Macroscopic cumulative fatigue damage of material under nonsymmetrical cycle

Hashin’s macroscopic theory of fatigue damage is further discussed and a new method has been proposed for prediction of cumulative fatigue damage of material and its lifetime under nonsymmetrical cyclic loading.

Some Results on the Range-Restricted GMRES Method

In this paper we reconsider the range-restricted GMRES (RRGMRES) method for solving nonsymmetric linear systems. We first review an important result for the usual GMRES method. Then we give an example to show that the range-restricted GMRES method does not admit such a result. Finally, we give a modified result for the range-restricted GMRES method. We point out that the modified version can be used to show that the range-restricted GMRES method is also a regularization method for solving linear ill-posed problems.

Preconditioned Bminpert Algorithms for Matrix Equation AX = B and Their Applications in Color Image Restoration

The purpose of this paper is to show the preconditioned BMinPert algorithm and analyse the practical implementation. Then a posteriori backward error for BGMRES is given. Furthermore, we discuss their applications in color image restoration. The key differences between BMinPert and other methods such as BFGMRES-S(m, pf), GsGMRES and BGMRES are illustrated with numerical experiments which expound the advantages of BMinPert in the presence of sensitive data with ill-condition problems.

Off-axial elliptical cosine-Gaussian beams and their propagation properties

In this paper, a new kind of light beam called off-axial elliptical cosine-Gaussian beam （ECosGBs） is defined by using the tensor method. An analytical propagation expression for the ECosGBs passing through axially nonsymmetrical optical systems is derived by using vector integration. The intensity distributions of ECosGBs on the input plane, on the output plane with the equivalent Fresnel number being equal to 0.1 and on the focal plane are respectively illustrated for the propagation properties. The results indicate that an ECosGB is eventually transformed into an elliptical cosh- Gaussian beam. In other words, ECosGBs and cosh-Gaussian beams act in a reciprocal manner after propagation.

Consensus of Second-order Multi-agent Systems with Nonsymmetric Interconnection and Heterogeneous Delays

In this paper, a consensus algorithm of multi-agent second-order dynamical systems with nonsymmetric interconnection and heterogeneous delays is studied. With the hypothesis of directed weighted topology graph with a globally reachable node, decentralized consensus condition is obtained by applying generalized Nyquist criterion. For the systems with both communication and input delays, it is shown that the consensus condition is dependent on input delays but independent of communication delays.

STRONG LAW OF LARGE NUMBERS AND ASYMPTOTIC EQUIPARTITION PROPERTY FOR NONSYMMETRIC MARKOV CHAIN FIELDS ON CAYLEY TREES

Some strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields （NSMC） on Cayley trees are studied. In the proof, a new technique for the study of strong limit theorems of Markov chains is extended to the case of Markov chain fields, The asymptotic equipartition properties with almost everywhere （a,e.） convergence for NSMC on Cayley trees are obtained,

BLOCK BIDIAGONALIZATION METHODS FOR MULTIPLE NONSYMMETRIC LINEAR SYSTEMS

The symmetric linear system gives us many simplifications and a possibility to adapt the computations to the computer at hand in order to achieve better performance. The aim of this paper is to consider the block bidiagonalization methods derived from a symmetric augmented multiple linear systems and make a comparison with the block GMRES and block biconjugate gradient methods.

Improvement of the minimal residual method for solving nonsymmetric linear systems

In this paper, the minimal residual （MRES） method for solving nonsymmetric equation systems was improved, the recurrence relation was deduced between the approximate solutions of the linear equation system Ax = b, and a more effective method was presented, which can reduce the operational count and the storage.

Basis-free expressions for derivatives of a subclass of nonsymmetric isotropic tensor functions

The present paper generalizes the method for solving the derivatives of symmetric isotropic tensor-valued functions proposed by Dui and Chen （2004） to a subclass of nonsymmetric tensor functions satisfying the commutative condition. This subclass of tensor functions is more general than those investigated by the existing methods. In the case of three distinct eigenvalues, the commutativity makes it possible to introduce two scalar functions, which will be used to construct the general nonsymmetric tensor functions and their derivatives. In the cases of repeated eigenvalues, the results are acquired by taking limits.

A Note on the Adaptive Simpler Block GMRES Method

The adaptive simpler block GMRES method was investigated by Zhong et al.(J Comput Appl Math 282:139-156, 2015) where the condition number of the adaptively chosen basis for the Krylov subspace was evaluated. In this paper, the new upper bound for the condition number is investigated. Numerical tests show that the new upper bound is tighter.

On Cubic Nonsymmetric Cayley Graphs

Let be a connected Cayley graph of group G, then Γ is called normal if the right regular representation of G is a normal subgroup of , the full automorphism group of Γ. For the case where G is a finite nonabelian simple group and Γ is symmetric cubic Cayley graph, Caiheng Li and Shangjin Xu proved that Γ is normal with only two exceptions. Since then, the normality of nonsymmetric cubic Cayley graph of nonabelian simple group aroused strong interest of people. So far such graphs which have been known are all normal. Then people conjecture that all of such graphs are either normal or the Cayley subset consists of involutions. In this paper we give an negative answer by two counterexamples. As far as we know these are the first examples for the non-normal cubic nonsymmetric Cayley graphs of finite nonabelian simple groups.

Integrability and solutions of a nonsymmetric discrete Korteweg-de Vries equation

In this paper,we present Lax pairs and solutions for a nonsymmetric lattice equation,which is a torqued version of the lattice potential Korteweg-de Vries equation.This nonsymmetric equation is special in the sense that it contains only one spacing parameter but consists of two consistent cubes with other integrable lattice equations.Using such a multidimensionally consistent property we are able to derive its two Lax pairs and also construct solutions using B?cklund transformations.

