Matricial Form Research Articles

A Note on Matricial Ways to Compute Burt’s Structural Holes

In this note, I derive simple formulas based on the adjacency matrix of a network to compute measures associated with Ronald S. Burt’s structural holes (effective size, redundancy, local constraint, and constraint), together with the measure called improved structural holes introduced in 2017. This can help to see these measures within a unified computation framework because they can all be expressed in matricial form. These formulas can also be used to define naïve algorithms based on matrix operations for their computation. Such naïve algorithms can be used for small- and medium-sized networks, where exploiting the sparsity of the matrices and efficient triangle listing techniques are not necessary.

Implementation of multi-component Zhdanov closure in SOLEDGE3X

The multi-component fluid closure derived by Zhdanov (2002 Transport Processes in Multicomponent Plasma (London: Taylor and Francis)) is implemented in the fluid code SOLEDGE3X-EIRENE to deal with arbitrary edge plasma composition. The closure assumes no distinction between species such as light versus heavy species separation. The work of Zhdanov is rewritten in a matricial form in order to clearly link friction forces and heat fluxes to the different species velocities and temperature gradients.

Application of the Hurricane-Based Optimization Algorithm to the Phase-Balancing Problem in Three-Phase Asymmetric Networks

This article addresses the problem of optimal phase-swapping in asymmetric distribution grids through the application of hurricane-based optimization algorithm (HOA). The exact mixed-integer nonlinear programming (MINLP) model is solved by using a master–slave optimization procedure. The master stage is entrusted with the definition of load connection at each stage by using an integer codification that ensures that, per node, only one from the possible six-load connections is assigned. In the slave stage, the load connection set provided by the master stage is applied with the backward/forward power flow method in its matricial form to determine the amount of grid power losses. The computational performance of the HOA was tested in three literature test feeders composed of 8, 25, and 37 nodes. Numerical results show the effectiveness of the proposed master–slave optimization approach when compared with the classical Chu and Beasley genetic algorithm (CBGA) and the discrete vortex search algorithm (DVSA). The reductions reached with HOA were 24.34%, 4.16%, and 19.25% for the 8-, 28-, and 37-bus systems; this confirms the literature reports in the first two test feeders and improves the best current solution of the IEEE 37-bus grid. All simulations are carried out in the MATLAB programming environment.

The Equivalence between Successive Approximations and Matricial Load Flow Formulations

This paper shows the equivalence of the matricial form of the classical backward/forward load flow formulation for distribution networks with the recently developed successive approximations (SA) load flow approach. Both formulations allow solving the load flow problem in meshed and radial distribution grids even if these are operated with alternating current (AC) or direct current (DC) technologies. Both load flow methods are completely described in this research to make a fair comparison between them and demonstrate their equivalence. Numerical comparisons in the 33- and 69-bus test feeder with radial topology show that both methods have the same number of iterations to find the solution with a convergence error defined as 1×10−10.

Polynomial sequences: elementary basic methods and application hints. A survey

The present paper contains a small survey on the principal and elementary methods for a systematic study of general polynomial sequences. For the set of polynomial sequences the algebraic structure of a group is given. Matricial forms, recurrence relations and conjugate sequences of polynomials are examined. For every element of a polynomial sequence determinant forms are determined by suitable Hessenberg matrices. Generating functions and derivation matrix are derived. Then, associated differential operator and Sheffer classification are considered. As an application, a general interpolation problem is hinted at. For a real valued function, the generalized Taylor polynomial and series are given. As an illustrative example, the shifted (with respect to the degree) Fibonacci polynomial sequence is considered.

Simulation of the concomitant process of nucleation-growth-coarsening of Al2Cu particles in a 319 foundry aluminum alloy

The precipitation of Al2Cu particles in a 319 T7 aluminum alloy has been modeled. A theoretical approach enables the concomitant computation of nucleation, growth and coarsening. The framework is based on an implicit scheme using the finite differences. The equation of continuity is discretized in time and space in order to obtain a matricial form. The inversion of a tridiagonal matrix gives way to determining the evolution of the size distribution of Al2Cu particles at t +Δt. The fluxes of in-between the boundaries are computed in order to respect the conservation of the mass of the system, as well as the fluxes at the boundaries. The essential results of the model are compared to TEM measurements. Simulations provide quantitative features on the impact of the cooling rate on the size distribution of particles. They also provide results in agreement with the TEM measurements. This kind of multiscale approach allows new perspectives to be examined in the process of designing highly loaded components such as cylinder heads. It enables a more precise prediction of the microstructure and its evolution as a function of continuous cooling rates.

Geometric classification of monogenic subspaces and uniparametric linear control systems

We present a geometric approach to the classification of monogenic invariant subspaces, alternative to the classical algebraic one, which allows us to obtain several matricial canonical forms for each class. Some applications are derived: canonical coordinates of a vector with regard to an endomorphism, and a canonical form for uniparametric linear control systems, not necessarily controllable, with regard to linear changes of state variables. Moreover, the pointwise construction can be extended to differentiable families of changes of basis when differentiable families of equivalent monogenic subspaces are considered.

