Search results for "model theory"
showing 10 items of 681 documents
Enumeration of L-convex polyominoes by rows and columns
2005
In this paper, we consider the class of L-convex polyominoes, i.e. the convex polyominoes in which any two cells can be connected by a path of cells in the polyomino that switches direction between the vertical and the horizontal at most once.Using the ECO method, we prove that the number fn of L-convex polyominoes with perimeter 2(n + 2) satisfies the rational recurrence relation fn = 4fn-1 - 2fn-2, with f0 = 1, f1 = 2, f2 = 7. Moreover, we give a combinatorial interpretation of this statement. In the last section, we present some open problems.
Caristi Type Selections of Multivalued Mappings
2015
Multivalued mappings and related selection theorems are fundamental tools in many branches of mathematics and applied sciences. In this paper we continue this theory and prove the existence of Caristi type selections for generalized multivalued contractions on complete metric spaces, by using some classes of functions. Also we prove fixed point and quasi-fixed point theorems.
M-valued Measure of Roughness for Approximation of L-fuzzy Sets and Its Topological Interpretation
2015
We develop a scheme allowing to measure the “quality” of rough approximation of fuzzy sets. This scheme is based on what we call “an approximation quadruple” \((L,M,\varphi ,\psi )\) where L and M are cl-monoids (in particular, \(L=M=[0,1]\)) and \(\psi : L \rightarrow M\) and \(\varphi : M \rightarrow L\) are satisfying certain conditions mappings (in particular, they can be the identity mappings). In the result of realization of this scheme we get measures of upper and lower rough approximation for L-fuzzy subsets of a set equipped with a reflexive transitive M-fuzzy relation R. In case the relation R is also symmetric, these measures coincide and we call their value by the measure of rou…
Common Fixed Point Theorems for Weakly Compatible Maps Satisfying a General Contractive Condition
2008
We introduce a new generalized contractive condition for four mappings in the framework of metric space. We give some common fixed point results for these mappings and we deduce a fixed point result for weakly compatible mappings satisfying a contractive condition of integral type.
On Branciari’s theorem for weakly compatible mappings
2010
AbstractIn a recent paper B. Samet and H. Yazidi [B. Samet, H. Yazidi, An extension of Banach fixed point theorem for mappings satisfying a contractive condition of integral type, Ital. J. Pure Appl. Math. (in press)] have obtained an interesting theorem for mappings satisfying a contractive condition of integral type. The aim of this note is to present a generalization of their main result.
Fixed points of weakly compatible mappings satisfying generalized $\varphi$-weak contractions
2014
In this paper, utilizing the notion of the common limit range property, we prove some new integral type common fixed point theorems for weakly compatible mappings satisfying a \(\varphi \)-weak contractive condition in metric spaces. Moreover, we extend our results to four finite families of self mappings, and furnish an illustrative example and an application to support our main theorem. Our results improve, extend, and generalize well-known results on the topic in the literature.
A new Cartan-type property and strict quasicoverings when p = 1 in metric spaces
2018
In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we prove a new Cartan-type property for the fine topology in the case $p=1$. Then we use this property to prove the existence of $1$-finely open \emph{strict subsets} and \emph{strict quasicoverings} of $1$-finely open sets. As an application, we study fine Newton-Sobolev spaces in the case $p=1$, that is, Newton-Sobolev spaces defined on $1$-finely open sets.
On Different Type Solutions of Boundary Value Problems
2016
We consider boundary value problems of the type x'' = f(t, x, x'), (∗) x(a) = A, x(b) = B. A solution ξ(t) of the above BVP is said to be of type i if a solution y(t) of the respective equation of variations y'' = fx(t, ξ(t), ξ' (t))y + fx' (t, ξ(t), ξ' (t))y' , y(a) = 0, y' (a) = 1, has exactly i zeros in the interval (a, b) and y(b) 6= 0. Suppose there exist two solutions x1(t) and x2(t) of the BVP. We study properties of the set S of all solutions x(t) of the equation (∗) such that x(a) = A, x'1(a) ≤ x' (a) ≤ x'2(a) provided that solutions extend to the interval [a, b].
Approximation of Elliptic Hemivariational Inequalities
1999
From the previous chapter we know that there exist many important problems in mechanics in which constitutive laws are expressed by means of nonmonotone, possibly multivalued relations (nonmonotone multivalued stress-strain or reaction-displacement relations,e.g). The resulting mathematical model leads to an inclusion type problem involving multivalued nonmonotone mappings or to a substationary type problem for a nonsmooth, nonconvex superpotential expressed in terms of calculus of variation. It is the aim of this chapter to give a detailed study of a discretization of such a type of problems including the convergence analysis. Here we follow closely Miettinen and Haslinger, 1995, Miettinen…
Images and Preimages of Null Sets
2013
In this chapter we study conditions that guarantee that our mapping maps sets of measure zero to sets of measure zero. We start with the problem in general Sobolev spaces, after which we establish a better result for mappings of finite distortion. Then we introduce a natural class of counterexamples to statements of this type and finally we give a weak condition under which the preimage of a set of measure zero has measure zero for mappings of finite distortion.