共查询到20条相似文献,搜索用时 15 毫秒
1.
For a system of ordinary differential equations of the form
,
, we obtain new upper bounds for the second norm of Green's matrix using the integral performance criterion for dichotomy and bounds of the Hausdorff set of the matrix A. These estimates are considerably better for many applications than some well-known ones. 相似文献
2.
On the basis of the Kharitonov theorem, sufficient conditions on an
matrix A are presented for the matrix
to be stable for arbitrary
,
. 相似文献
3.
Zhen‐Yun Peng 《Numerical Linear Algebra with Applications》2008,15(4):373-389
In this paper, two new matrix‐form iterative methods are presented to solve the least‐squares problem: and matrix nearness problem: where matrices and are given; ??1 and ??2 are the set of constraint matrices, such as symmetric, skew symmetric, bisymmetric and centrosymmetric matrices sets and SXY is the solution pair set of the minimum residual problem. These new matrix‐form iterative methods have also faster convergence rate and higher accuracy than the matrix‐form iterative methods proposed by Peng and Peng (Numer. Linear Algebra Appl. 2006; 13 : 473–485) for solving the linear matrix equation AXB+CYD=E. Paige's algorithms, which are based on the bidiagonalization procedure of Golub and Kahan, are used as the framework for deriving these new matrix‐form iterative methods. Some numerical examples illustrate the efficiency of the new matrix‐form iterative methods. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
4.
We consider a complex version of a Dirac-Kähler-type equation, the eight-component complex Dirac-Kähler equation with a nonvanishing mass, which can be decomposed into two Dirac equations by only a nonunitary transformation. We also write an analogue of the complex Dirac-Kähler equation in five dimensions. We show that the complex Dirac-Kähler equation is a special case of a Bhabha-type equation and prove that this equation is invariant under the algebra of purely matrix transformations of the Pauli-Gürsey type and under two different representations of the Poincaré group, the fermionic (for a two-fermion system) and bosonic
-representations. The complex Dirac-Kähler equation is also written in a manifestly covariant bosonic form as an equation for the system (
, ,
) of irreducible self-dual tensor, scalar, and vector fields. We illustrate the relation between the complex Dirac-Kähler equation and the known 16-component Dirac-Kähler equation.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 143, No. 1, pp. 64–82, April, 2005. 相似文献
5.
Let be the set of nonnegative integers and the ring of integers. Let
be the ring of N × N matrices over generated by the following two matrices: one obtained from the identity matrix by shifting the ones one position to the right and the other one position down. This ring plays an important role in the study of directly finite rings. Calculation of invertible and idempotent elements of
yields that the subrings generated by them coincide. This subring is the sum of the ideal
consisting of all matrices in
with only a finite number of nonzero entries and the subring of
generated by the identity matrix. Regular elements are also described. We characterize all ideals of
, show that all ideals are finitely generated and that not all ideals of
are principal. Some general ring theoretic properties of
are also established. 相似文献
6.
The Hoff equation
describes the H-beam buckling dynamics. We show that the phase space of the Hoff equation is a simple
Banach manifold modeled on a subspace complementary to the kernel
. 相似文献
7.
Pavel Rehak 《Czechoslovak Mathematical Journal》2001,51(2):303-321
We study oscillatory properties of the second order half-linear difference equation
. It will be shown that the basic facts of oscillation theory for this equation are essentially the same as those for the linear equation
. We present here the Picone type identity, Reid Roundabout Theorem and Sturmian theory for equation (HL). Some oscillation criteria are also given. 相似文献
8.
We obtain necessary and sufficient conditions for the solvability of the augmentation and modification problems of order
for Hermitian matrices. The augmentation problem consists in the construction of a Hermitian
-matrix with a given
-block
in block
-representation and with the prescribed eigenvalues. The modification problem consists in the construction of a Hermitian
-matrix
of rank not greater than
so that the obtained matrix, being added to a given Hermitian
-matrix
, will have the required spectrum. We give an estimate for the minimal number of different eigenvalues of the solutions to these problems. 相似文献
9.
The Dirichlet problem for the equation
is studied in the semi-circle
. The restrictions on F are established under which the problem is uniquely solvable in the definite generalized sense. 相似文献
10.
11.
