A relatively simple scheme for calculating these integrals is presented. The upper bound is obtained as a general expression formulated via a variational principle, and a class of possible trial functions is indicated. The trial functions for the lower-bound estimate are discussed. The scheme is ...
Studying the Upper Bounds of the Numbers of Zeros of Abelian Integrals by the Law of Polynomials For the quadratic reversible systems of genus one, all of their periodic orbits are higher-order algebraic curves. When they are perturbed by polynomials o... L Hong,J Liu,X Hong - 《Internation...
The upper and lower bounds on the voltage standing wave ratio (VSWR) at port 1 of a 3-port circulator with a complex load under any phase conditions at port 2 and a nonideal termination at port 3 is of some interest in microwave engineering. The purpose of this letter is to give a so...
Hence, Proposition 6.26 in [37] implies the existence of a finitely additive probability π˜A in PP_(⋅|A) such that where the left-side integrals are usual Stieltjes integrals [2]. Since it follows i.e., both P_(F∩K|A) and P‾(Fc∩K|A) are obtained integrating with respec...
In the latter paper we obtain an explicit upper boundof the number of zeros for a wide class of Abelian integrals.doi:10.17323/1609-4514-2005-5-4-781-828Glutsyuk, AlexeyarXivA.A. Glutsyuk, Upper bounds of topology of complex polynomials in two variables, Moscow Math. J., (To appear)...
Upper and lower bounds are given for the three lowest frequencies of vibration of clamped rectangular orthotropic plates. The bounds were obtained by using a recently developed method which gives estimates for the vibrational frequencies in terms of easily evaluated integrals of trial functions. ...
INTEGRALSA simple method is developed for obtaining upper and lower bounds for the apsidal angle which occurs in the theory of the heavy symmetrical top. This method is employed to give a quick derivation and an improvement of the upper and lower bounds obtained by W. Kohn. An advantage of ...
It relies heavily on conformal transformation and it expresses for the first time the trans-resistances and the lower envelope in terms of Jacobi functions, elliptic integrals, and the modular lambda elliptic function. New simple formulae for the asymptotic limit of a very large hole are also ...
The answer K to this question is known as the moment Bautin index, and we provide the first general upper bound: K2+degq+3(degP1)2. The proof is based on qualitative analysis of linear ODEs, applied to Cauchy-type integrals of certain algebraic functions. The moment Bautin index plays ...
Multiple integralsWe propose a new proof of the Laplace approximation for multiple integrals and consequently find new bounds for the approximation error. The main advantages of our approach are its simplicity, an explicit form of the bounds and small coefficient in the main error term, which ...