Influence of irregularities in the electrolyte on the cathodic protection of steel: A numerical and experimental study

This paper shows how the last algebraic matricial form can be obtained when the finite element method is used to approximate the potential distribution of a cathodic protection system that includes low conductivity irregularities in the electrolyte away from, close to and directly on the cathode. In order to study the influence of the resistivity of these irregularities on the possibilities of steel protection, five conductivities were analysed. The numerical results, validated with COMSOL® Multiphysics, show the importance of considering irregularities in the domain in order to prevent systems from becoming unprotected. The experimental data agrees with the theoretical data.

A new conservative method for the unsteady heat equation

A new conservative finite difference scheme for the unsteady heat equation is proposed. The new numerical scheme is a simplified version of mimetic methods, it satisfies a discrete version of Green’s theorem, and it does not use ghost points at any stage of its development. Its formulation will be presented in terms of a simple matricial form, which covers the full range of time evaluations. This feature allows us to present a complete and elegant convergence analysis. Its precision is quadratic at the boundary so an overall higher order convergence rate, compared with finite difference methods, is achieved in space. Numerical tests show the advantage of the new scheme when its linear systems are solved by iterative Krylov methods.

Intersections of Schubert varieties and eigenvalue inequalities in an arbitrary finite factor

The intersection ring of a complex Grassmann manifold is generated by Schubert varieties, and its structure is governed by the Littlewood–Richardson rule. Given three Schubert varieties S 1 , S 2 , S 3 with intersection number equal to one, we show how to construct an explicit element in their intersection. This element is obtained generically as the result of a sequence of lattice operations on the spaces of the corresponding flags, and is therefore well defined over an arbitrary field of scalars. Moreover, this result also applies to appropriately defined analogues of Schubert varieties in the Grassmann manifolds associated with a finite von Neumann algebra. The arguments require the combinatorial structure of honeycombs, particularly the structure of the rigid extremal honeycombs. It is known that the eigenvalue distributions of self-adjoint elements a , b , c with a + b + c = 0 in the factor R ω are characterized by a system of inequalities analogous to the classical Horn inequalities of linear algebra. We prove that these inequalities are in fact true for elements of an arbitrary finite factor. In particular, if x , y , z are self-adjoint elements of such a factor and x + y + z = 0 , then there exist self-adjoint a , b , c ∈ R ω such that a + b + c = 0 and a (respectively, b , c ) has the same eigenvalue distribution as x (respectively, y , z ). A (‘complete’) matricial form of this result is known to imply an affirmative answer to an embedding question formulated by Connes. The critical point in the proof of this result is the production of elements in the intersection of three Schubert varieties. When the factor under consideration is the algebra of n × n complex matrices, our arguments provide new and elementary proofs of the Horn inequalities, which do not require knowledge of the structure of the cohomology of the Grassmann manifolds.

Uma abordagem intervalar para a caracterização de intervalos de disparo em redes de Petri temporais

As redes de Petri temporais são uma das extensões das redes de Petri convencionais para modelagem e análise de sistemas a eventos discretos temporizados. A cada transição da rede é associado um intervalo de tempo, o qual delimita o instante de disparo da transição. A análise das redes de Petri temporais tem sido feita por métodos enumerativos que relacionam todos os estados alcançáveis da rede. Neste artigo, usando recursos da álgebra intervalar e utilizando o conceito de classe de estados, é apresentada uma abordagem para resolver problemas relacionados à caracterização de intervalos de tempo de disparo em redes de Petri temporais. A partir de uma expressão algébrica, desenvolvida para cálculo de intervalos de tempo entre duas classes de estados consecutivas, obtém-se uma equação intervalar que possibilita o cálculo de intervalos de tempo entre duas classes de estados quaisquer. Assim, é possível calcular o intervalo de tempo para ocorrência de uma seqüência de eventos. Utilizando um método de redução da rede, a equação intervalar assume a forma matricial e, com isso, amplia a classe das redes de Petri temporais à qual a equação intervalar é aplicável. Por fim, uma aplicação explorando as potencialidades da equação intervalar no cálculo de medidas características de um sistema a eventos discretos temporizados é apresentada.

Pharmacoscintigraphic evaluation of lipid dry powder budesonide formulations for inhalation

Lung deposition of new formulations of budesonide, using solid lipid microparticles (SLmP) as a pharmaceutically acceptable filler and carrier for inhalation aerosols, and administered from a dry powder inhaler (Cyclohaler ®), were compared with that from Pulmicort ® Turbuhaler ®. Six healthy volunteers took part in a three-way randomized cross-over study, and inhaled a nominal dose of 400 μg budesonide, labelled with 99mTc, on each study day. Lung deposition was determined by gamma scintigraphy and by a pharmacokinetic method. The percentage of dose (SD) in the whole lung was 49.9 (3.7)% for the lipidic matricial form (M) and 62.8 (4.9)% for the lipidic physical blend formulation (PB). These results corresponded well with the in vitro fine particle assessment. In comparison with data recorded in literature for in vivo deposition obtained with Pulmicort ® Turbuhaler ®, it was estimated that lung deposition was 1.5 and 2.0 times higher for the M and PB formulations, respectively. Furthermore, the relative drug availability obtained from the pharmacokinetic evaluation, expressed as the percentage of pulmonary absorption of the comparator product, was 154% and 220% for M and PB, respectively. The results of the present study indicate that pulmonary administration using SLmP gives a prominent and significant increase in budesonide lung deposition.

