Well‐posedness of initial boundary value problems on longitudinal impact on a composite linear viscoelastic bar

We investigate the correctness of the initial boundary value problem of longitudinal impact on a piecewise‐homogeneous semi‐infinite bar consisting of a semi‐infinite elastic part and finite length visco‐elastic part whose hereditary properties are described by linear integral relations with an arbitrary difference kernel. Introducing nonstationary regularization in boundary conditions and in the contact conditions, the well‐posedness of the considered problem is proved. Copyright © 2017 John Wiley & Sons, Ltd.     

On level-transitivity and exponential growth

We prove that if the group generated by an invertible and reversible Mealy automaton acts level-transitively on a regular rooted tree, then the semigroup generated by the dual automaton has exponential growth, hence giving a decision procedure of exponential growth for a restricted family of automaton (semi)groups.     

Twisted hopf comodule algebras

For k a commutative ring, H a k‐bialgebra and A a right H‐comodule k‐algebra, we define a new multiplication on the H‐comodule A to obtain a twisted algebra” A^T, T sumHom(H,End (A)). If ^T is convolution invertible, the categories of relative right Hopf modules over A and A^Tare isomorphic. Similarly a convolution invertible left twisting gives an isomorphism of the categories of relative left Hopf modules. We show that crossed products are invertible twistings of the tensor product, and obtain, as a corollary, a duality theorem for crossed products     

An intuitionistic formula hierarchy based on high‐school identities

We revisit the notion of intuitionistic equivalence and formal proof representations by adopting the view of formulas as exponential polynomials. After observing that most of the invertible proof rules of intuitionistic (minimal) propositional sequent calculi are formula (i.e., sequent) isomorphisms corresponding to the high‐school identities, we show that one can obtain a more compact variant of a proof system, consisting of non‐invertible proof rules only, and where the invertible proof rules have been replaced by a formula normalization procedure. Moreover, for certain proof systems such as the G4ip sequent calculus of Vorob'ev, Hudelmaier, and Dyckhoff, it is even possible to see all of the non‐invertible proof rules as strict inequalities between exponential polynomials; a careful combinatorial treatment is given in order to establish this fact. Finally, we extend the exponential polynomial analogy to the first‐order quantifiers, showing that it gives rise to an intuitionistic hierarchy of formulas, resembling the classical arithmetical hierarchy, and the first one that classifies formulas while preserving isomorphism.     

Delayed reflection of the energy flow at a potential step for dispersive wave packets

We study Klein–Gordon equations with constant coefficients and different dispersion relations on two one‐dimensional semi‐infinite media coupled with transmission conditions. We obtain lower and upper bounds of the reflected part of the energy flow at the connecting point when the frequency band involved in the initial signal is sufficiently narrow. We detect a phenomenon of delayed reflection for low frequency wave packets, which is in accordance with the recent experiments of Haibel and Nimtz. The result is then generalized for a star‐shaped network of n semi‐infinite branches connected at one point. Copyright © 2004 John Wiley & Sons, Ltd.     

On invertible terraces for non‐abelian groups

We give several constructions for invertible terraces and invertible directed terraces. These enable us to give the first known infinite families of invertible terrraces, both directed and undirected, for non‐abelian groups. In particular, we show that all generalized dicyclic groups of orders 24k + 4 and 24k + 20 have an invertible directed terrace and that all groups of the form A × G have an invertible terrace, where A is an (possibly trivial) abelian group of odd order and G is any one of: (i) a generalized dihedral group of order 12k + 2 or 12k + 10; (ii) a generalized dicyclic group of order 24k + 4 or 24k + 20; (iii) a non‐abelian group of order n with 10 ≤ n ≤ 21; (iv) a non‐abelian binary group of order n with 24 ≤ n ≤ 42. © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 437–447, 2007     

线性算子的摄动定理

该文利用Mbekhta M于1987年引入的两个子空间来研究线性算子的摄动. 证明了如下结论：设X=K(T)+W, 其中K(T), W均闭, dim［K(T)∩N(T)］< ∞. 若TWW, TW闭, 且存在闭子空间N, 使W=［W∩N(T)］N, 则： 当S∈B(X)可逆, ST= TS, SWW, 且‖S‖充分小时， T-S为上半Fredholm算子. 在上条件下, 若dimN<∞, K(T′)闭, 则T-S为Fredholm算子, 且R(T-S)=X.     

