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11.
V. L. Topunov 《Acta Appl Math》1989,16(2):191-206
In this paper, an application of the Riquer-Thomas-Janet theory is described for the problem of transforming a system of partial differential equations into a passive form, i.e., to a special form which contains explicitly both the equations of the initial system and all their nontrivial differential consequences. This special representation of a system markedly facilitates the subsequent integration of the corresponding differential equations. In this paper, the modern approach to the indicated problem is presented. This is the approach adopted in the Knuth-Bendix procedure [13] for critical-pair/completion and then Buchberger's algorithm for completion of polynomial ideal bases [13] (or, alternatively, for the construction of Groebner bases for ideals in a differential operator ring [14]). The algorithm of reduction to the passive form for linear system of partial differential equations and its implementation in the algorithmic language REFAL, as well as the capabilities of the corresponding program, are outlined. Examples illustrating the power and efficiency of the system are presented. 相似文献
12.
13.
Peter Dräxler 《Journal of Pure and Applied Algebra》2002,169(1):33-42
We show that the cleaving functors introduced in [Bautista et al., Invent. Math. 81 (1985) 217] as a tool for proving infinite representation type of finite-dimensional algebras can also be used to establish controlled wildness. The main application is that an algebra is controlled wild if there is an indecomposable projective module with a Loewy factor having a homogeneous direct summand which is of length at least 3. As a second application we derive Han's covering criterion. 相似文献
14.
In this paper we give a realization of some symmetric space G/K as a closed submanifold P of G. We also give several equivalent representations of the submanifold P. Some properties of the set gK∩P are also discussed, where gK is a coset space in G. 相似文献
15.
The moduli space of torus sextics with the configuration of singularities {A2+A5+2E6} has two connected components. We compute the fundamental groups π1(CP2−C) for sextics C in both components and study their differences. 相似文献
16.
J. Carlos Díaz-Ramos Ramón Vázquez-Lorenzo 《Differential Geometry and its Applications》2006,24(4):433-442
Explicit examples of Osserman 4-manifolds with exactly two distinct eigenvalues of the Jacobi operators, α and β=4α≠0, are given. The former has multiplicity two and is a double root of the minimal polynomial of the Jacobi operators. 相似文献
17.
A. M. Vinogradov 《Acta Appl Math》1989,15(1-2):3-21
The main notions and results which are necessary for finding higher symmetries and conservation laws for general systems of partial differential equations are given. These constitute the starting point for the subsequent papers of this volume. Some problems are also discussed. 相似文献
18.
A Volterra type integral equation in a Hilbert space with an additional linear operator L and a spectral parameter depending
on time is considered. If the parameter does not belong to the spectrum of L unconditional solvability of the considered problem
is proved. In the case where the initial value of the parameter coincides with some isolated point of the spectrum of the
operator L sufficient conditions for solvability are established. The obtained results are applied to the partial integral
equations associated with a contact problem of the theory of elasticity. 相似文献
19.
Saida Sultanic 《Integral Equations and Operator Theory》2006,55(4):573-595
The central question of this paper is the one of finding the right analogue of the Commutant Lifting Theorem for the Bergman
space La2. We also analyze the analogous problem for weighted Bergman spaces La,α2, − 1 < α < ∞. 相似文献
20.
Michel Hébert 《Archive for Mathematical Logic》1991,31(2):133-143
Summary We give a syntactic characterization of (finitary) theories whose categories of models are closed under the formation of connected limits (respectively the formation of pullbacks and substructures) in the category of all structures. They are also those theories whose consistent extensions by new atomic facts admit in each component an initial structure (respectively an initial term structure), and also thoseT for whichM(T) is locally finitely multi-presentable in a canonical way. We also show that these two properties of theories are nonuniform. 相似文献