Related papers: On testing integrability
Perturbative Symmetry Approach is formulated in symbolic representation. Easily verifiable integrability conditions of a given equation are constructed in the frame of the approach. Generalisation for the case of non-local and non-evolution…
The general concept of symmetry is realized in manifold ways in different realms of reality, such as plants, animals, minerals, mathematical objects or human artefacts in literature, fine arts and society. In order to arrive at a common…
Some thermodynamical properties of solids, such as heat capacity and magnetic susceptibility, have recently been shown to be linked to the amount of entanglement in a solid. However this entanglement may appear a mere mathematical artifact…
We study the finite satisfiability problem for the two-variable fragment of first-order logic extended with counting quantifiers (C2) and interpreted over linearly ordered structures. We show that the problem is undecidable in the case of…
Multidimensional combinatorial substitutions are rules that replace symbols by finite patterns of symbols in $\mathbb Z^d$. We focus on the case where the patterns are not necessarily rectangular, which requires a specific description of…
: In studies of discrete structures, functions are frequently used that express proximity, but are not metrics. We consider a class of such functions that is characterized by a normalization condition and an inequality that plays the same…
Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…
We first partly develop a mathematical notion of stable consistency intended to reflect the actual consistency property of human beings. Then we give a generalization of the first and second G\"odel incompleteness theorem to stably…
Partially ordered sets (posets) play a universal role as an abstract structure in many areas of mathematics. For finite posets, an explicit enumeration of distinct partial orders on a set of unlabelled elements is known only up to a…
A generalization of highly symmetric frames is presented by considering also projective stabilizers of frame vectors. This allows construction of highly symmetric line systems and study of highly symmetric frames in a more unified manner.…
Order and symmetry are main structural principles in mathematics. We give five examples where on the face of it order is not apparent, but deeper investigations reveal that they are governed by order structures. These examples are finite…
Errors quoted on results are often given in asymmetric form. An account is given of the two ways these can arise in an analysis, and the combination of asymmetric errors is discussed. It is shown that the usual method has no basis and is…
We consider the sequential composite binary hypothesis testing problem in which one of the hypotheses is governed by a single distribution while the other is governed by a family of distributions whose parameters belong to a known set…
Partial symmetries are described by generalized group structures known as symmetric inverse semigroups. We use the algebras arising from these structures to realize supersymmetry in (0+1) dimensions and to build many-body quantum systems on…
We show the absence of continuous symmetry breaking in 2D lattice systems without any smoothness assumptions on the interaction. We treat certain cases of interactions with integrable singularities. We also present cases of singular…
In the framework of certain general probability theories of single systems, we identify various nonclassical features such as incompatibility, multiple pure-state decomposability, measurement disturbance, no-cloning and the impossibility of…
Given a functional for a one-dimensional physical system, a classical problem is to minimize it by finding stationary solutions and then checking the positive definiteness of the second variation. Establishing the positive definiteness is,…
Based on a generalized cosine measure between two symmetric matrices, we propose a general framework for one-sample and two-sample tests of covariance and correlation matrices. We also develop a set of associated permutation algorithms for…
This paper examines the potential role of unit consistency as a system design principle. Unit-consistent generalized matrix inverses and unit-invariant matrix decompositions are derived in support of this principle. Applications of the…
The symmetry of polygons can be characterized by the number of symmetry axes they have. For $n$-polygons with $p$ or $p^2$ vertices $p\geq3$ there exist few symmetry categories, depending from the number of symmetry-axes the have. Further…