A System of Sylvester-type Quaternion Matrix Equations with Ten Variables

Acta Mathematica Sinica, English Series - This paper studies a system of three Sylvester-type quaternion matrix equations with ten variables $${A_i}{X_i} + {Y_i}{B_i} + {C_i}{Z_i}{D_i} + {F_i}{Z_{i...     

The Constrained Solutions of Two Matrix Equations

We study the symmetric positive semidefinite solution of the matrix equation AX ₁ A ^T + BX ₂ B ^T = C, where A is a given real m×n matrix, B is a given real m×p matrix, and C is a given real m×m matric, with m, n, p positive integers; and the bisymmetric positive semidefinite solution of the matrix equation D ^T XD = C, where D is a given real n×m matrix, C is a given real m×m matrix, with m, n positive integers. By making use of the generalized singular value decomposition, we derive general analytic formulae, and present necessary and sufficient conditions for guaranteeing the existence of these solutions. Received December 17, 1999, Revised January 10, 2001, Accepted March 5, 2001     

Infinitesimal Classification of Systems of Two First Order Partial Differential Equations in Two Variables

Systems of two first order PDE with respect to two functions of two variables are considered. A classification of symbols of such systems with respect to the natural action of the group of local changes of dependent and independent variables is given. Bibliography: 6 titles.     

Global Well-Posedness of Incompressible Navier-Stokes Equations with Two Slow Variables

In this paper,the global well-posedness of the three-dimensional incompressible Navier-Stokes equations with a linear damping for a class of large initial data slowly varying in two directions are proved by means of a simpler approach.     

环Z/p~kZ上的两类矩阵方程

利用环上矩阵方法,研究了环Z/pkZ上的两类矩阵方程,确定了这两类矩阵方程的解数.     

Some Geometric Aspects of Integrability of Differential Equations in Two Independent Variables

The relation between scalar evolution equations which are the integrability condition of sl(2,R)-valued linear problems with parameter (kinematic integrability) and those which possess recursion operators (formal integrability) is studied: using that kinematically integrable equations describe one-parameter families of pseudo-spherical surfaces and vice versa, it is shown that every second order formally integrable evolution equation is kinematically integrable, and that this result cannot be extended as proven to the third-order case.Conservation laws of kinematically integrable equations obtained from their underlying pseudo-spherical structure are compared with the ones one finds from the Riccati equation version of their associated linear problems. Symmetries (generalized/nonlocal) for these equations are also studied, by considering infinitesimal deformations of the associated pseudo-spherical surfaces.Finally, conservation laws for equations describing pseudo-spherical surfaces immersed in a flat three-space are found, and the class of equations describing Calapso–Guichard surfaces is introduced.     

AHP中判断矩阵的满意的一致性的研究

对层次分析法(AHP)中的判断矩阵,给出了它具有满意的一致性的充分必要条件,也就是,给出了检验它是否有满意的一致性的一种方法,在否定的情况下,还给出了修正它的一种方法使得它的每个主子矩阵都有满意的一致性.     

利用矩阵初等行变换直接求得矩阵方程的通解

给出利用矩阵初等行变换直接求得矩阵方程通解的方法 .其表达、证明及解法均较文 [1 ]直接简捷     

Modified Locally One Dimensional Methods for Parabolic Partial Differential Equations in Two Space Variables

In this note we consider the locally one dimensional methodas discussed in Gourlay & Mitchell (1969, 1972) and indicatehow this scheme can be used to solve accurately a parabolicpartial differential equation in two space variables.     

Boundary Value Problems for Odd Order Forward-Backward-Type Differential Equations with Two Time Variables

We study solvability of boundary value problems for odd order differential equations in time variables. The presence of a discontinuous alternating coefficient is a peculiarity of these equations. We prove existence and uniqueness theorems for the regular solutions of such an equation, i.e. those that have all Sobolev generalized derivatives entering the equation under study.     

Solution of Band Matrix Equations by Projection-Recurrence

The solution space of the matrix equation Hx=u is decomposed by a projection which leads to a recurrence for H^-1. For tridiagonal H it is shown that the elements of H^-1 can always be completely factorized. An explicit expression is obtained for H^-1 when H is tridiagonal with constant interior elements and arbitrary boundary elements. This result reduces to a particularly simple form when H is Toeplitz. For general N×N tridiagonal H, the maximum number of arithmetic operations to obtain any element of H^-1 is asymptotic to 6N, and to obtain H^-1 it is N²+14N. To obtain the vector x the number of operations ranges from 8N to 11N.     

Sensitivity Analysis of Asset Flow Differential Equations and Volatility Comparison of Two Related Variables

In this study, I apply forward sensitivity analysis to the dynamical system of nonlinear asset flow differential equations (AFDEs). I find that all parameters in AFDEs are needed and can be estimated from market prices and net asset values data. Moreover, the market price is the most fluctuating state variable, and the coefficient for the trend-based investor' sentiment is the dominant parameter. Furthermore, I define and compare the extreme value-based volatilities of market price and net asset value for closed-end funds. I find that the extreme value-based volatility of market price is higher than that of net asset value for the vast majority of closed-end funds for both overlapping and non-overlapping cases.     

Stability of Functional Equations in Several Variables

We prove a generalization of Hyers＇ theorem on the stability of approximately additive mapping and a generalization of Badora＇s theorem on an approximate ring homomorphism. We also obtain a more general stability theorem, which gives the stability theorems on Jordan and Lie homomorphisms. The proofs of the theorems given in this paper follow essentially the D. H. Hyers-Th. M. Rassias approach to the stability of functional equations connected with S. M. Ulam＇s problem.     

Slow and Fast Variables in Non-autonomous Difference Equations

In this paper we present an existence and smoothness result for center-like invariant manifolds of non-autonomous difference equations with slow and fast state-space variables. This result can be seen as a first step to obtain Fenichel's geometric theory for difference equations. Hereby, our basic tool is an abstract integral manifold theorem.     

Chebyshev Methods for the Numerical Solution of Parabolic Partial Differential Equations in Two and Three Space Variables

Chebyshev methods for the numerical solution of parabolic partialdifferential equations in a region which can be transformedto either a square or a circular cylinder are developed. Theseprocedures are an extension of the method of Knibb & Scraton(1971). To illustrate the technique the solution of the heatconduction equation within an elliptical region is consideredin detail. The Chebyshev method given for this problem requiresconsiderably less computer time than the method of Dew &Scraton (1973). In the case when the space operators commutea highly efficient alternating direction Chebyshev method isgiven.