Matrix-Based FDTD Parallel Algorithm for Big Areas and Its Applications to High-Speed Wireless Communications

A formulation of the finite-difference time-domain (FDTD) equations as a system of linear equations in matricial form is used to develop a novel parallel algorithm that solves the variables of a 2-D FDTD simulation using less memory than required by the common FDTD algorithm, at the cost of some increase in the number of operations. For the sake of speeding-up the simulation of urban channels for personal wireless communications, the geometry of those channels and its relation with a numerical Green's function is used to increase the speed of this algorithm. Simulations are carried out in order to propose a FDTD-based model of urban microcells and their delay profiles, and some comparisons against uniform theory of diffraction based models are discussed. Finally, propagation of time division multiple access and code division multiple access signals of high bit rate in those channels are simulated, and the results allows us to evaluate the effect of multipath interference in high speed wireless communications

Polynomially parameter-dependent Lyapunov functions for robust stability of polytopic systems: an LMI approach

In this note, robust stability of state-space models with respect to real parametric uncertainty is considered. Specifically, a new class of parameter-dependent quadratic Lyapunov functions for establishing stability of a polytope of matrices is introduced, i.e., the homogeneous polynomially parameter-dependent quadratic Lyapunov functions (HPD-QLFs). The choice of this class, which contains parameter-dependent quadratic Lyapunov functions whose dependence on the uncertain parameters is expressed as a polynomial homogeneous form, is motivated by the property that a polytope of matrices is stable if and only there exists an HPD-QLF. The main result of the note is a sufficient condition for determining the sought HPD-QLF, which amounts to solving linear matrix inequalities (LMIs) derived via the complete square matricial representation (CSMR) of homogeneous matricial forms and the Lyapunov matrix equation. Numerical examples are provided to demonstrate the effectiveness of the proposed approach.

Complex Variational Axial Mode Matching Method for Single-Mode and Overmoded Dielectric Resonators

The generalization of the axial mode matching method to calculate electromagnetic properties is here considered for single-mode as well as overmoded (whispering gallery) dielectric resonators having geometric cylindrical symmetry but nondiagonal dielectric permittivity and magnetic permeability. In particular, a compact matricial form of the complex-valued variational constraint governing this configuration is calculated. The reliability of this method is proved numerically by the matching of the Ehrenfest–Boltzmann theorem predictions extended also in the nonperturbative range, and by a filling factor matching test. An experimental measurement is also compared with the results. This method can be applied in new ferromagnetic semiconductors physics that should behave gyroelectromagnetically in opportune experimental conditions.

On the calculation of the multiplicity of a real eigenvalue of Hessenberg matrix

In this article, we describe three algorithms: the first one is used to compute the multiplicity of a real eigenvalue of a Hessenberg matrix A ∈ R n× n in o( n 3); the second for the computation of the determinant of a Hessenberg matrix in o( n 2) and the third for the computation of the multiplicity of a real root of a polynomial in o( n 2). It is a new matricial form and represents generalized Horner scheme.

Contribution to subcellular localization of superoxide dismutase isoforms of spruce needles and oak leaves

Summary The aim of this work was to determine the number and the types of superoxide dismutase (EC 1.15.1.1) from spruce needles and oak leaves as well as to examine their localization at the subcellular level. The obtained results show that spruce needles contain one mitochondrial, matricial Mn-SOD form and four Cu,Zn-SOD isozymes. One of these forms, SOD 4, was located in the chloroplast where it seemed to be bound to the thylakoids. Concerning oak leaves, five SOD forms were detected, all belonging to the Cu,Zn-SOD type. SOD 1 was found in the mitochondria whereas SOD 5 was a chloroplastic, stromatal form.

Use of a matricial form of the T.D.H.F. Equations for the calculation of the hyperpolarisability tensor of a particular model

A particular electronic system is conceived in order to test a method we established previously to solve time-dependent - Hartree-Fock equations. We then calculate the 3 rd order hyperpolarisability tensor of the system, subject to electromagnetic radiation. The result is compared to the one obtained by a variation-perturbation method. This comparison is quite satisfactory.

Shorted operators and the structure of operators with numerical radius one

The theory of the shorted operator is used to prove that if w(T)≤1, then T can be written in the form T=2(I-C*C)1/2C. Using this form, Ando has exhibited a matricial form for a unitary 2-dilation of T.

Sur la theorie quantique des equations de hartree‐fock dependant du temps. III. Déatermination d'un ensemble unique de spin orbitales

AbstractWe modify the matricial form of the TDHF equations we suggested in an earlier article, and impose a further constraint, called unicity constraint, to the equations' solutions. Indeed, this further constraint, combined with the orthonormalization conditions already taken into account, allows the TDHF equations a form accepting only one spin‐orbital set as a solution.