. Sauerbrey in 1959 as a method for correlating changes in the oscillation frequency of a [[piezoelectric]] [[crystal]] with the mass deposited on it. He simultaneously developed a method for measuring the characteristic frequency and its changes by using the crystal as the frequency determining component of an oscillator circuit. His method continues to be used as the primary tool in [[quartz crystal microbalance]] experiments for conversion of frequency to mass and is valid in nearly all applications.
Do you have a heart for customer service? If so, you can make money online answering phone calls for businesses. Additionally, you can make money by chatting online with a business's customer to help them solve problems and answer their questions. There are many customer service sites available including: LiveOps, Working Solutions [http://www.comoganhardinheiro101.com/?p=71 como ganhar dinheiro na internet] and ACD Direct.  For more information about [http://comoficarrico.comoganhardinheiro101.com ganhe dinheiro] visit http://comoficarrico.comoganhardinheiro101.com Write online to make money. There are quite a few legitimate companies that pay people to write articles online. You can find many different companies that will pay you to write different content with varying topics. If you enjoy writing, you should do research to look for companies that will pay you to write online. <br><br><br>


The equation is derived by treating the deposited mass as though it were an extension of the thickness of the underlying quartz.<ref name="Sauerbrey">{{Citation
If you have the ability to type quickly, you may consider transcription jobs. You need to have good headphones and the ability to keep up with what is being said. Often, the companies will have their own formatting guidelines. Familiarize yourself with these prior to beginning. Once you have, you can begin transcribing. [http://www.comoganhardinheiro101.com/category/opcoes-binarias/ ganhar dinheiro pela internet] What do you do? Do it for pay! A number of websites offer you points when you search through them and/or make purchases of items that you were planning to buy anyway. Take the points you earn and trade them for gift cards, gifts and sometimes even cash. Sites thatprovide this opportunity include Swagbucks and Mypoints.<br><br>As you can see from the above article, it is easy to understand how to make money online when you get the knowledge through great tips. You can join the millions of people worldwide who make money each day, if you [http://www.comoganhardinheiro101.com/ganhar-dinheiro-pela-internet-com-opcoes-binarias/ como ganhar dinheiro] pay close attention to the tips that you have just read. Making money online is a skill, and if you continue to study good tips and ideas such as these, there is no reason why you cannot make lots of money online.<br><br>Don't buy every book about making money online. Most of the time, these books are sold by people whose claim to fame is that they are teaching people how to make money [http://www.comoganhardinheiro101.com/index.php ganhar dinheiro pela internet] online. Before you buy an e-book or book about making money, make sure that you know a little about the author, and that you have seen testimonials about the book.<br><br>Take advantage of paid per post if you have extra time and need to make money online. People will need you to make posts on their site to promote a product or give a good review, which will help them in the long run. In return, they will pay you a nice sum. Do you enjoy [http://www.comoganhardinheiro101.com/category/opcoes-binarias/ ganhar dinheiro na internet] writing? If so, you can make cash by becoming a freelance writer. Just be aware that most freelance writing sites prefer writers with experience. But, there are other sites that will hire you if you pass a test. It's a bonus if you have knowledge on particular subjects. <br><br><br>Many sites require a payment for information that they claim will allow you to make a lot of [http://Ganhardinheironainternet.comoganhardinheiro101.com/ money online]. A good rule of thumb is to never pay anything to get that type of information. Legitimate sites may ask you to qualify by taking a test, but they will not require any type of payment. [http://www.comoganhardinheiro101.com/index.php ganhar dinheiro na internet] People love handmade goods. They are very trendy right now, so if you are artsy, go make some money! So, if you are the creative type, whether it's sewing, knitting or any other craft work, now is the time to produce your goods. Both Etsy and eBay could be generating an income for you.<br><br>If you want to do something creative, consider ways to create viral videos. Brainstorm ideas that you think are rip riotously hilarious, then start putting them into action. Post them on YouTube, turn on ads and, if they work, watch the money start rolling in! Learn about marketing to see how you can get them even more popular. [http://www.comoganhardinheiro101.com/?p=90 ganhando dinheiro na internet] If you know how to prepare taxes, you can earn money online. Apply for the necessary government licenses and then begin offering your services online. Many of today's top producers work from home with only their laptop and an email address. For best results, continually advertise your services throughout the year.<br><br>Affiliate marketing can be a good way to earn money online if you have a lot of time and energy to spend on website setup and promotion. Affiliate marketers market the products of others in a number of ways. You can create a website and promote [http://www.comoganhardinheiro101.com/tag/negocio-mais-rentavel-da-internet/ ganhe dinheiro] it. Creating a blog or posting on the blogs of others in your niche is also an excellent way to share product information. Making smart use of social media and e mail marketing are also possibilities for successful affiliate marketing.<br><br>
  | last = Sauerbrey
  | first = Günter
  | title = Verwendung von Schwingquarzen zur Wägung dünner Schichten und zur Mikrowägung
  | journal = Zeitschrift für Physik
  | volume = 155
  | issue = 2
  | pages = 206–222
  |date=April 1959
  | doi = 10.1007/BF01337937 |bibcode = 1959ZPhy..155..206S }}</ref>
<ref name="QCM">QCM100 – Quartz Crystal  Microbalance Theory and Calibration, Stanford Research Systems.</ref>  Because of this, the mass to frequency correlation (as determined by Sauerbrey’s equation) is largely independent of electrode geometry. This has the benefit of allowing mass determination without calibration, making the set-up desirable from a cost and time investment standpoint.