An incomplete generalized minimum backward perturbation algorithm for large nonsymmetric linear systems

This paper gives the truncated version of the generalized minimum backward error algorithm(GMBACK)—the incomplete generalized minimum backward perturbation algorithm(IGMBACK)for large nonsymmetric linear systems.It is based on an incomplete orthogonalization of the Krylov vectors in question,and gives an approximate or quasi-minimum backward perturbation solution over the Krylov subspace.Theoretical properties of IGMBACK including finite termination,existence and uniqueness are discussed in details,and practical implementation issues associated with the IGMBACK algorithm are considered.Numerical experiments show that,the IGMBACK method is usually more efficient than GMBACK and GMRES,and IMBACK,GMBACK often have better convergence performance than GMRES.Specially,for sensitive matrices and right-hand sides being parallel to the left singular vectors corresponding to the smallest singular values of the coefficient matrices,GMRES does not necessarily converge,and IGMBACK,GMBACK usually converge and outperform GMRES.

Mixed monotone decomposition of dynamical systems with application

The notions of mixed monotone decomposition of dynamical systems are introduced. The fundamental idea is to make an elaborate use of the natural growth and decay mechanism inherent in the structure of a dynamical systems to decompose its dynamics into increase and decrease parts, and thereby to constitute an augmented dynamical system as the so_called "two_sided comparison system" of the original one. The corresponding two_sided comparison theorems show that the solution of the comparison system gives lower and upper bounds of that of the original system. Therefore, the properties of a dynamical system can be obtained through the study of its two_sided comparison system. Compared with the conventional comparison method in literature, the mixed monotone decomposition method developed herein takes in a natural way structural properties of dynamical systems into account instead of requiring strict conditions of (quasi_)monotonicity on them, and could yields refined, usually nonsymmetrical, state estimates, and thus is more suitable for systems with nonsymmetrical state constraints. As an application of the method, a sufficient condition is established for the global asymptotic stability of the trivial solution of a class of continuous_time systems with nonsymmetrical state saturation. The condition is given in terms of coefficients and state saturation levels of such systems, and contains as a special case a recent result on systems with symmetric state saturation in literature.

TOTAL GENERALIZED MINIMUM BACKWARD ERROR ALGORITHM FOR SOLVING NONSYMMETRIC LINEAR SYSTEMS

This paper extendes the results by E.M. Kasenally([7]) on a Generalized Minimum Backward Error Algorithm for nonsymmetric linear systems Ax = b to the problem in which pertubations are simultaneously permitted on A and b. The approach adopted by Kasenally has been to view the approximate solution as the exact solution to a perturbed linear system in which changes are permitted to the matrix A only. The new method introduced in this paper is a Krylov subspace iterative method which minimizes the norm of the perturbations to both the observation vector b and the data matrix A and has better performance than the Kasenally's method and the restarted GMRES method([12]). The minimization problem amounts to computing the smallest singular value and the corresponding right singular vector of a low-order upper-Hessenberg matrix. Theoratical properties of the algorithm are discussed and practical implementation issues are considered. The numerical examples are also given.

Strong Law of Large Numbers and Asymptotic Equipartition Probability for Nonsymmetric Markov Chain Indexed by Cayley Tree

In this paper,we study the strong law of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain（NSMC） indexed by Cayley tree with any finite states.The asymptotic equipartition properties with almost everywhere（a.e.） convergence for NSMC indexed by Cayley tree are obtained.This article generalizes a recent result.

ON THE GENERALIZED DETERIORATED POSITIVE SEMI-DEFINITE AND SKEW-HERMITIAN SPLITTING PRECONDITIONER

For nonsymmetric saddle point problems,Huang et al.in [Numer.Algor.75 (2017), pp.1161-1191]established a generalized variant of the deteriorated positive semi-definite and skew-Hermitian splitting (GVDPSS)preconditioner to expedite the convergence speed of the Krylov subspace iteration methods like the GMRES method.In this paper,some new convergence properties as well as some new numerical results are presented to validate the theoretical results.

The Normalized Cochain Complex of a Nonsymmetric Cyclic Operad with Multiplication is a Quesney Homotopy BV Algebra

We show that the normalized cochain complex of a nonsymmetric cyclic operad with multiplication is a Quesney homotopy BV algebra;as a consequence,the cohomology groups form a Batalin-Vilkovisky algebra,which is a result due to L.Menichi.We provide ample examples.

Doubling Algorithm for Nonsymmetric Algebraic Riccati Equations Based on a Generalized Transformation

We consider computing the minimal nonnegative solution of the nonsymmetric algebraic Riccati equation with M-matrix.It is well known that such equations can be efficiently solved via the structure-preserving doubling algorithm(SDA)with the shift-and-shrink transformation or the generalized Cayley transformation.In this paper,we propose a more generalized transformation of which the shift-and-shrink transformation and the generalized Cayley transformation could be viewed as two special cases.Meanwhile,the doubling algorithm based on the proposed generalized transformation is presented and shown to be well-defined.Moreover,the convergence result and the comparison theorem on convergent rate are established.Preliminary numerical experiments show that the doubling algorithm with the generalized transformation is efficient to derive the minimal nonnegative solution of nonsymmetric algebraic Riccati equation with M-matrix.

USING THE SKEW-SYMMETRIC ITERATIVE METHODS FOR SOLUTION OF AN INDEFINITE NONSYMMETRIC LINEAR SYSTEMS

The concept of the field of value to localize the spectrum of the iteration matrices of the skew-symmetric iterative methods is further exploited. Obtained formulas are derived to relate the fields of values of the original matrix and the iteration matrix. This allows us to determine theoretically that indefinite nonsymmetric linear systems can be solved by this class of iterative methods.