Search results for "Applied Mathematics"
showing 10 items of 4379 documents
Fixed Points for Weakα-ψ-Contractions in Partial Metric Spaces
2013
Recently, Samet et al. (2012) introduced the notion ofα-ψ-contractive mappings and established some fixed point results in the setting of complete metric spaces. In this paper, we introduce the notion of weakα-ψ-contractive mappings and give fixed point results for this class of mappings in the setting of partial metric spaces. Also, we deduce fixed point results in ordered partial metric spaces. Our results extend and generalize the results of Samet et al.
Periodic Groups Covered by Transitive Subgroups of Finitary Permutations or by Irreducible Subgroups of Finitary Transformations
1999
Let X be either the class of all transitive groups of finitary permutations, or the class of all periodic irreducible finitary linear groups. We show that almost primitive X-groups are countably recognizable, while totally imprimitive X-groups are in general not countably recognizable. In addition we derive a structure theorem for groups all of whose countable subsets are contained in totally imprimitive X-subgroups. It turns out that totally imprimitive p-groups in the class X are countably recognizable.
Mappings of finite distortion: The zero set of the Jacobian
2003
This paper is part of our program to establish the fundamentals of the theory of mappings of finite distortion [6], [1], [8], [13], [14], [7] which form a natural generalization of the class of mappings of bounded distortion, also called quasiregular mappings. Let us begin with the definition. We assume that Ω ⊂ Rn is a connected open set. We say that a mapping f : Ω → Rn has finite distortion if:
Dimensions of random affine code tree fractals
2014
We calculate the almost sure Hausdorff dimension for a general class of random affine planar code tree fractals. The set of probability measures describing the randomness includes natural measures in random $V$-variable and homogeneous Markov constructions.
Mixed intersections of non quasi-analytic classes
2008
Given two semi-regular matrices M and M' and two open subsets O and O' [resp. two compact subsets K and K'] of Rr and Rs respectively, we introduce the spaces E(M×M')(O × O') and D(M×M')(O × O') [resp. D(M×M')(K × K')]. In this paper we study their locally convex properties and the structure of their elements. This leads in [10] to tensor product representations of these spaces and to some kernel theorems.
Chromatic Sums for Colorings Avoiding Monochromatic Subgraphs
2013
Abstract Given graphs G and H, a vertex coloring c : V ( G ) → N is an H-free coloring of G if no color class contains a subgraph isomorphic to H. The H-free chromatic number of G, χ ( H , G ) , is the minimum number of colors in an H-free coloring of G. The H-free chromatic sum of G , Σ ( H , G ) , is the minimum value achieved by summing the vertex colors of each H-free coloring of G. We provide a general bound for Σ ( H , G ) , discuss the computational complexity of finding this parameter for different choices of H, and prove an exact formulas for some graphs G. For every integer k and for every graph H, we construct families of graphs, G k with the property that k more colors than χ ( …
Kernel theorems in the setting of mixed nonquasi-analytic classes
2008
Abstract Let Ω 1 ⊂ R r and Ω 2 ⊂ R s be nonempty and open. We introduce the Beurling–Roumieu spaces D ( ω 1 , ω 2 } ( Ω 1 × Ω 2 ) , D ( M , M ′ } ( Ω 1 × Ω 2 ) and obtain tensor product representations of them. This leads for instance to kernel theorems of the following type: every continuous linear map from the Beurling space D ( ω 1 ) ( Ω 1 ) (respectively D ( M ) ( Ω 1 ) ) into the strong dual of the Roumieu space D { ω 2 } ( Ω 2 ) (respectively D { M ′ } ( Ω 2 ) ) can be represented by a continuous linear functional on D ( ω 1 , ω 2 } ( Ω 1 × Ω 2 ) (respectively D ( M , M ′ } ( Ω 1 × Ω 2 ) ).
Codimension growth of two-dimensional non-associative algebras
2007
Let F be a field of characteristic zero and let A be a two-dimensional non-associative algebra over F. We prove that the sequence c n (A), n =1,2,..., of codimensions of A is either bounded by n + 1 or grows exponentially as 2 n . We also construct a family of two-dimensional algebras indexed by rational numbers with distinct T-ideals of polynomial identities and whose codimension sequence is n + 1, n > 2.
Metric regularity and subdifferential calculus in Banach spaces
1995
In this paper we give verifiable conditions in terms of limiting Frechet subdifferentials ensuring the metric regularity of a multivalued functionF(x)=−g(x)+D. We apply our results to the study of the limiting Frechet subdifferential of a composite function defined on a Banach space.
Produktintegration mit nicht-�quidistanten St�tzstellen
1980
For the numerical evaluation of $$\int\limits_a^b {(t - a)^{\alpha - 1} x(t)dt}$$ , 0<?<1 andx `smooth', product integration rules are applied. It is known that high-order rules, e.g. Gauss-Legendre quadrature, become `normal'-order rules in this case. In this paper it is shown that the high order is preserved by a nonequidistant spacing. Furthermore, the leading error terms of this product integration method and numerical examples are given.