The semi‐iterative method applied to the hyper‐power iteration

The semi‐iterative method (SIM) is applied to the hyper‐power (HP) iteration, and necessary and sufficient conditions are given for the convergence of the semi‐iterative–hyper‐power (SIM–HP) iteration. The root convergence rate is computed for both the HP and SIM–HP methods, and the quotient convergence rate is given for the HP iteration. Copyright © 2005 John Wiley & Sons, Ltd.     

Semi‐linear wave models with power non‐linearity and scale‐invariant time‐dependent mass and dissipation,II

This paper is a continuation of our recent paper 8 . We will consider the semi‐linear Cauchy problem for wave models with scale‐invariant time‐dependent mass and dissipation and power non‐linearity. The goal is to study the interplay between the coefficients of the mass and the dissipation term to prove global existence (in time) of small data energy solutions assuming suitable regularity on the L² scale with additional L¹ regularity for the data. In order to deal with this L² regularity in the non‐linear part, we will develop and employ some tools from Harmonic Analysis.     

Numerical solution of the heat equation with nonlinear boundary conditions in unbounded domains

The numerical solution of the heat equation in unbounded domains (for a 1D problem‐semi‐infinite line and for a 2D one semi‐infinite strip) is considered. The artificial boundaries are introduced and the exact artificial boundary conditions are derived. The original problems are transformed into problems on finite domains. The space semi‐discretization by finite element method and the full approximation by the implicit‐explicit Euler's method are presented. The solvability of the full discretization schemes is analyzed. Computational examples demonstrate the accuracy and the efficiency of the algorithms. Also, the behavior of blowing up solutions is examined numerically. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 379–399, 2007     

Semi‐transitive graphs

In this paper, we first consider graphs allowing symmetry groups which act transitively on edges but not on darts (directed edges). We see that there are two ways in which this can happen and we introduce the terms bi‐transitive and semi‐transitive to describe them. We examine the elementary implications of each condition and consider families of examples; primary among these are the semi‐transitive spider‐graphs PS(k,N;r) and MPS(k,N;r). We show how a product operation can be used to produce larger graphs of each type from smaller ones. We introduce the alternet of a directed graph. This links the two conditions, for each alternet of a semi‐transitive graph (if it has more than one) is a bi‐transitive graph. We show how the alternets can be used to understand the structure of a semi‐transitive graph, and that the action of the group on the set of alternets can be an interesting structure in its own right. We use alternets to define the attachment number of the graph, and the important special cases of tightly attached and loosely attached graphs. In the case of tightly attached graphs, we show an addressing scheme to describe the graph with coordinates. Finally, we use the addressing scheme to complete the classification of tightly attached semi‐transitive graphs of degree 4 begun by Marus?ic? and Praeger. This classification shows that nearly all such graphs are spider‐graphs. © 2003 Wiley Periodicals, Inc. J Graph Theory 45: 1–27, 2004     

A (3+1)‐dimensional Painlevé integrable model obtained by deformation

To find some non‐trivial higher‐dimensional integrable models (especially in (3+1) dimensions) is one of the most important problems in non‐linear physics. An efficient deformation method to obtain higher‐dimensional integrable models is proposed. Starting from (2+1)‐dimensional linear wave equation, a (3+1)‐dimensional non‐trivial non‐linear equation is obtained by using a non‐invertible deformation relation. Further, the Painlevé integrability of the resulting model is also proved. Copyright © 2002 John Wiley & Sons, Ltd.     

Semi‐analytical integration of the 8‐node plane element stiffness matrix using symbolic computation

The semi‐analytical integration of an 8‐node plane strain finite element stiffness matrix is presented in this work. The element is assumed to be super‐parametric, having straight sides. Before carrying out the integration, the integral expressions are classified into several groups, thus avoiding duplication of calculations. Symbolic manipulation and integration is used to obtain the basic formulae to evaluate the stiffness matrix. Then, the resulting expressions are postprocessed, optimized, and simplified in order to reduce the computation time. Maple symbolic‐manipulation software was used to generate the closed expressions and to develop the corresponding Fortran code. Comparisons between semi‐analytical integration and numerical integration were made. It was demonstrated that semi‐analytical integration required less CPU time than conventional numerical integration (using Gaussian‐Legendre quadrature) to obtain the stiffness matrix. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

