Constant elasticity of variance model: Difference between revisions

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In [[mathematical analysis]], '''constructive function theory''' is a field which studies the connection between the smoothness of a [[Function (mathematics)|function]] and its degree of [[approximation theory|approximation]].<ref>{{cite web|url=http://encyclopedia2.thefreedictionary.com/Constructive+Theory+of+Functions|title=Constructive Theory of Functions}}</ref><ref>{{SpringerEOM|id=Constructive_theory_of_functions|title=Constructive theory of functions|first=S.A.|last=Telyakovskii}}</ref> It is closely related to [[approximation theory]]. The term was coined by [[Sergei Bernstein]].
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==Example==
 
Let ''f'' be a 2''π''-periodic function. Then ''f'' is ''α''-[[Hölder condition|Hölder]] for some 0&nbsp;<&nbsp;''α''&nbsp;<&nbsp;1 if and only if for every natural ''n'' there exists a [[trigonometric polynomial]] ''P<sub>n</sub>'' of degree ''n'' such that
: <math> \max_{0 \leq x \leq 2\pi} | f(x) - P_n(x) | \leq \frac{C(f)}{n^\alpha}, </math>
where ''C''(''f'') is a positive number depending on ''f''. The "only if" is due to [[Dunham Jackson]], see [[Jackson's inequality]]; the "if" part is due to [[Sergei Bernstein]], see [[Bernstein's theorem (approximation theory)]].
 
==Notes==
{{Reflist}}
 
==References==
 
* {{Cite book |first=N. I. |last=Achiezer |author-link=Naum Akhiezer|title=Theory of approximation |others=Translated by Charles J. Hyman |publisher=Frederick Ungar Publishing |location=New York |year=1956 }}
* {{cite book|mr=0196340|last=Natanson|first=I. P.|author-link=Isidor Natanson|title=Constructive function theory. Vol. I. Uniform approximation|publisher=Frederick Ungar Publishing Co.|location=New York|year=1964}}
: {{cite book|mr=0196341|last=Natanson|first=I. P.|author-link=Isidor Natanson|title=Constructive function theory. Vol. II. Approximation in mean|publisher=Frederick Ungar Publishing Co.|location=New York|year=1965}}
: {{cite book|mr=0196342|last=Natanson|first=I. P.|author-link=Isidor Natanson|title=Constructive function theory. Vol. III. Interpolation and approximation quadratures|publisher=Ungar Publishing Co.|location=New York|year=1965}}
 
[[Category:Approximation theory]]
[[Category:Smooth functions]]

Latest revision as of 15:51, 10 March 2014

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It can be fairly enjoyable for a group of ladies to get collectively and go on a camping trip. It"s enjoyable to get away with other girls without having possessing to be concerned about significant other folks or children. Camping is a true chance to relax and unwind. When you happen to be with a group that isn"t all loved ones you get the best of both worlds. You happen to be in a position to get about a campfire with your close friends and talk about anything. Nonetheless, when you want some time alone to read or meditate you never have to really feel obligated to be with the group. Make sure even though that just before you ever go to be alone that you let the other individuals know where you are going to be and how extended you anticipate to be. Safety need to constantly be a concern when camping.

There also comes a fantastic sense of fulfillment when you go camping with a group of women. This impressive Women On Steroids Are Not Safe As Well! - Shartick Italia encyclopedia has a pile of splendid warnings for why to ponder this hypothesis. There is a sense of independence being aware of that you had been capable to survive with no all the modern conveniences. Girls typically are observed as unable to camp. The truth of the matter is much more that girls don"t go camping even though developing up as considerably as guys do. Boys go camping with pals, with their dads, and with organizations like the boy scouts. Girls normally only go camping with their family members if their family members likes to camp. So, girls just grow up with less camping instruction. Nonetheless, with the advent of the web, girls are now able to learn all there is to know about camping from the comfort of house.

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