*Correspondence: [email protected] Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China Abstract As a particular expression of stochastic delay differential equations, stochastic pantograph differential equations have been widely used in nonlinear dynamics, quantum mechanics, and electrodynamics. In this paper, we mainly study the stability of analytical solution...

In this paper, we describe a conic approach to the stability theory of uncertain polynomials. We present necessary and sufficient conditions for a conic set p0 + K of polynomials to be Hurwitz stable (K is a convex cone of polynomials of degree ≤ n and deg p0 = n). As analytical tools we derive an edge theorem and Rantzer type conditions for marginal stability (semi-stability). The results are ...

Compulsators are being designed at ever increasing energies and energy densities and are required to deliver energy to the load in less than 10 ms. These require high speeds of operation and dense spacing of conductors. Diffusion of magnetic fields into the conductors and the formation of nonuniform, time-dependent distribution of eddy currents become dominant design considerations due to their...

This paper investigates the efficiency loss of selfish routing simultaneously with user equilibrium (UE) player and Cournot-Nash (CN) players. The upper bound of the efficiency loss of UE-CN mixed equilibrium with polynomial cost functions is obtained by the scaling method and the nonlinear programming method, respectively. It is shown that the upper bound of efficiency loss obtained by the sca...

Aim of the paper is to investigate approximate analytical solution of time-dependent partial differential equation using a semi-analytical method, the Optimal Homotopy Asymptotic Method (OHAM). To show the efficiency of the proposed method, we consider one-dimensional heat and advection-diffusion equations. OHAM uses simple computations with pretty good enough approximate solution, which has an...

It is widely believed that Krylov subspace iterative methods are better than Chebyshev semi-iterative methods. When the solution of a linear system with a symmetric and positive definite coefficient matrix is required, the Conjugate Gradient method will compute the optimal approximate solution from the appropriate Krylov subspace, that is, it will implicitly compute the optimal polynomial. Henc...

Finite field multiplier is widely applied in many domains such as coding theory and cryptography. In this paper, it is purposed to propose a concurrent all-cell error detection semi-systolic polynomial basis multiplier based on coding theory which can realize high-speed calculation and high efficient error detection with low resource consumption. First, our method is created to choose an apprec...

In this paper we propose a quadratically convergent algorithm for finding the largest eigenvalue of a nonnegative homogeneous polynomialmapwhere theNewtonmethod is used to solve an equivalent system of nonlinear equations. The semi-symmetric tensor is introduced to reveal the relation between homogeneous polynomial map and its associated semi-symmetric tensor. Based on this relation a globally ...

A method for describing the quantum kink states in the semi-classical limit of several (1+1)-dimensional field theoretical models is developed. We use the generalized zeta function regularization method to compute the one-loop quantum correction to the masses of the kink in the sine-Gordon and cubic sinh-Gordon models and another two P(φ)2 systems with polynomial self-interactions.