Second moments of twisted Koecher-Maass series

Imai considered the twisted Koecher-Maass series for Siegel cusp forms of degree?2, twisted by Maass cusp forms and Eisenstein series, and used them to prove the converse theorem for Siegel modular forms. They do not have Euler products, and it is not even known whether they converge absolutely for Re(s)>1. Hence the standard convexity arguments do not apply to give bounds. In this paper, we obtain the average version of the second moments of the twisted Koecher-Maass series, using Titchmarsh??s method of Mellin inversion. When the Siegel modular form is a Saito Kurokawa lift of some half integral weight modular form, a theorem of Duke and Imamoglu says that the twisted Koecher Maass series is the Rankin-Selberg L-function of the half-integral weight form and Maass form of weight?1/2. Hence as a corollary, we obtain the average version of the second moment result for the Rankin-Selberg L-functions attached to half integral weight forms.     

LIMIT CYCLES OF THE GENERALIZED POLYNOMIAL LINARD DIFFERENTIAL EQUATION

We investigate the generalized polynomial Linard differential equations. Using the averaging theory of first and second order, we obtain the maximum number of limit cycles of the system.     

LIMIT CYCLES FOR A CLASS OF FIFTH-ORDER DIFFERENTIAL EQUATIONS

In this paper, we study a fifth-order differential equation. Using the averaging theory, we investigate the limit cycles of the equation.     

EXISTENCE OF SOLUTIONS TO A THIRD-ORDER THREE-POINT BOUNDARY VALUE PROBLEM

In this paper,we study the existence of solutions to a third-order three-point boundary value problem.By imposing certain restrictions on the nonlinear term,we prove the existence of at least one solution to the boundary value problem by the method of lower and upper solutions.We are interested in the construction of lower and upper solutions.     

EXISTENCE OF SOLUTIONS TO 2m-ORDER PERIODIC BOUNDARY VALUE PROBLEM

In this paper, we are concerned with the existence of nontrivial solutions to a 2m-order nonlinear periodic boundary value problem. By the infinite dimensional Morse theory, under some conditions on nonlinear term, we obtain that there exist at least two nontrivial solutions.     

OSCILLATION CRITERIA FOR SECOND ORDER NONLINEAR NEUTRAL PERTURBED DYNAMIC EQUATIONS ON TIME SCALES

In this paper,we discuss the oscillatory behavior of a class of nonlinear neutral perturbed dynamic equations on time scales.Some new oscillation criteria are obtained for such dynamic equations.Finally,an example that dwells upon the sharp conditions of our result is also included.     

GENERALIZED DAHLQUIST CONSTANT WITH APPLICATIONS IN SYNCHRONIZATION ANALYSIS EXCITED BY PARAMETER WHITE-NOISE OF TYPICAL NEURAL NETWORKS

In this paper,a novel and effective approach to impulsive synchronization analysis excited by parameter white-noise of neural networks is investigated using the nonlinear operator named the generalized Dahlquist constant.The proposed approach offers a design procedure for impulsive synchronization of a large class of neural networks.Numerical simulations,where the theoretical results are applied to typical neural networks with and without delayed item,demonstrate the effectiveness and feasibility of the proposed technique.     

EXISTENCE OF POSITIVE SOLUTION TO NONLINEAR STURM-LIOUVILLE SINGULAR BVP

In this paper,we consider the system of Sturm-Liouville singular BVP and present a sufficient and necessary condition for the existence of positive solutions by means of the fixed point theorem for regular cones.     

On the time-dependent moments of Markovian queues with reneging

We give an explicit representation for the time-dependent moments of a Markovian queueing system with reneging. Our expressions are comparable in form to the moment expressions for the M/M/1 queue found in Abate and Whitt (Queueing Syst. 2:41–65, 1987; Adv. Appl. Probab. 20:145–178, 1988). We also illustrate how to use these expressions to derive analogous moment expressions for a reflected Ornstein–Uhlenbeck process, with reflection at zero.