Related papers: The Orchard relation of a generic symmetric or ant…
Variational and divergence symmetries are studied in this paper for linear equations of maximal symmetry in canonical form, and the associated first integrals are given in explicit form. All the main results obtained are formulated as…
Paper is devoted to extremal problems in geometric function theory of complex variables associated with estimates of functionals defined on the systems of non-overlapping domains. In particular, we strengthen some known result in this…
We describe generating functions for several important families of classical symmetric functions and shifted Schur functions. The approach is originated from vertex operator realization of symmetric functions and offers a unified method to…
We study semifinite harmonic functions on the zigzag graph, which corresponds to Pieri's rule for the fundamental quasisymmetric functions $\{F_{\lambda}\}$. The main problem, which we solve here, is to classify the indecomposable…
We study the properties of the set where a generalized function of bounded variation has infinite approximate limit, highlighting in this way the main geometric difference with functions of bounded variation. To this aim we prove a new…
We survey the theory of totally symmetric sets, with applications to homomorphisms of symmetric groups, braid groups, linear groups, and mapping class groups.
For the class of systems of PDEs, for which infinitesimal translations (with respect to some (in)dependent variables) possess specific finite-dimensional invariant subspaces of the space of generalized symmetries of the system considered.…
Let $D$ be an oriented link diagram with the set of regions $\operatorname{r}_{D}$. We define a symmetric map (or matrix) $\operatorname{\tau}_{D}\colon\operatorname{r}_{D}\times \operatorname{r}_{D} \to \mathbb{Z}[x]$ that gives rise to an…
Motivated by applications for simulating quantum many body functions, we propose a new universal ansatz for approximating anti-symmetric functions. The main advantage of this ansatz over previous alternatives is that it is bi-Lipschitz with…
A unifying scheme of classical special functions of hypergeometric type obeying orthogonality or biorthogonality relations is described. It expands the Askey scheme of classical orthogonal polynomials and its $q$-analogue based on the…
We characterize those compact sets for which the Dirichlet problem has a solution within the class of continuous $m$-subharmonic functions defined on a compact set, and then within the class of $m$-harmonic functions.
We define a number of related combinatorial objects, each of which possesses a surprising symmetry. We include several applications such as a combinatorial explanation for certain fixed points of the involution $\omega$ on the ring of…
Recently there was a substantial progress in understanding of supersymmetric theories (in particular, their BPS spectrum) in space-times of different dimensions due to the exact computation of superconformal indices and partition functions…
We study linear relations among correlation functions on a lattice obtained from integration-by-parts identities. We use the framework of twisted cocycles and determine for a scalar theory a basis of correlation functions, in which all…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
In this paper we establish a new equivalence relation on the spaces of almost periodic functions which allows us to prove a result like Bohr's equivalence theorem extended to the case of all these functions.
We study the fundamental properties of pointwise semi-Lipschitz functions between asymmetric spaces, which are the natural asymmetric counterpart of pointwise Lipschitz functions. We also study the influence that partial symmetries of a…
We study the relation between the Laplacian associated to an odd metric on a supermanifold and harmonic superfunctions, through the application of the calculus of variations to a supersymmetric sigma model.
The polynomial relationship between elementary symmetric functions (Cauchy enumeration formula) is formulated via a ``raising operator" and Fock space construction. A simple graphical proof of this relation is proposed. The new operator…
We establish a necessary and sufficient condition on a continuous function on $[-1,1]$ under which the family of functions on the unit sphere $\mathbb{S}^{d-1}$ constructed in the described manner is fundamental in $C(\mathbb{S}^{d-1})$. In…