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1.
The convergence of a finite element scheme approximating a nonlinear system of integro-differential equations is proven. This system arises in mathematical modeling of the process of a magnetic field penetrating into a substance. Properties of existence, uniqueness and asymptotic behavior of the solutions are briefly described. The decay of the numerical solution is compared with both the theoretical and finite difference results. 相似文献
2.
In this paper we establish a new characterisation of star-regular categories, using a property of internal reflexive graphs, which is suggested by a recent result due to O. Ngaha Ngaha and the first author. We show that this property is, in a suitable sense, invariant under regular completion of a category in the sense of A. Carboni and E.M. Vitale. Restricting to pointed categories, where star-regularity becomes normality in the sense of the second author, this reveals an unusual behaviour of the exactness property of normality (i.e. the property that regular epimorphisms are normal epimorphisms) compared to other closely related exactness properties studied in categorical algebra. 相似文献
3.
In this paper we obtain an intrinsic syntactical characterization of protomodularity, via so-called categorical difference terms, similar to the one known in the case of varieties involving binary terms d satisfying d(x, x) = d(y, y). We also show that purely categorical modifications of the condition in the characterization give characterizations of Mal’tsev
and additive categories, thus revealing a new conceptual link between these three classes of categories, and hence, also between
the corresponding classes of varieties. 相似文献
4.
We develop an elementary approach to the classical descent problems for modules and algebras, and their generalizations, based on the theory of monads. 相似文献
5.
After investigating all conceivable properties of decidable objects and maps in left exact categories with well-behaved finite sums (‘lextensive categories’), we give a characterization in such categories of decidable morphisms which are (finite) coverings (in an appropriate sense). Finally, we give two applications of this result, to separable algebras and to local homeomorphisms. In both cases it explains categorically the advantage of two well-known notions — strongly separable algebras and local homeomorphisms with path lifting property, respectively. 相似文献
6.
We introduce a notion of a subtractive category. It generalizes the notion of a pointed subtractive variety of universal algebras in the sense of A. Ursini. Subtractive categories are closely related to Mal’tsev and additive categories: (i) a category C with finite limits is a Mal’tsev category if and only if for every object X in C the category Pt(X)=((X,1X)↓(C↓X)) of “points over X” is subtractive; (ii) a pointed category C with finite limits is additive if and only if C is subtractive and half-additive.Mathematics Subject Classifications (2000) 18C99, 18E05, 08B05. 相似文献
7.
Zurab Guguchia Hugo Keller Annette Bussmann-Holder Jürgen Köhler Reinhard K. Kremer 《The European Physical Journal B - Condensed Matter and Complex Systems》2013,86(10):1-4
Specific heat and magnetization measurements demonstrate that the antiferromagnetic (AFM) phase transition at T N = 5.7 K of EuTiO3 is rapidly suppressed with Sr doping in Eu x Sr1?x TiO3. Close to x = 0.25, T N = 0 K and AFM order vanishes. Above this critical concentration a finite transition temperature to an AFM phase is observed. The exchange couplings are derived as a function of x and the corresponding low temperature phase diagram is presented. 相似文献
8.
We define relative Goursat categories and prove relative versions of the equivalent conditions defining regular Goursat categories. These include 3-permutability of equivalence relations, preservation of equivalence relations under direct images, a condition on so-called Goursat pushouts, and the denormalised 3×3 Lemma. This extends recent work by Gran and Rodelo on a new characterisation of Goursat categories to a relative context. 相似文献
9.
Methods of internal-category theory are applied to show that the split epimorphisms in a category C are exactly the morphisms which are effective for descent with respect to any fibration over C (or to any C-indexed category). In the same context, composition-cancellation rules for effective descent morphisms are established and being applied to (suitably defined) locally-split epimorphisms. 相似文献
10.
If (, M)is a factorization system on a category C, we define new classes of maps as follows: a map f:AB is in if each of its pullbacks lies in (that is, if it is stably in ), and is in M
* if some pullback of it along an effective descent map lies in M(that is, if it is locally in M). We find necessary and sufficient conditions for (, M
*) to be another factorization system, and show that a number of interesting factorization systems arise in this way. We further make the connexion with Galois theory, where M
*is the class of coverings; and include self-contained modern accounts of factorization systems, descent theory, and Galois theory. 相似文献