Related papers: The Replace Operator
Let $A$ and $B$ be compact operators over a topological space $X$ and suppose that these operators are normal and have same distinct eigenvalues at each point. By obstruction theory, we establish a necessary and sufficient condition for $A$…
The class of uniformly computable real functions with respect to a small subrecursive class of operators computes the elementary functions of calculus, restricted to compact subsets of their domains. The class of conditionally computable…
A new mathematical notation is proposed for the iteration of functions. It facilitates the application of the iteration of functions in mathematical and logical expressions, definitions of sets, and formulations of algorithms. Illustrations…
The aim of this paper is first to give necessary and sufficient condition of existence (of free boundaries) for both Laplacian and bi-Laplacian operators in the case where the overdetermined condition is not constant. second, by using some…
By the operator of relative complementation is meant a mapping assigning to every element x of an interval [a,b] of a lattice L the set x^{ab} of all relative complements of x in [a,b]. Of course, if L is relatively complemented then x^{ab}…
For a complex number s, the s-order integral of function f fulfilling some conditions is defined as action of an operator, noted J^s, on f. The definition of the operator J^s is given firstly for the case of complex number s with positive…
We extend the theory of distributional kernel operators to a framework of generalized functions, in which they are replaced by integral kernel operators. Moreover, in contrast to the distributional case, we show that these generalized…
Interpretation methods and their restrictions to polynomials have been deeply used to control the termination and complexity of first-order term rewrite systems. This paper extends interpretation methods to a pure higher order functional…
Algorithms like those for differentiating functional expressions manipulate the syntactic structure of mathematical expressions in a mathematically meaningful way. A formalization of such an algorithm should include a specification of its…
Our aim is to construct a finite automaton recognizing the set of words that are at a bounded distance from some word of a given regular language. We define new regular operators, the similarity operators, based on a generalization of the…
We introduce an abstract framework for elliptic boundary value problems in a variational form. Given a non-negative quadratic form in a Hilbert space, a boundary pair consists of a bounded operator, the boundary operator, and an auxiliary…
The defining conditions for the irreducible tensor operators associated with the unitary irreducible corepresentions of compact quantum group algebras are deduced first in both the right and left regular coaction formalisms. In each case it…
This paper deals with belief base revision that is a form of belief change consisting of the incorporation of new facts into an agent's beliefs represented by a finite set of propositional formulas. In the aim to guarantee more reliability…
Ordered logics and type systems have been used in a variety of applications including computational linguistics, memory allocation, stream processing, logical frameworks, parametricity, and enforcing security protocols. In most…
We investigate the quantifier alternation hierarchy in first-order logic on finite words. Levels in this hierarchy are defined by counting the number of quantifier alternations in formulas. We prove that one can decide membership of a…
Given a regular language $L$, we study the language of words $\mathsf{D}(L)$, that distinguish between pairs of different left-quotients of $L$. We characterize this distinguishability operation, show that its iteration has always a fixed…
The compact explicit expressions for formal exact operator solutions to Cauchy problem for sufficiently general systems of nonlinear differential equations (ODEs and PDEs) in the form of chronological operator exponents are given. The…
We introduce the notion of regular operator mappings of several variables generalising the notion of spectral function. This setting is convenient for studying maps more general than what can be obtained from the functional calculus, and it…
Superposition rules form a class of functions that describe general solutions of systems of first-order ordinary differential equations in terms of generic families of particular solutions and certain constants. In this work we extend this…
We propose an analysis of corrections which models some of the requirements corrections place on context. We then show that this analysis naturally extends to the interaction of corrections with pronominal anaphora on the one hand, and…