Search results for "Graph theory"
showing 10 items of 784 documents
Cocharacters of Bilinear Mappings and Graded Matrices
2012
Let Mk(F) be the algebra of k ×k matrices over a field F of characteristic 0. If G is any group, we endow Mk(F) with the elementary grading induced by the k-tuple (1,...,1,g) where g ∈ G, g2 ≠ 1. Then the graded identities of Mk(F) depending only on variables of homogeneous degree g and g − 1 are obtained by a natural translation of the identities of bilinear mappings (see Bahturin and Drensky, Linear Algebra Appl 369:95–112, 2003). Here we study such identities by means of the representation theory of the symmetric group. We act with two copies of the symmetric group on a space of multilinear graded polynomials of homogeneous degree g and g − 1 and we find an explicit decomposition of the …
Quasi *-Algebras of Operators in Rigged Hilbert Spaces
2002
In this chapter, we will study families of operators acting on a rigged Hilbert space, with a particular interest in their partial algebraic structure. In Section 10.1 the notion of rigged Hilbert space D[t] ↪ H ↪ D × [t ×] is introduced and some examples are presented. In Section 10.2, we consider the space.L(D, D ×) of all continuous linear maps from D[t] into D × [t ×] and look for conditions under which (L(D, D ×), L +(D)) is a (topological) quasi *-algebra. Moreover the general problem of introducing in L(D, D ×) a partial multiplication is considered. In Section 10.3 representations of abstract quasi *-algebras into quasi*-algebras of operators are studied and the GNS-construction is …
Multiplicative Loops of Quasifields Having Complex Numbers as Kernel
2017
We determine the multiplicative loops of locally compact connected 4-dimensional quasifields Q having the field of complex numbers as their kernel. In particular, we turn our attention to multiplicative loops which have either a normal subloop of dimension one or which contain a subgroup isomorphic to $$Spin_3({\mathbb {R}})$$ . Although the 4-dimensional semifields Q are known, their multiplicative loops have interesting Lie groups generated by left or right translations. We determine explicitly the quasifields Q which coordinatize locally compact translation planes of dimension 8 admitting an at least 16-dimensional Lie group as automorphism group.
Higher order Peregrine breathers solutions to the NLS equation
2015
The solutions to the one dimensional focusing nonlinear Schrödinger equation (NLS) can be written as a product of an exponential depending on t by a quotient of two polynomials of degree N (N + 1) in x and t. These solutions depend on 2N − 2 parameters : when all these parameters are equal to 0, we obtain the famous Peregrine breathers which we call PN breathers. Between all quasi-rational solutions of the rank N fixed by the condition that its absolute value tends to 1 at infinity and its highest maximum is located at the point (x = 0, t = 0), the PN breather is distinguished by the fact that PN (0, 0) = 2N + 1. We construct Peregrine breathers of the rank N explicitly for N ≤ 11. We give …
Hierarchy of solutions to the NLS equation and multi-rogue waves.
2014
The solutions to the one dimensional focusing nonlinear Schrödinger equation (NLS) are given in terms of determinants. The orders of these determinants are arbitrarily equal to 2N for any nonnegative integer $N$ and generate a hierarchy of solutions which can be written as a product of an exponential depending on t by a quotient of two polynomials of degree N(N+1) in x and t. These solutions depend on 2N-2 parameters and can be seen as deformations with 2N-2 parameters of the Peregrine breather P_{N} : when all these parameters are equal to 0, we recover the P_{N} breather whose the maximum of the module is equal to 2N+1. Several conjectures about the structure of the solutions are given.
Synthesis of pyrido[2,3-d]pyrimidinones by the reaction of aminopyrimidin-4-ones with benzylidene meldrum's acid derivatives
1997
A series of pyrido[2,3-d]pyrimidine-4,7-diones 5a-h were prepared from 6-amino-4-pyrimidones 1 and benzylidene Meldrum's acid derivatives 2 by cyclization reactions in boiling nitrobenzene. The structure of 5, determined by nmr measurements, reveals a selective orientation of 1 and 2 in the addition step.
Approximate 3D Partial Symmetry Detection Using Co-occurrence Analysis
2015
This paper addresses approximate partial symmetry detection in 3D point clouds, a classical and foundational tool for analyzing geometry. We present a novel, fully unsupervised method that detects partial symmetry under significant geometric variability, and without constraints on the number and arrangement of instances. The core idea is a matching scheme that finds consistent co-occurrence patterns in a frame-invariant way. We obtain a canonical partition of the input shape into building blocks and can handle ambiguous data by aggregating co-occurrence information across both all building block instances and the area they cover. We evaluate our method on several benchmark data sets and dem…
Attracteurs de Lorenz de variété instable de dimension arbitraire
1997
Abstract We construct the first examples of flows with robust multidimensional Lorenz-like attractors: the singularity contained in the attractor may have any number of expanding eigenvalues, and the attractor remains transitive in a whole neighbourhood of the initial flow. These attractors support a Sinai-Ruelle-Bowen SRB-measure and, contrary to the usual (low-dimensional) Lorenz models, they have infinite modulus of structural stability.
On $MC$-hypercentral triply factorized groups
2007
A group G is called triply factorized in the product of two subgroups A, B and a normal subgroup K of G ,i fG = AB = AK = BK. This decomposition of G has been studied by several authors, investigating on those properties which can be carried from A, B and K to G .I t is known that if A, B and K are FC-groups and K has restrictions on the rank, then G is again an FC-group. The present paper extends this result to wider classes of FC-groups. Mathematics Subject Classification: 20F24; 20F14
The importance of kinematic twists and genuine saturation effects in dijet production at the Electron-Ion Collider
2021
We compute the differential yield for quark anti-quark dijet production in high-energy electron-proton and electron-nucleus collisions at small $x$ as a function of the relative momentum $\boldsymbol{P}_\perp$ and momentum imbalance $\boldsymbol{k}_\perp$ of the dijet system for different photon virtualities $Q^2$, and study the elliptic and quadrangular anisotropies in the relative angle between $\boldsymbol{P}_\perp$ and $\boldsymbol{k}_\perp$. We review and extend the analysis in [1], which compared the results of the Color Glass Condensate (CGC) with those obtained using the transverse momentum dependent (TMD) framework. In particular, we include in our comparison the improved TMD (ITMD…