Примери за използване на Theta functions на Английски и техните преводи на Български
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Forsyth's thesis proved deep results on double theta functions.
Theta functions are of great importance in mathematical physics because of their role in the inverse problem for periodic and quasi-periodic flows.
Most of Schottky's work concerns elliptic,abelian and theta functions.
Later in his career he studied the relations between hyperelliptic theta functions, irrational binary invariants, the Weddle surface and the Kummer surface.
An application of finite geometry to the characteristic theory of the odd and even theta functions(1913);
Some of his later publications include Configurations defined by theta functions published in the Duke Mathematical Journal in 1939.
He spent January to May in 1882 at Johns Hopkins University where he lectured on Abelian and Theta Functions.
As a graduate student at Penn,I wrote my thesis on mock theta functions under Rademacher 's direction.
In the second of the papers Thomae also showed that the roots of a polynomial can be expressed in terms of hyperelliptic theta functions.
His results on this topic provided connections between number theory, theta functions, and the transformations of abelian functions. .
Jacobi's fundamental work on the theory of elliptic functions, which had so impressed Legendre,was based on four theta functions.
He wrote the important Abel's Theorem andthe Allied Theory of Theta Functions in 1897 and another major contribution Multiply Periodic Functions in 1907.
In the second of the papers Thomae also showed that the roots of a polynomial can be expressed in terms of hyperelliptic theta functions.
In 1929 Coble published the monograph Algebraic geometry and theta functions in the American Mathematical Society Colloquium Publications, being the tenth such volume.
The research which Wiltheiss carried out was mostly in the area of abelian functions, in particular studying hyperelliptic functions and theta functions.
That methodology was also apparent in some of the lectures at the Bourbaki seminar,such as Weil's on theta functions or Schwartz's on Kodaira's big Annals paper on harmonic integrals.
He discovered many of the fundamental properties of theta functions, including the functional equation and the Jacobi triple product formula, as well as many other results on q-series and hypergeometric series.
Fine writes from the viewpoint of a number theorist, and his slim volume is rich with examples andresults from the theory of partitions, the study of Ramanujan's mock theta functions, and modular equations.
Kloosterman solved the general case in two papers The behaviour of general theta functions under the modular group and the characters of binary modular congruence groups which occupy 130 pages of the Annals of Mathematics in 1946.
Many were completely novel; his original and highly unconventional results,such as the Ramanujan prime, the Ramanujan theta function, partition formulae and mock theta functions, have opened entire new areas of work and inspired a vast amount of further research.
In 1896 Wirtinger published a work of major importance on the general theta function.
Also bringing these areas together was his work on the geometric theory of the theta function and Kähler geometry.
An infant's brain functions mostly in delta and theta, the slowest frequencies of the brain.
Our new definition of the trig functions was that sine of theta is equal to the y-coordinate, right, this is y-coordinate where it intersects the unit circle.
Other brain waves such as beta,delta and theta waves as well as biological functions such as nerve regeneration, bone growth, ligament healing occur at extremely low frequencies, frequencies that resonate with those found naturally on earth.
And we could also write this, you know, we could say, well,this r is a function of theta.
We want to convert this to a function of r and theta.
We could write r of theta, right?r is a function of theta.
And the sine of theta is the y-value on the unit function-- on the unit circle.
The tangent of theta-- this is just the straight-up, vanilla,non-inverse function tangent--that's equal to the sine of theta over the cosine of theta.