The Sauerbrey equation is defined as:
To really make money online, consider setting up your own site and having all the control. You could sell things as an affiliate or offer professional services, among many other things. While working for others can earn you a nice income, there's nothing like raking in all the profits and calling [http://www.comoganhardinheiro101.com/?p=90 como ganhar dinheiro pela internet] all the shots yourself! As stated above, there are lots of ways to increase your online income. Use these suggestions to help como ganhar dinheiro you get started. You will be amazed at how quickly the money can add up. Come back to this page and others like it to continue growing your online work portfolio as you go.<br><br>Take advantage of paid per post if you have extra time and need to make money online. People will need you to make posts on their site to promote a product or give a good review, which will help them in the long run. In return, they will pay you a nice sum. Do you enjoy [http://www.comoganhardinheiro101.com/?p=14 como ganhar dinheiro pela internet] writing? If so, you can make cash by becoming a freelance writer. Just be aware that most freelance writing sites prefer writers with experience. But, there are other sites that will hire you if you pass a test. It's a bonus if you have knowledge on particular subjects.
 
:<math>\Delta f = -\frac{2f_0^2}{A \sqrt{ \rho_q \mu_q } }\Delta m</math>.
 
Equation 1 – Sauerbrey’s equation
 
:<math>f_0</math> – [[Resonant frequency]] (Hz)
:<math> \Delta f</math> – Frequency change (Hz)
:<math> \Delta m </math> – Mass change (g)
:<math> A </math> – [[Piezoelectric effect|Piezoelectrically]] active crystal area (Area between electrodes, cm<sup>2</sup>)
:<math> \rho_q</math>  – [[Density]] of quartz (<math> \rho_q</math> = 2.648 g/cm<sup>3</sup>)
:<math> \mu_q </math> – [[Shear modulus]] of quartz for AT-cut crystal (<math> \mu_q </math> = 2.947x10<sup>11</sup> g/cm.s<sup>2</sup>)
 
 
Because the film is treated as an extension of thickness, Sauerbrey’s equation only applies to systems in which the following three conditions are met: the deposited mass must be rigid, the deposited mass must be distributed evenly and the frequency change <math> \Delta f /f </math> < 0.02.<ref>A. K. Srivastava and P. Sakthivel, J. Vac. Sci. Technol. A 19(1),97-100  Jan/Feb 2001</ref>
 
If the change in frequency is greater than 2%, that is, <math> \Delta f /f </math> > 0.02, the Z-match method must be used to determine the change in mass.<ref name="QCM"/>
The formula for the Z-match method is:<ref name="QCM"/>
 
:<math> \frac{\Delta m}{A}\ = \frac{N_q \rho_q}{\pi Z f_L}\tan^{-1} \left [ Z\tan \left ( \pi \frac{f_U-f_L}{f_U} \right ) \right ] </math>
 
Equation 2 – Z-match method
 
:<math> f_L </math> – Frequency of loaded crystal (Hz)
:<math> f_U </math> – Frequency of unloaded crystal, i.e. Resonant frequency (Hz)
:<math> N_q </math> – Frequency constant for AT-cut quartz crystal (1.668x10<sup>13</sup>Hz.Å)
:<math> \Delta m </math> – Mass change (g)
:<math> A </math> – Piezoelectrically active crystal area (Area between electrodes, cm<sup>2</sup>)
:<math> \rho_q </math> – Density of quartz (<math> \rho_q </math> = 2.648 g/cm<sup>3</sup>)
:<math> Z </math> – <math> Z = \sqrt{ \left ( \frac{\rho_q\mu_q}{\rho_f\mu_f}\ \right ) } </math>
:<math> \rho_f </math> – Density of the film (Varies: units are g/cm<sup>3</sup>)
:<math> \mu_q </math> – Shear modulus of quartz (<math> \mu_q</math> = 2.947x10<sup>11</sup> g/cm.s<sup>2</sup>)
:<math> \mu_f </math> – Shear modulus of film (Varies: units are g/cm.s<sup>2</sup>)
 
== Limitations ==
The Sauerbrey equation was developed for oscillation in air and only applies to rigid masses attached to the crystal. It has been shown that quartz crystal microbalance measurements can be performed in liquid, in which case a [[viscosity]] related decrease in the resonant frequency will be observed:
 
:<math>\Delta f = { -\ f_0^{3/2} ( \eta_l \rho_l / \pi \rho_q \mu_q )^{1/2} } </math>
 
where <math>\rho_l</math> is the density of the liquid and <math>\eta_l</math> is the viscosity of the liquid (Kanazawa and Gordon 1985).
 
