Related papers: A Peirce decomposition for generalized Jordan trip…
In isotropic strain gradient elasticity, we decompose the strain gradient tensor into its irreducible pieces under the n-dimensional orthogonal group O(n). Using the Young tableau method for traceless tensors, four irreducible pieces (n>2),…
This work deals with the presence of defect structures in generalized sine-Gordon models. The models are described by periodic potentials, with substructure having one, two, three or more distinct topological sectors, with multiplicity one,…
In this paper we prove the generalized Kaplansky conjecture for the Jordan algebras of the type $J_n$ in particular for self adjoint $2\times 2$ matrices over $\R$, over $\C$, $\HH$ and $\Oct$. In fact, we prove that the image of…
We study the conformal groups of Jordan algebras along the lines suggested by Kantor. They provide a natural generalization of the concept of conformal transformations that leave 2-angles invariant to spaces where "p-angles" can be defined.…
We present a generalized partial transposition separability criterion for the density matrix of a multipartite quantum system. This criterion comprises as special cases the famous Peres-Horodecki criterion and the recent realignment…
For more than 150 years the structure of the periodic system of the chemical elements has intensively motivated research in different areas of chemistry and physics. However, there is still no unified picture of what a periodic system is.…
We compare three notions of genericity of separable metric structures. Our analysis provides a general model theoretic technique of showing that structures are generic in descriptive set theoretic (topological) sense and in measure…
We present an effective method for computing parametric primary decomposition via comprehensive Gr\"obner systems. In general, it is very difficult to compute a parametric primary decomposition of a given ideal in the polynomial ring with…
There exists a biderivation structure on the polynomial algebra $\mathscr{A}[n] = K[x_1,\dots,x_n],$ where $K$ is a field with $\operatorname{char}(K)\ne 2$, defined by $f \circ h = \sum_{i=1}^n \frac{\partial f}{\partial…
The central component of a polygon triangulation is defined as the triangle or diameter that contain its geometric center. More generally, every polygon dissection contains a central component. Using this notion, we derive new recurrences…
Given an odd prime $p$, we identify composition factors of the reduction modulo $p$ of spin irreducible representations of the covering groups of symmetric groups indexed by partitions with 2 parts and find some decomposition numbers.
The purpose of this note is to prove the following. Suppose $\R$ is a semiprime unity ring having an idempotent element e $\left(e \neq 0, e \neq 1\right)$ which satisfies mild conditions. It is shown that every additive generalized Jordan…
Triangular decomposition is one of the standard ways to represent the radical of a polynomial ideal. A general algorithm for computing such a decomposition was proposed by A. Szanto. In this paper, we give the first complete bounds for the…
The current article continues a series of papers on decomposition of unipotents and its applications. Let $G(\Phi,R)$ be a Chevalley group with a reduced irreducible root system $\Phi$ over a commutative ring $R$. Fix $h\in G(\Phi,R)$. Call…
By defining two important terms called basic perturbation vectors and obtaining their linear bounds, we obtain the linear componentwise perturbation bounds for unitary factors and upper triangular factors of the generalized Schur…
Let $\mathcal A$ and $\mathcal B$ be unital rings and $\mathcal M$ be a $(\mathcal A, \mathcal B)$-bimodule, which is faithful as a left $\mathcal A$-module and also as a right $\mathcal B$-module. Let ${\mathcal U}={\rm Tri}(\mathcal A,…
We show that while the number of coprime compositions of a positive integer $n$ into $k$ parts can be expressed as a $\mathbb{Q}$-linear combinations of the Jordan totient functions, this is never possible for the coprime partitions of $n$…
In his 1963 paper, Dirac [1] gave `A Remarkable Representation of the 3 + 2 de- Sitter Group'. We reproduce this representation using a generalised Jordan map which is motivated by the infinitesimal symplectic transformations related to the…
The Jordan Canonical Form of a matrix is highly sensitive to perturbations, and its numerical computation remains a formidable challenge. This paper presents a regularization theory that establishes a well-posed least squares problem of…
The concepts of Generalized Parton Distributions (GPD) are reviewed in an introductory and phenomenological fashion. These distributions provide a rich and unifying picture of the nucleon structure. Their physical meaning is discussed. The…