Related papers: On a criterion for a cutoff regularization in the …
A finite number of rational functions are compatible if they satisfy the compatibility conditions of a first-order linear functional system involving differential, shift and q-shift operators. We present a theorem that describes the…
Regular resolution is a refinement of the resolution proof system requiring that no variable be resolved on more than once along any path in the proof. It is known that there exist sequences of formulas that require exponential-size proofs…
The problem is considered as to whether a monotone function defined on a subset P of a Euclidean space can be strictly monotonically extended to the whole space. It is proved that this is the case if and only if the function is {\em…
For discrete spectrum of 1D second-order differential/difference operators (with or without potential (killing), with the maximal/minimal domain), a pair of unified dual criteria are presented in terms of two explicit measures and the…
In this paper we give a necessary and sufficient criterion for representability of a matroid over an algebraic closed field. This leads to an algorithm, based on an extension of Groebner Bases, in order to decide if a given matroid is…
We use the Cauchy-Crofton formula to show that every definable cell (bounded by a ball with rational radius) in an O-minimal expansion of a field extension of the real numbers satisfies the Whitney arc property.
Program transformation is an appealing technique which allows to improve run-time efficiency, space-consumption and more generally to optimize a given program. Essentially it consists of a sequence of syntactic program manipulations which…
The present paper, along with its sequel, establishes the correspondence between the properties of the solutions of a class of PDEs and the geometry of sets in Euclidean space. We settle the question of whether (quantitative) absolute…
Lineability is a property enjoyed by some subsets within a vector space X. A subset A of X is called lineable whenever A contains, except for zero, an infinite dimensional vector subspace. If, additionally, X is endowed with richer…
This Note derives regularity bounds for a Gevrey criterion when the Cauchy problem of elliptic equations is solved by regularization. When utilizing the regularization, one knows that checking such criterion is basically problematic, albeit…
Almost all problems in applied mathematics, including the analysis of dynamical systems, deal with spaces of real-valued functions on Euclidean domains in their formulation and solution. In this paper, we describe the the tool Ariadne,…
In the context of the correspondence between real functions on the unit circle and inner analytic functions within the open unit disk, that was presented in previous papers, we show that the constructions used to establish that…
A new classification of real functions and other related real objects defined within a compact interval is proposed. The scope of the classification includes normal real functions and distributions in the sense of Schwartz, referred to…
We characterize order preserving continuous surjections between compact linearly ordered spaces which admit an averaging operator, together with estimates of the norm of such an operator. This result is used to the study of strengthenings…
Functions with uniform level sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used, e.g., in multicriteria optimization, decision theory, mathematical…
A proof of the isometric embedding of a given two-metric in E^3 of class C^1. The method uses the theory of first order partial differential equations. The curvature of the metric plays no role in the proof.
Standard decision theory seeks conditions under which a preference relation can be compressed into a single real-valued function. However, when preferences are incomplete or intransitive, a single function fails to capture the agent's…
Proving program termination is typically done by finding a well-founded ranking function for the program states. Existing termination provers typically find ranking functions using either linear algebra or templates. As such they are often…
A family of real functions {g_\alpha} defining a spectral regularization method with optimal qualification is considered. Sufficient condition on the family and on the optimal qualification guaranteeing the existence of saturation are…
One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry…