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In the present paper, classical tools of convex analysis are used to study the solution set to a certain class of set-inclusive generalized equations. A condition for the solution existence and global error bounds is established, in the…
We propose a new interpretation of doubly special relativity based on the distinction between the momenta and the translation generators in its phase space realization. We also argue that the implementation of the theory does not…
A group invariant for links in thickened closed orientable surfaces is studied. Associated polynomial invariants are defined. The group detects nontriviality of a virtual link and determines its virtual genus.
Lorentz covariant generalisations of the notions of supersymmetry, superspace and self-duality are discussed. The essential idea is to extend standard constructions by allowing tangent vectors and coordinates which transform according to…
Various characterizations of finite convex geometries are well known. This note provides similar characterizations for possibly infinite convex geometries whose lattice of closed sets is strongly coatomic and lower continuous. Some classes…
Characterizations of all continuous, additive and $\mathrm{GL}(n)$-equivariant endomorphisms of the space of convex functions on a Euclidean space $\mathbb{R}^n$, of the subspace of convex functions that are finite in a neighborhood of the…
symmetry, group classification, differential invariants, Lie-classical method,infinitesimal criterion method, RDC equation, KPP equation, similarity solutions.
We study the space of vector-valued (twisted) conjugate invariant functions on a connected reductive group.
We define generalized vector fields, and contraction and Lie derivatives with respect to them. Generalized commutators are also defined.
We introduce the notion of porous invariants for multipath (or branching/nondeterministic) affine loops over the integers; these invariants are not necessarily convex, and can in fact contain infinitely many 'holes'. Nevertheless, we show…
We carry out group analysis of a class of generalized fifth-order Korteweg-de Vries equations with time dependent coefficients. Admissible transformations, Lie symmetries and similarity reductions of equations from the class are classified…
The theory of gravitation field within the special theory of relativity is analyzed.
In this paper we study local unitary invariants of a multi-partite quantum state that are monotonic, on average, under local operations and classical communication (locc). In particular we focus on local unitary invariants that are…
The concept of the Lorentz-invariant mass of a group of particles is shown to be applicable to biphoton states formed in the process of spontaneous parametric down conversion. The conditions are found when the Lorentz-invariant mass is…
This article is a continuation of work on construction and calculation various of modifications of invariant based on the use Euclidean metric values attributed to elements of manifold triangulation. We again address the well investigated…
A set of integral relations for rotational and translational zero modes in the vicinity of the classical soliton solution are derived from the particle-like properties of the latter. The validity of these all relations is considered for a…
The problems in variation here concerned are such as to admit a continuous group (in Lie's sense); the conclusions that emerge from the corresponding differential equations find their most general expression in the theorems formulated in…
In this paper we classify invariant noncommutative connections in the framework of the algebra of endomorphisms of a complex vector bundle. It has been proven previously that this noncommutative algebra generalizes in a natural way the…
This is an overview of the present-day versions of monadology with some applications to vector lattices and linear inequalities.
A new class of integrable mappings and chains is introduced. Corresponding $(1+2)$ integrable systems invariant with respect to such discrete transformations are presented in an explicit form. Their soliton-type solutions are constructed in…