Related papers: Three Problems of "Distinction"
We introduce a new class of problems lying halfway between questions about graph capacity and intersection. We say that two binary sequences x and y of the same length have a skewincidence if there is a coordinate i for which x_i=y_{i+1}=1…
This article introduces recursive relations allowing the calculation of the number of partitions with constraints on the minimum and/or on the maximum fragment size.
We find generators for the algebra of rational differential invariants for general and degenerate Kundt spacetimes and relate this to other approaches to the equivalence problem for Lorentzian metrics. Special attention is given to…
We study equivalence relation of the set of triangles generated by similarity and operation on a triangle to get a new one by joining division points of three edges with the same ratio. Using the moduli space of similarity classes of…
The problems connected with equivalent norms lie at the heart of Banach space theory. This is a short survey on some recent as well as classical results and open problems in renormings of Banach spaces.
In condensed matter theory many invaluable models rely on the possibility of subsuming fundamental particle interactions in constitutive relations for macroscopic fields in near equilibrium assemblies of particles. Should one wish to…
We present a finite-order system of recurrence relations for a permanent of circulant matrices containing a band of k any-value diagonals on top of a uniform matrix (for k = 1, 2, and 3) as well as the method for deriving such recurrence…
We reformulate Special Relativity by a quaternionic algebra on reals. Using {\em real linear quaternions}, we show that previous difficulties, concerning the appropriate transformations on the $3+1$ space-time, may be overcome. This implies…
In this paper we investigate cumulative hierarchies of functions on structures, or cumulative powers, and study their properties. Particularly, we show how they extend the preservation phenomena of reduced powers, direct powers and…
Divergence chain rules for channels relate the divergence of a pair of channel inputs to the divergence of the corresponding channel outputs. An important special case of such a rule is the data-processing inequality, which tells us that if…
A structure called a decision making problem is considered. The set of outcomes (consequences) is partially ordered according to the decision maker's preferences. The problem is how these preferences affect a decision maker to prefer one of…
We consider entailment problems involving powerful constraint languages such as frontier-guarded existential rules in which we impose additional semantic restrictions on a set of distinguished relations. We consider restricting a relation…
In the paper is considered two problems on extension of operators whose range space for the first problem (or domain space for the second one) belongs to the fixed class of finite equivalence, which is generated by a given Banach space $X$.…
Transcendental numbers play an important role in many areas of science. This paper contains a short survey on transcendental numbers and some relations among them. New inequalities for transcendental numbers are stated in Section 2 and…
When the distribution of the data used to train a classifier differs from that of the test data, i.e., under dataset shift, well-established routines for calibrating the decision scores of the classifier, estimating the proportion of…
In this paper two related simplification problems for systems of linear inequalities describing precedence relation systems are considered. Given a precedence relation system, the first problem seeks a minimum subset of the precedence…
Given k sets such that no one is contained in another, there is an associated lattice on the power set P([k]) corresponding to inclusion relations among unions of the sets. Two lattices on P([k]) are equivalent if there is a permutation of…
The smallness of the cosmological constant is one of the basic problems in particle physics and cosmology. Various attempts have been made to explain this mystery, but no satisfactory solution has been found yet. The appearance of extra…
We consider the longest common subsequence problem in the context of subsequences with gap constraints. In particular, following Day et al. 2022, we consider the setting when the distance (i. e., the gap) between two consecutive symbols of…
Quantum capacities are fundamental quantities that are notoriously hard to compute and can exhibit surprising properties such as superadditivity. Thus, a vast amount of literature is devoted to finding tight and computable bounds on these…