doubly periodic वाक्य
उदाहरण वाक्य
मोबाइल
- Doubly periodic square array of SRRs are used to illustrate the methodology.
- This function will then be necessarily doubly periodic.
- The totality of meromorphic doubly periodic functions with given periods defines an algebraic function field associated to that curve.
- Stagnation zones theorems are closely related to pre-Liouville theorem about conversion of the entire doubly periodic function into the identical constant.
- The doubly periodic function is thus a two-dimensional extension of the simpler singly periodic function, which repeats itself in a single dimension.
- Scherk described two complete embedded minimal surfaces in 1834; his first surface is a doubly periodic surface, his second surface is singly periodic.
- As an arbitrary mapping from pairs of reals ( or complex numbers ) to reals, a doubly periodic function can be constructed with little effort.
- If a doubly periodic function is also a poles in other words, a meromorphic function then a lot of information about such a function can be obtained by applying some basic theorems from complex analysis.
- Certain elliptic functions ( doubly periodic functions ) denoted cm and sm satisfying the identity cm ( " z " ) 3 + sm ( " z " ) 3 = 1 are known as Dixon's elliptic functions.
- The Weierstrass theory also includes the Weierstrass zeta function, which is an indefinite integral of & # 8472; and not doubly periodic, and a theta function called the Weierstrass sigma function, of which his zeta-function is the log-derivative.
- The Weierstrass functions are doubly periodic; that is, they are periodic with respect to a lattice ?; in essence, the Weierstrass functions are naturally defined on a torus " T " = "'C "'/ ?.
- By starting with the Weierstrass p-function and associating with it a group of doubly periodic functions with two simple poles, he was able to give a simple derivation of the Jacobian elliptic functions, as well as modifying the existing notation to provide a more systematic approach to the subject.
- To solve equations ( 1.1 ) and ( 1.2 ) for a free-standing, doubly periodic surface, we consider an infinite 2D periodic surface occupying the entire x-y plane, and assume a discrete plane wave expansion for all currents, fields and potentials ( Tsao [ 1982 ], Scott [ 1989 ], Fourier optics ):
- Given a doubly periodic metric on \ mathbb R ^ 2 ( e . g . an imbedding in \ mathbb R ^ 3 which is invariant by a \ mathbb Z ^ 2 isometric action ), there is a nonzero element g \ in \ mathbb Z ^ 2 and a point p \ in \ mathbb R ^ 2 such that \ operatorname { dist } ( p, g . p ) ^ 2 \ leq \ frac { 2 } { \ sqrt { 3 } } \ operatorname { area } ( F ), where F is a fundamental domain for the action, while \ operatorname { dist } is the Riemannian distance, namely least length of a path joining p and g . p.
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