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1.
By using an approach developed by one of the authors, approximate solutions of the soft periodic boundary conditions for a two-cell reaction diffusion model have been obtained. The system is considered with reactant A and autocatalyst B. The reaction is taken cubic in the autocatalyst in the two-cell with linear exchange through A. The formal exact solution is obtained which is symmetric with respect to the mid-point of the container. Approximate solutions are found through the Picard iterative sequence of solutions constructed after the exact one. It is found that the solution obtained is not unique. When the initial conditions are periodic, the most dominant modes initiate to traveling waves in systems with moderate size. Symmetric configurations forming a parabolic one for large time are observed. In systems of large size, spatially symmetric chaos are produced which are stationary in time. Furthermore, it is found the symmetric pattern formation hold irrespective of the condition of linear instability against small spatial disturbance.  相似文献
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The existence and uniqueness of strong solution of many-point boundary-value problems for some differential-operational equations and its continuous dependence on the coefficients are investigated. The tool employed in our analysis is the method of an energy inequality.  相似文献
4.
In this paper, we study the existence of periodic solutions for a nonlinear integral equation of periodic functions involving Weyl-Riesz fractional integral operator under the mixed generalized Lipschitz, Carathéodory and monotonicity conditions. The fixed point theorems due to Dhage are the main tool in carrying out our proofs.  相似文献
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In this paper we exploit the monomiality principle to discuss and introduce a new class of Laguerre-Konhauser polynomials. We study their properties (differential equations, generating functions, recurrence relations, expansions and so on), and discuss the link with ordinary case.  相似文献
6.
In this paper, an extension of the Hermite matrix polynomials is introduced. Some relevant matrix functions appear in terms of the two-variable Hermite matrix polynomials. Furthermore, in order to give qualitative properties of this family of matrix polynomials, the Chebyshev matrix polynomials of the second kind are introduced.  相似文献
7.
For n-tuplesA=(A 1,...,A n ) andB=(B 1,...,B n ) of operators on a Hilbert spaceH, letR A,B denote the operator onL(H) defined by . In this paper we prove that
whereW is the joint spatial numerical range andW 0 is the numerical range. We will show also that this inclusion becomes an equality whenR A,B is taken to be a generalized derivation, and it is strict whenR A,B is taken to be an elementary multiplication operator induced by non scalar self-adjoints operators.  相似文献
8.
For a ring extension is called a universally catenarian pair if every domain , is universally catenarian. When R is a field it is shown that the only universally catenarian pairs are those satisfying . For several satisfactory results are given. The second purpose of this paper is to study going-down pairs (Definition 5.1). We characterize these pairs of rings and we establish a relationship between universally catenarian, going-down and residually algebraic pairs. Received: 1 July 1999; in final form: 5 June 2000 / Published online: 17 May 2001  相似文献
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In the present paper, we derive some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain matrix operators on the sequence spaces of generalized means. Further, by applying the Hausdorff measure of noncompactness, we obtain the necessary and sufficient conditions for such operators to be compact.  相似文献
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