==References==
{{reflist}}
 
==Further reading==
* K.K. Kanazawa and J.G. Gordon, Analytical Chemistry, '''57'''(1985) 1770-1771
 
[[Category:Electrical phenomena]]
[[Category:Transducers]]
[[Category:Weighing instruments]]

Revision as of 17:20, 1 March 2014

Do you have a heart for customer service? If so, you can make money online answering phone calls for businesses. Additionally, you can make money by chatting online with a business's customer to help them solve problems and answer their questions. There are many customer service sites available including: LiveOps, Working Solutions como ganhar dinheiro na internet and ACD Direct. For more information about ganhe dinheiro visit http://comoficarrico.comoganhardinheiro101.com Write online to make money. There are quite a few legitimate companies that pay people to write articles online. You can find many different companies that will pay you to write different content with varying topics. If you enjoy writing, you should do research to look for companies that will pay you to write online.


If you have the ability to type quickly, you may consider transcription jobs. You need to have good headphones and the ability to keep up with what is being said. Often, the companies will have their own formatting guidelines. Familiarize yourself with these prior to beginning. Once you have, you can begin transcribing. ganhar dinheiro pela internet What do you do? Do it for pay! A number of websites offer you points when you search through them and/or make purchases of items that you were planning to buy anyway. Take the points you earn and trade them for gift cards, gifts and sometimes even cash. Sites thatprovide this opportunity include Swagbucks and Mypoints.

As you can see from the above article, it is easy to understand how to make money online when you get the knowledge through great tips. You can join the millions of people worldwide who make money each day, if you como ganhar dinheiro pay close attention to the tips that you have just read. Making money online is a skill, and if you continue to study good tips and ideas such as these, there is no reason why you cannot make lots of money online.

Don't buy every book about making money online. Most of the time, these books are sold by people whose claim to fame is that they are teaching people how to make money ganhar dinheiro pela internet online. Before you buy an e-book or book about making money, make sure that you know a little about the author, and that you have seen testimonials about the book.

Take advantage of paid per post if you have extra time and need to make money online. People will need you to make posts on their site to promote a product or give a good review, which will help them in the long run. In return, they will pay you a nice sum. Do you enjoy ganhar dinheiro na internet writing? If so, you can make cash by becoming a freelance writer. Just be aware that most freelance writing sites prefer writers with experience. But, there are other sites that will hire you if you pass a test. It's a bonus if you have knowledge on particular subjects.


Many sites require a payment for information that they claim will allow you to make a lot of money online. A good rule of thumb is to never pay anything to get that type of information. Legitimate sites may ask you to qualify by taking a test, but they will not require any type of payment. ganhar dinheiro na internet People love handmade goods. They are very trendy right now, so if you are artsy, go make some money! So, if you are the creative type, whether it's sewing, knitting or any other craft work, now is the time to produce your goods. Both Etsy and eBay could be generating an income for you.

If you want to do something creative, consider ways to create viral videos. Brainstorm ideas that you think are rip riotously hilarious, then start putting them into action. Post them on YouTube, turn on ads and, if they work, watch the money start rolling in! Learn about marketing to see how you can get them even more popular. ganhando dinheiro na internet If you know how to prepare taxes, you can earn money online. Apply for the necessary government licenses and then begin offering your services online. Many of today's top producers work from home with only their laptop and an email address. For best results, continually advertise your services throughout the year.

Affiliate marketing can be a good way to earn money online if you have a lot of time and energy to spend on website setup and promotion. Affiliate marketers market the products of others in a number of ways. You can create a website and promote ganhe dinheiro it. Creating a blog or posting on the blogs of others in your niche is also an excellent way to share product information. Making smart use of social media and e mail marketing are also possibilities for successful affiliate marketing.

To really make money online, consider setting up your own site and having all the control. You could sell things as an affiliate or offer professional services, among many other things. While working for others can earn you a nice income, there's nothing like raking in all the profits and calling como ganhar dinheiro pela internet all the shots yourself! As stated above, there are lots of ways to increase your online income. Use these suggestions to help como ganhar dinheiro you get started. You will be amazed at how quickly the money can add up. Come back to this page and others like it to continue growing your online work portfolio as you go.

Take advantage of paid per post if you have extra time and need to make money online. People will need you to make posts on their site to promote a product or give a good review, which will help them in the long run. In return, they will pay you a nice sum. Do you enjoy como ganhar dinheiro pela internet writing? If so, you can make cash by becoming a freelance writer. Just be aware that most freelance writing sites prefer writers with experience. But, there are other sites that will hire you if you pass a test. It's a bonus if you have knowledge on particular subjects.

Retrieved from "https://en.formulasearchengine.com/index.php?title=Non-negative_matrix_factorization&oldid=245947"