Search results for "Linear Algebra"
showing 10 items of 552 documents
Relativistic SU(6) wave functions as the basis of modern approaches to hadronic wave functions
1991
The connections between various models of hadrons and the relativistic SU(6) wave functions are established. In formal terms and by concrete example it is shown how the Bargman-Wigner fields of freely moving quarks and antiquarks of equal velocity form the basis of the above approaches. This places modern attempts in their historical setting and allows for a more unified analysis of the various schemes.
Flavour geometry and effective Yukawa couplings in the MSSM
2010
We present a new geometric approach to the flavour decomposition of an arbitrary soft supersymmetry-breaking sector in the MSSM. Our approach is based on the geometry that results from the quark and lepton Yukawa couplings, and enables us to derive the necessary and sufficient conditions for a linearly-independent basis of matrices related to the completeness of the internal [SU(3) circle times U(1)](5) flavour space. In a second step, we calculate the effective Yukawa couplings that are enhanced at large values of tan beta for general soft supersymmetry-breaking mass parameters. We highlight the contributions due to non-universal terms in the flavour decompositions of the sfermion mass mat…
QCD isospin breaking in meson masses, decay constants and quark mass ratios
2001
The procedure to calculate masses and matrix-elements in the presence of mixing of the basis states is explained in detail. We then apply this procedure to the two-loop calculation in Chiral Perturbation Theory of pseudoscalar masses and decay constants including quark mass isospin breaking. These results are used to update our analysis of $K_{\ell4}$ done previously and obtain a value of $m_u/m_d$ in addition to values for the low-energy-constants $L_i^r$.
About two equivalent descriptions of quark antisymmetrization
1992
We analyze the wave function for a two-hadron system when the quark symmetrization principle is incorporated. Two alternative mathematical descriptions are considered. The representation method of Hund constructs a system of generators of thesinglet⊗singlet type. The method of Young-Froebenius incorporates hidden-color components in order to describe the representation basis. By taking a naive model we show that the two descriptions, are equivalent and thus no physical meaning should be attached to their mathematical differences. The results of our analysis are then applied to the more realisticN-N (deuteron) system. We end by discussing the structure of the Pauli correlations which we comp…
Coloring Linear Algebra
2016
[EN] We present an example of how we can introduce basic concepts on Linear Algebra in a first course of an Engineering School. We use the RGB pattern color which allows us to decompose a color into three primary colors (namely, red, green, blue). By using this model we give a natural connexion between the additivity of the color decomposition and the notions on linear algebra (as vector space, linear combination and convex linear span of vectors). To visualize these connexions we use Geogebra.
Analysis of inhomogeneously filled waveguides using a bi-orthonormal-basis method
2000
A general theoretical formulation to analyze inhomogeneously filled waveguides with lossy dielectrics is presented in this paper. The wave equations for the tranverse-field components are written in terms of a nonself-adjoint linear operator and its adjoint. The eigenvectors of this pair of linear operators define a biorthonormal-basis, allowing for a matrix representation of the wave equations in the basis of an auxiliary waveguide. Thus, the problem of solving a system of differential equations is transformed into a linear matrix eigenvalue problem. This formulation is applied to rectangular waveguides loaded with an arbitrary number of dielectric slabs centered at arbitrary points. The c…
AKNS and NLS hierarchies, MRW solutions, $P_n$ breathers, and beyond
2018
We describe a unified structure of rogue wave and multiple rogue wave solutions for all equations of the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy and their mixed and deformed versions. The definition of the AKNS hierarchy and its deformed versions is given in the Sec. II. We also consider the continuous symmetries of the related equations and the related spectral curves. This work continues and summarises some of our previous studies dedicated to the rogue wave-like solutions associated with AKNS, nonlinear Schrodinger, and KP hierarchies. The general scheme is illustrated by the examples of small rank n, n ⩽ 7, rational or quasi-rational solutions. In particular, we consider rank-2 and …
Reorientational dynamics in simple supercooled liquids
1998
Abstract The geometry of the reorientational dynamics in the van der Waals liquid, toluene, and the hydrogen bond network, glycerol, are compared. Both systems have contributions from small angle fluctuations. In glycerol the fraction of these small angle fluctuations is much larger than in toluene, due to the stronger anisotropic interactions in the former substance. The average reorientational angle in both systems is similar and on the order of 10 ∘ . In addition we analyze the stretching of the rotational correlation functions of rank one and two. In both cases we find that the second rank correlation function has a more pronounced stretching than the corresponding first rank correlatio…
Second-order tensorial calibration for kinetic spectrophotometric determination
1996
Abstract Kinetic-diode array spectrophotometric detection, as well as other multichannel techniques when used in non-equilibrium conditions, constitute second-order instrumentation. The second-order response provided will be bilinear, under certain conditions even trilinear, thus allowing the use of the generalized rank annihilation method (GRAM) and the trilinear decomposition method (TLD). Both numerically simulated and experimental data were used to evaluate the performance of these calibration techniques. The conditions in which the ‘second-order advantage’ (the possibility of quantifying the analytes in the presence of unknown reactions or interferences) is preserved were investigated.…
Low-Rank Tucker-2 Model for Multi-Subject fMRI Data Decomposition with Spatial Sparsity Constraint
2022
Tucker decomposition can provide an intuitive summary to understand brain function by decomposing multi-subject fMRI data into a core tensor and multiple factor matrices, and was mostly used to extract functional connectivity patterns across time/subjects using orthogonality constraints. However, these algorithms are unsuitable for extracting common spatial and temporal patterns across subjects due to distinct characteristics such as high-level noise. Motivated by a successful application of Tucker decomposition to image denoising and the intrinsic sparsity of spatial activations in fMRI, we propose a low-rank Tucker-2 model with spatial sparsity constraint to analyze multi-subject fMRI dat…