A non‐commutative Landau‐Zener formula

We study semi‐classical measures of families of solutions to a 2 × 2 Dirac system with 0 mass, which presents bands crossing. We focus on constant electro‐magnetic fields. The fact that these fields are orthogonal or not leads to different geometric situations. In the first case, one reduces to some well‐understood model problem. For studying the second case, we introduce some two‐scale semi‐classical measures associated with symplectic submanifold. These measures are operator‐valued measures and the transfer of energy at the crossing is described by a non‐commutative Landau‐Zener formula for these measures. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Order optimal preconditioners for fully implicit Runge‐Kutta schemes applied to the bidomain equations

The partial differential equation part of the bidomain equations is discretized in time with fully implicit Runge–Kutta methods, and the resulting block systems are preconditioned with a block diagonal preconditioner. By studying the time‐stepping operator in the proper Sobolev spaces, we show that the preconditioned systems have bounded condition numbers given that the Runge–Kutta scheme is A‐stable and irreducible with an invertible coefficient matrix. A new proof of order optimality of the preconditioners for the one‐leg discretization in time of the bidomain equations is also presented. The theoretical results are verified by numerical experiments. Additionally, the concept of weakly positive‐definite matrices is introduced and analyzed. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq Eq 27: 1290–1312, 2011     

Future pricing through homogeneous semi‐Markov processes

An Erratum for this article has been published in Applied Stochastic Models in Business and Industry 2005; (in press) This paper presents a future pricing model based on the discrete time homogeneous semi‐Markov process (DTHSMP). The model is adapted to the real data of the Italian primary future stock index. After showing the pricing model, the DTHSMP solution is given. The solution of the semi‐Markov process gives, for each period of the considered horizon time, and for each starting state, the probability distribution of the future price. Copyright © 2005 John Wiley & Sons, Ltd.     

Method of lines with boundary elements for 1‐D transient diffusion‐reaction problems

Time‐dependent differential equations can be solved using the concept of method of lines (MOL) together with the boundary element (BE) representation for the spatial linear part of the equation. The BE method alleviates the need for spatial discretization and casts the problem in an integral format. Hence errors associated with the numerical approximation of the spatial derivatives are totally eliminated. An element level local cubic approximation is used for the variable at each time step to facilitate the time marching and the nonlinear terms are represented in a semi‐implicit manner by a local linearization at each time step. The accuracy of the method has been illustrated on a number of test problems of engineering significance. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2006     

A numerical method for the Landau–Lifshitz equation with magnetostriction

We present a numerical scheme for Landau–Lifshitz–Gilbert equation coupled with the equation of elastodynamics. The considered physical model describes the behaviour of ferromagnetic materials when magnetomechanical coupling is taken into account. The time‐discretization is based on the backward Euler method with projection. In the numerical approximation, the two equations are decoupled by a suitable linearization in order to solve the magnetic and mechanic part separately. The resulting semi‐implicit scheme is linear and allows larger time‐steps than explicit methods. We prove stability and error estimates for the presented time discretization in 2D. Finally, we test the accuracy of the scheme on an academic numerical example with known exact solution. Copyright © 2005 John Wiley & Sons, Ltd.     

Perturbations of Invertible Operators and Stability of g-Frames in Hilbert Spaces

In this paper, we study the perturbations of invertible operators and stability of g-frames in Hilbert spaces. In particular, we obtain some conditions under which the perturbations of an invertible operator are still an invertible operator, the perturbations of a right invertible operator or a surjective operator are still a right invertible operator or surjective operator. Then we apply the perturbations of invertible operators to study the stability of g-frames which is close related with the invertibility (or right invertibility) property of operators.     

Subgrid stabilization of Galerkin approximations of linear contraction semi‐groups of class C0 in Hilbert spaces

This article presents a stabilized Galerkin technique for approximating linear contraction semi‐groups of class C⁰ in a Hilbert space. The main result of this article is that this technique yields an optimal approximation estimate in the graph norm. The key idea is two‐fold. First, it consists in introducing an approximation space that is broken up into resolved scales and subgrid scales, so that the bilinear form associated with the generator of the semi‐group satisfies a uniform inf‐sup condition with respect to this decomposition. Second, the Galerkin approximation is slightly modified by introducing an artificial diffusion on the subgrid scales. Numerical tests show that the method applies also to nonlinear semi‐groups. © 2001 John Wiley & Sons., Inc. Numer Methods Partial Differential Eq 17: 1–25, 2001