Search results for "T matrix"
showing 10 items of 39 documents
Fast Distributed Subspace Projection via Graph Filters
2018
A significant number of linear inference problems in wireless sensor networks can be solved by projecting the observed signal onto a given subspace. Decentralized approaches avoid the need for performing such an operation at a central processor, thereby reducing congestion and increasing the robustness and the scalability of the network. Unfortunately, existing decentralized approaches either confine themselves to a reduced family of subspace projection tasks or need an infinite number of iterations to obtain the exact projection. To remedy these limitations, this paper develops a framework for computing a wide class of subspace projections in a decentralized fashion by relying on the notio…
On a matrix group constructed from an {R,s+1,k}-potent matrix
2014
Let R is an element of C-nxn be a {k}-involutory matrix (that is, R-k = I-n) for some integer k >= 2, and let s be a nonnegative integer. A matrix A is an element of C-nxn is called an {R,s + 1, k}-potent matrix if A satisfies RA = A(s+1)R. In this paper, a matrix group corresponding to a fixed {R,s + 1, k}-potent matrix is explicitly constructed, and properties of this group are derived and investigated. This group is then reconciled with the classical matrix group G(A) that is associated with a generalized group invertible matrix A.
Diffusion processes involving multiple conserved charges: a first study from kinetic theory and implications to the fluid-dynamical modeling of heavy…
2020
The bulk nuclear matter produced in heavy ion collisions carries a multitude of conserved quantum numbers: electric charge, baryon number, and strangeness. Therefore, the diffusion processes associated to these conserved charges cannot occur independently and must be described in terms of a set of coupled diffusion equations. This physics is implemented by replacing the traditional diffusion coefficients for each conserved charge by a diffusion coefficient matrix, which quantifies the coupling between the conserved quantum numbers. The diagonal coefficients of this matrix are the usual charge diffusion coefficients, while the off-diagonal entries describe the diffusive coupling of the charg…
Universal formulas for characteristic classes on the Hilbert schemes of points on surfaces
2007
This article can be seen as a sequel to the first author's article ``Chern classes of the tangent bundle on the Hilbert scheme of points on the affine plane'', where he calculates the total Chern class of the Hilbert schemes of points on the affine plane by proving a result on the existence of certain universal formulas expressing characteristic classes on the Hilbert schemes in term of Nakajima's creation operators. The purpose of this work is (at least) two-fold. First of all, we clarify the notion of ``universality'' of certain formulas about the cohomology of the Hilbert schemes by defining a universal algebra of creation operators. This helps us to reformulate and extend a lot of the f…
Characterizations of {K,s+1}-Potent Matrices and Applications
2012
Recently, situations where a matrix coincides with some of its powers have been studied. This kind of matrices is related to the generalized inverse matrices. On the other hand, it is possible to introduce another class of matrices that involve an involutory matrix, generalizing the well-known idempotent matrix, widely useful in many applications. In this paper, we introduce a new kind of matrices called {K,s+1}-potent, as an extension of the aforementioned ones. First, different properties of {K,s+1}-potent matrices have been developed. Later, the main result developed in this paper is the characterization of this kind of matrices from a spectral point of view, in terms of powers of the ma…
Everywhere differentiability of viscosity solutions to a class of Aronsson's equations
2017
For any open set $\Omega\subset\mathbb R^n$ and $n\ge 2$, we establish everywhere differentiability of viscosity solutions to the Aronsson equation $$ =0 \quad \rm in\ \ \Omega, $$ where $H$ is given by $$H(x,\,p)==\sum_{i,\,j=1}^na^{ij}(x)p_i p_j,\ x\in\Omega, \ p\in\mathbb R^n, $$ and $A=(a^{ij}(x))\in C^{1,1}(\bar\Omega,\mathbb R^{n\times n})$ is uniformly elliptic. This extends an earlier theorem by Evans and Smart \cite{es11a} on infinity harmonic functions.
Fast Decentralized Linear Functions via Successive Graph Shift Operators
2019
Decentralized signal processing performs learning tasks on data distributed over a multi-node network which can be represented by a graph. Implementing linear transformations emerges as a key task in a number of applications of decentralized signal processing. Recently, some decentralized methods have been proposed to accomplish that task by leveraging the notion of graph shift operator, which captures the local structure of the graph. However, existing approaches have some drawbacks such as considering special instances of linear transformations, or reducing the family of transformations by assuming that a shift matrix is given such that a subset of its eigenvectors spans the subspace of i…
Functional Differential and Difference Equations with Applications
2012
and Applied Analysis 3 solutions to a class of nonlocal boundary value problems for linear homogeneous secondorder functional differential equations with piecewise constant arguments are obtained. The last but not the least, this issue features a number of publications that report recent progress in the analysis of problems arising in various applications. In particular, dynamics of delayed neural network models consisting of two neurons with inertial coupling were studied, properties of a stochastic delay logistic model under regime switching were explored, and analysis of the permanence and extinction of a single species with contraception and feedback controls was conducted. Other applie…
Diagonalization of large matrices: a new parallel algorithm.
2015
On the basis of a dressed matrices formalism, a new algorithm has been devised for obtaining the lowest eigenvalue and the corresponding eigenvector of large real symmetric matrices. Given an N × N matrix, the proposed algorithm consists in the diagonalization of (N - 1)2 × 2 dressed matrices. Both sequential and parallel versions of the proposed algorithm have been implemented. Tests have been performed on a Hilbert matrix, and the results show that this algorithm is up 340 times faster than the corresponding LAPACK routine for N = 10(4) and about 10% faster than the Davidson method. The parallel MPI version has been tested using up to 512 nodes. The speed-up for a N = 10(6) matrix is fair…
On Mathematical Modelling of Metals Distribution in Peat Layers
2014
In this paper we consider averaging and finite difference methods for solving the 3-D boundary-value problem in multilayered domain. We consider the metals Fe and Ca concentration in the layered peat blocks. Using experimental data the mathematical model for calculation of concentration of metals in different points in peat layers is developed. A specific feature of these problems is that it is necessary to solve the 3-D boundary-value problems for elliptic type partial differential equations (PDEs) of second order with piece-wise diffusion coefficients in the layered domain. We develop here a finite-difference method for solving of a problem of one, two and three peat blocks with periodica…