Related papers: Parry condition, existence and uniqueness of alter…
We assume that every element of a matrix has a small, individual error, and model it by an external number, which is the sum of a nonstandard real number and a neutrix, the latter being a convex (external) set having the group property. The…
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…
Spurious ambiguity is the phenomenon whereby distinct derivations in grammar may assign the same structural reading, resulting in redundancy in the parse search space and inefficiency in parsing. Understanding the problem depends on…
In this paper we discourse basises of representable algebras. This question lead to arithmetic problems. We prove algorithmical solvability of exponential-Diophantine equations in rings represented by matrices over fields of positive…
We define a proof system for exceptions which is close to the syntax for exceptions, in the sense that the exceptions do not appear explicitly in the type of any expression. This proof system is sound with respect to the intended…
Starting from the classic contraction mapping principle, we establish a general, flexible, variational setting that turns out to be applicable to many situations of existence in Differential Equations. We show its potentiality with some…
We study substitutive systems generated by nonprimitive substitutions and show that transitive subsystems of substitutive systems are substitutive. As an application we obtain a complete characterisation of the sets of words that can appear…
In this paper we prove unique continuation principles for some systems of elliptic partial differential equations satisfying a suitable superlinearity condition. As an application, we obtain nonexistence of nontrivial (not necessarily…
I shall describe a general model-theoretic task to construct expansions of pseudofinite structures and discuss several examples of particular relevance to computational complexity. Then I will present one specific situation where finding a…
We present an auxiliary space theory that provides a unified framework for analyzing various iterative methods for solving linear systems that may be semidefinite. By interpreting a given iterative method for the original system as an…
We study a generalization of additive bases into a planar setting. A planar additive basis is a set of non-negative integer pairs whose vector sumset covers a given rectangle. Such bases find applications in active sensor arrays used in,…
In this paper, we investigate statistics on alternating words under correspondence between ``possible reflection paths within several layers of glass'' and ``alternating words''. For $v=(v_1,v_2,\cdots,v_n)\in\mathbb{Z}^{n}$, we say $P$ is…
We introduce an extension of the propositional calculus to include abstracts of predicates and quantifiers, employing a single rule along with a novel comprehension schema and a principle of extensionality, which are substituted for the…
Proven-in-use arguments are needed when pre-developed products with an in-service history are to be used in different environments than those they were originally developed for. A product may include software modules or may be stand-alone…
Waring problem for homogeneus forms asks for additive decomposition of a form $f$ into powers of linear forms. A classical problem is to determine when such a decomposition is unique. In this note I refine the work in arXiv:math/0406288v1…
We introduce a new version of arithmetic in all finite types which extends the usual versions with primitive notions of extensionality and extensional equality. This new hybrid version allows us to formulate a strong form of extensionality,…
An alternative parameterization of R-matrix theory is presented which is mathematically equivalent to the standard approach, but possesses features which simplify the fitting of experimental data. In particular there are no level shifts and…
We introduce and study non-uniform expansions of real numbers, given by two non-integer bases.
The aim of this paper is to establish some metrical coincidence and common fixed point theorems with an arbitrary relation under an implicit contractive condition which is general enough to cover a multitude of well known contraction…
This paper describes an alternative method of generating fixed points of certain substitution systems. This method centres on taking infinite words consisting of one repeated letter per word. These infinite words are then interlaced to form…