Related papers: On harmonic representation of means
Systems of equations with sets of integers as unknowns are considered. It is shown that the class of sets representable by unique solutions of equations using the operations of union and addition $S+T=\makeset{m+n}{m \in S, \: n \in T}$ and…
We consider the problem of whether it is possible to improve the Novikov inequalities for closed 1-forms, or any other inequalities of a similar nature, if we assume, additionally, that the given 1-form is harmonic with respect to some…
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…
We classify globally irreducible representations of alternating groups and double covers of symmetric and alternating groups. In order to achieve this classification we also completely characterise irreducible representations of such groups…
We present a unified approach to representations of quantum mechanics on noncommutative spaces with general constant commutators of phase-space variables. We find two phases and duality relations among them in arbitrary dimensions.…
We study a generalization of the classical correspondence between homogeneous quadratic polynomials, quadratic forms, and symmetric/alternating bilinear forms to forms in $n$ variables. The main tool is combinatorial polarization, and the…
A simple method called symbolic representation for piecewise linear functions on the real line is introduced and used to compute the numbers of periodic points of all periods for some such functions. Since, for every positive integer m, the…
We consider Diophantine inequalities of the kind |f(x)| \le m, where F(X) \in Z[X] is a homogeneous polynomial which can be expressed as a product of d homogeneous linear forms in n variables with complex coefficients and m\ge 1. We say…
In this work we present a definition for coherence and compatibility of multilinear mappings and homogenous polynomial classes. These definitions are more restricted than the ones proposed before. We began analyzing this new definition in a…
Classical result states that for two continuous and strict means $M,\,N \colon I^2 \to I$ ($I$ is an interval) there exists a unique $(M,N)$-invariant mean $K \colon I^2 \to I$, i.e. such a mean that $K \circ (M,N)=K$ and, moreover, the…
Multiple harmonic-like numbers are studied using the generating function approach. A closed form is stated for binomial sums involving these numbers and two additional parameters. Several corollaries and examples are presented which are…
Symmetries and reductions of some algebraic equations are considered. Transformations that preserve the form of several algebraic equations, as well as transformations that reduce the degree of these equations, are described. Illustrative…
We develop a new approach to recurrence and the existence of non-constant harmonic functions on infinite weighted graphs. The approach is based on the capacity of subsets of metric boundaries with respect to intrinsic metrics. The main tool…
We show that, for a (not necessarily continuous) weakly contractive mean-type mapping $\mathbf{M} \colon I^p\to I^p$ (where $I$ is an interval and $p \in \mathbb{N}$), the functional equation $K \circ \mathbf{M}=K$ has at most one solution…
We compute the homology of the matching complex $M(\Gamma)$, where $\Gamma$ is the complete hypergraph on $n\geq 2$ vertices, and analyse the $S_n$-representations carried by this homology. These results are achieved using standard…
For any positive integer $N$, we describe a natural complex representation of the symmetric group $\Sigma_N$ on the vector space spanned by its involutions that contains each irreducible representation exactly once.
In this paper, we use a regularized theta lifting to construct harmonic Maass forms corresponding to binary theta functions of weight $k \ge 2$ under the $\xi$-operator. As a result, we show that their holomorphic parts have algebraic…
We extend the symbolic representation to the ring of N=1 supersymmetric differential polynomials, and demonstrate that operations on the ring, such as the super derivative, Frechet derivative and super commutator, can be carried out in the…
We prove partition regularity of the configuration $x,y,x+y,y/x$ in a strong infinitary form that extends Hindman's Theorem. We study the related issue of partition regularity of configurations involving products of a degree one polynomial…
Let $H:M_m\to M_m$ be a holomorphic function of the algebra $M_m$ of complex $m\times m$ matrices. Suppose that $H$ is orthogonally additive and orthogonally multiplicative on self-adjoint elements. We show that either the range of $H$…