New oscillation and nonoscillation criteria are established for the equation
,where p :]1,+[ R is the locally integrable function. These criteria generalize and complement the well known criteria of E. Hille, Z. Nehari, A. Wintner, and P. Hartman. 相似文献
12.
We consider the possibility of using the quantum inverse scattering method to study the superconformal field theory and its integrable perturbations. The classical limit of the considered constructions is based on the
(1|2) super-KdV hierarchy. We introduce the quantum counterpart of the monodromy matrix corresponding to the linear problem associated with the L-operator and use the explicit form of the irreducible representations of
q(1|2) to obtain the fusion relations for the transfer matrices (i.e., the traces of the monodromy matrices in different representations).Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 2, pp. 252–264, February, 2005. 相似文献
13.
Satoshi Tanaka 《Czechoslovak Mathematical Journal》2001,51(3):573-583
The higher order neutral functional differential equation
is considered under the following conditions:
is strictly increasing in
is nonnegative on
and nondecreasing in
. A necessary and sufficient condition is derived for the existence of certain positive solutions of (1). 相似文献
14.
When mathematical models describing various processes are analysed, the fact of existence of a positive solution is often among the basic features. In this paper, a general delayed discrete equation
is considered. Sufficient conditions concerning f are formulated in order to guarantee the existence of a positive solution for k . An upper estimate for it is given as well. The appearance of the positive solution takes its origin in the nature of the equation considered since the results hold only for delayed equations (i.e. for n > 0) and not for the case of an ordinary equation (with n = 0). 相似文献
15.
Michal Vyroai 《Applications of Mathematics》2005,50(1):63-81
We consider a stochastic process X
t
x
which solves an equation
where A and are real matrices and BH is a fractional Brownian motion with Hurst parameter H (1/2,1). The Kolmogorov backward equation for the function u(t,x) =
f(X
t
x
) is derived and exponential convergence of probability distributions of solutions to the limit measure is established.This research has been supported by the grant no. 201/01/1197 of the Grant Agency of the Czech Republic.This revised version was published online in April 2005 with a corrected issue number. 相似文献
16.
The paper is concerned with oscillation properties of n-th order neutral differential equations of the form
where c is a real number with
with (t) < t and
.Sufficient conditions are established for the existence of positive solutions and for oscillation of bounded solutions of the above equation. Combination of these conditions provides necessary and sufficient conditions for oscillation of bounded solutions of the equation. Furthermore, the results are generalized to equations in which c is a function of t and a certain type of a forcing term is present. 相似文献
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17.
This paper deals with the study of the stability of nonautonomous retarded functional differential equations using the theory of dichotomic maps. After some preliminaries, we prove the theorems on simple and asymptotic stability. Some examples are given to illustrate the application of the method. Main results about asymptotic stability of the equation
and of itsnonlinear generalization
are established. 相似文献
18.
Yury J. Ionin 《Designs, Codes and Cryptography》1998,13(2):147-158
Let M be a set of incidence matrices of symmetric (v,k,)-designs and G a group of mappings M M. We give a sufficient condition for the matrix W M, where M M and W is a balanced generalized weighing matrix over G, to be the incidence matrix of a larger symmetric design. This condition is then applied to the designs corresponding to McFarland and Spence difference sets, and it results in four families of symmetric (v,k, )-designs with the following parameters k and (m and d are positive integers, p and q are prime powers): (i)
; (ii)
; (iii)
; (iv)
. 相似文献
19.
Gary F. Birkenmeier Henry E. Heatherly Jin Yong Kim Jae Keol Park 《Acta Mathematica Hungarica》2002,95(1-2):101-114
Let
be a unital K-algebra, where K is a commutative ring with unity. An idempotent
is {\it left semicentral\/} if
, and
is {\it SCI-generated\/} if it is generated as a K-module by left semicentral idempotents. This paper develops the basic properties of SCI-generated algebras and characterizes those that are also prime, semiprime, primitive, or subdirectly irreducible. Minimal ideals and the socle of SCI-generated algebras are investigated. Conditions are found to describe a large class of SCI-generated algebras via generalized triangular matrix representations. SCI-generated piecewise domains are characterized. Examples are given that illustrate the breadth and diversity of the class of SCI-generated algebras. 相似文献