From the Toda lattice to the Volterra lattice and back

We discuss the relationship between the multiple Hamiltonian structures of the generalized Toda lattices and that of the generalized Volterra lattices.     

Volterra算子及其伴随算子线性组合的数值域

经典Volterra算子$V$及其伴随算子$V^*$在复空间$L^2[0,1]$中起着关键作用. 关于$V$和$V^*$的线性组合的性质, 我们给出了确保$z_1V+z_2V^*(z_1,z_2\in\mathbb{C})$满足增生性质的等价条件. 本文描述了$(u+iv)I+mV+nV^*(u,v,m,n\in\mathbb{R},m+n\geq0)$数值域的精确表示.     

Non-synchronous oscillations in four-dimensional nonlinear semelparous Leslie matrix models

In a certain class of semelparous Leslie matrix models, either a positive equilibrium is stable and an invariant set on the boundary of the nonnegative cone is unstable or vice versa generically if the model dimension is two or three. This dynamic dichotomy is expected to be failed in the four-dimensional case. Our study focuses on a semelparous Leslie matrix model with specific nonlinearities and rigorously proves that the dynamic dichotomy does not hold in the four-dimensional case. This result is derived by showing that the four-dimensional semelparous Leslie matrix model can be uniformly persistent with respect to the boundary of the nonnegative cone even if there exists an unstable positive equilibrium. In such a situation, there are no missing age-classes but population oscillation occurs.     

Study on convergence and error of a numerical method for solving systems of nonlinear Fredholm–Volterra integral equations of Hammerstein type

The aim of this paper is to present an efficient analytical and numerical procedure for solving systems of nonlinear Fredholm–Volterra integral equations of the Hammerstein type with the aid of fixed point techniques and the usual Schauder basis in an adequate Banach space.     

A new scheme for solving nonlinear Stratonovich Volterra integral equations via Bernoulli’s approximation

In this paper, an efficient method for solving nonlinear Stratonovich Volterra integral equations is proposed. By using Bernoulli polynomials and their stochastic operational matrix of integration, these equations can be reduced to the system of nonlinear algebraic equations with unknown Bernoulli coefficient which can be solved by numerical methods such as Newton’s method. Also, an error analysis is valid under fairly restrictive conditions. Furthermore, in order to show the accuracy and reliability of the proposed method, the new approach is compared with the block pulse functions method by some examples. The obtained results reveal that the proposed method is more accurate and efficient than the block pulse functions method.     

一类弱奇性Volterra积分微分方程的级数展开数值解法

本文考察了一类弱奇性积分微分方程的级数展开数值解法,并给出了相应的收敛性分析.理论分析结果表明,若用已知函数的谱配置多项式逼近已知函数,那么方程的数值解以谱精度逼近方程的真解.数值实验数据也验证了这一理论分析结果.     

The Kinematics of Plate Models: A Geometrical Deduction

We present a deduction of the Kirchhoff–Love and Reissner–Mindlin kinematics of a simply-connected plate by using the formal asymptotic development method applied to the compatibility conditions of Saint-Venant and the formula of Cesàro–Volterra. This formal deduction is purely geometrical because we do not use any information coming from the loading or the constitutive behavior.      

Identification of Nonlinear Aeroelastic Systems Based on the Volterra Theory: Progress and Opportunities

The identification of nonlinear aeroelastic systems based on the Volterra theory of nonlinear systems is presented. Recent applications of the theory to problems in computational and experimental aeroelasticity are reviewed. Computational results include the development of computationally efficient reduced-order models (ROMs) using an Euler/Navier–Stokes flow solver and the analytical derivation of Volterra kernels for a nonlinear aeroelastic system. Experimental results include the identification of aerodynamic impulse responses, the application of higher-order spectra (HOS) to wind-tunnel flutter data, and the identification of nonlinear aeroelastic phenomena from flight flutter test data of the active aeroelastic wing (AAW) aircraft.     

Plane Collision Problem for Two Identical Elastic Parabolic Bodies—Direct Central Impact

A direct central collision of two identical infinite cylindrical bodies is studied. A nonstationary plane elastic problem is solved. The variable boundary of the contact area is determined. A mixed boundary problem is formulated. Its solution is represented by Fourier series. An infinite system of Volterra equations of the second kind for the unknown expansion coefficients is derived by satisfying boundary conditions. The basic characteristics of the collision process are determined numerically depending on the curvature of the frontal surface of the bodies