Related papers: 10-commutator and 13-commutator
Let $0< n,\alpha,\beta\in\mathbb{N}$ be such that $\gcd{(\alpha,\beta)}=1$. We carry out the evaluation of the convolution sums $\underset{\substack{ {(k,l)\in\mathbb{N}^{2}} \\ {\alpha\,k+\beta\,l=n} } }{\sum}\sigma(k)\sigma_{3}(l)$ and…
The purpose of this work is to pursue classification of geproci sets. Specifically we classify $[m,n]$-geproci sets which consist of $m=4$ points on each of $n$ skew lines, assuming the skew lines have two transversals in common. We show…
A symmetric tensor is called copositive if it generates a multivariate form taking nonnegative values over the nonnegative orthant. Copositive tensors have found important applications in polynomial optimization and tensor complementarity…
It is known that for every spatial complete graph on $n\ge 7$ vertices, the summation of the second coefficients of the Conway polynomials over the Hamiltonian knots is congruent to $r_{n}$ modulo $(n-5)!$, where $r_{n} = (n-5)!/2$ if…
We classify all the supersymmetric configurations of ungauged N=2,d=4 supergravity coupled to n vector multiplets and determine under which conditions they are also classical solutions of the equations of motion. The supersymmetric…
We construct a noncommutative version of a general renormalizable SO(10) GUT with Higgses in the 210, $\overline{126}, 45, 10$ and 120 irreps of SO(10) and a Peccei-Quinn symmetry. Thus, we formulate the noncommutative counterpart of a…
We construct one parameter families of three qubit separable states with length ten, which is strictly greater than the whole dimension eight. These states are located on the boundary of the convex set of all separable states, but they are…
We analyze the structure of the algebra N of symmetric polynomials in non-commuting variables in so far as it relates to its commutative counterpart. Using the "place-action" of the symmetric group, we are able to realize the latter as the…
Given a sequence converging to zero, we consider the set of numbers which are sums of (infinite, finite, or empty) subsequences. When the original sequence is not absolutely summable, the subsum set is an unbounded closed interval which…
This paper is a modern exposition of old ideas. The setting is a Euclidian space $E$ of dimension $n$ with associated vector space $V$ of dimension $n$. A (non-zero) sliding vector is a vector in $V$ that is free to move, but only within a…
The symmetry classification method is applied to the string-like scalar fields in two-dimensional space-time. When the configurational space is three-dimensional and reducible we present the complete list of the systems admiting higher…
An odd vector field $Q$ on a supermanifold $M$ is called homological, if $Q^2=0$. The operator of Lie derivative $L_Q$ makes the algebra of smooth tensor fields on $M$ into a differential tensor algebra. In this paper, we give a complete…
A decomposition of a natural number n is a sequence of consecutive natural numbers that sums to n. We construct a one-to-one correspondence between the odd factors of a natural number and its decompositions. We study the decompositions by…
We formulate N-fold supersymmetry in quantum mechanical systems with reflection operators. As in the cases of other systems, they possess the two significant characters of N-fold supersymmetry, namely, almost isospectrality and weak…
The class of $\left(\binom{n+1}{2}_{n-1} \binom{n+1}{3}_3\right)$-configurations which contain at least $n-2$ $K_n$-graphs coincides with the class of so called systems of triangle perspectives i.e. of configurations which contain a bundle…
Let $P$ be a set of $n$ points in general position on the plane. A set of closed convex polygons with vertices in $P$, and with pairwise disjoint interiors is called a convex decomposition of $P$ if their union is the convex hull of $P$,…
We show that the skein vector space of the 3-torus is finitely generated. We show that it is generated by 9 elements: the empty set, some simple closed curves representing the non null elements of the first homology group with coefficients…
We develop a theory of measures, differential forms and Fourier tramsforms on some infinite-dimensional real vector spaces by generalizing the following two constructions: (a) The construction of the semiinfinite wedge power of a Tate…
We have obtained the supersymmetric extension of spectral triple which specify a noncommutative geometry(NCG). We assume that the functional space H constitutes of wave functions of matter fields and their superpartners included in the…
In the past year several constructions of non-invertible symmetries in Quantum Field Theory in $d\geq 3$ have appeared. In this paper we provide a unified perspective on these constructions. Central to this framework are so-called theta…