Displaying similar documents to “Nonnegative definite hermitian matrices with increasing principal minors”

A note on majorization transforms and Ryser’s algorithm

Geir Dahl (2013)

Special Matrices

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The notion of a transfer (or T -transform) is central in the theory of majorization. For instance, it lies behind the characterization of majorization in terms of doubly stochastic matrices. We introduce a new type of majorization transfer called L-transforms and prove some of its properties. Moreover, we discuss how L-transforms give a new perspective on Ryser’s algorithm for constructing (0; 1)-matrices with given row and column sums.

Factorizable matrices

Miroslav Fiedler, Frank J. Hall (2013)

Special Matrices

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We study square matrices which are products of simpler factors with the property that any ordering of the factors yields a matrix cospectral with the given matrix. The results generalize those obtained previously by the authors.

An approach based on matrix polynomials for linear systems of partial differential equations

N. Shayanfar, M. Hadizadeh (2013)

Special Matrices

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In this paper, an approach based on matrix polynomials is introduced for solving linear systems of partial differential equations. The main feature of the proposed method is the computation of the Smith canonical form of the assigned matrix polynomial to the linear system of PDEs, which leads to a reduced system. It will be shown that the reduced one is an independent system of PDEs having only one unknown in each equation. A comparison of the results for several test problems reveals...

Fractional Maximal Functions in Metric Measure Spaces

Toni Heikkinen, Juha Lehrbäck, Juho Nuutinen, Heli Tuominen (2013)

Analysis and Geometry in Metric Spaces

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We study the mapping properties of fractional maximal operators in Sobolev and Campanato spaces in metric measure spaces. We show that, under certain restrictions on the underlying metric measure space, fractional maximal operators improve the Sobolev regularity of functions and map functions in Campanato spaces to Hölder continuous functions. We also give an example of a space where fractional maximal function of a Lipschitz function fails to be continuous.

A numerically efficient approach to the modelling of double-Qdot channels

A. Shamloo, A.P. Sowa (2013)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

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We consider the electronic properties of a system consisting of two quantum dots in physical proximity, which we will refer to as the double-Qdot. Double-Qdots are attractive in light of their potential application to spin-based quantum computing and other electronic applications, e.g. as specialized sensors. Our main goal is to derive the essential properties of the double-Qdot from a model that is rigorous yet numerically tractable, and largely circumvents the complexities of an ab...

Quantum optimal control using the adjoint method

Alfio Borzì (2012)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

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Control of quantum systems is central in a variety of present and perspective applications ranging from quantum optics and quantum chemistry to semiconductor nanostructures, including the emerging fields of quantum computation and quantum communication. In this paper, a review of recent developments in the field of optimal control of quantum systems is given with a focus on adjoint methods and their numerical implementation. In addition, the issues of exact controllability and optimal...

On certain transformations of Archimedean copulas: Application to the non-parametric estimation of their generators

Elena Di Bernardino, Didier Rullière (2013)

Dependence Modeling

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We study the impact of certain transformations within the class of Archimedean copulas. We give some admissibility conditions for these transformations, and define some equivalence classes for both transformations and generators of Archimedean copulas. We extend the r-fold composition of the diagonal section of a copula, from r ∈ N to r ∈ R. This extension, coupled with results on equivalence classes, gives us new expressions of transformations and generators. Estimators deriving directly...

Fully implicit ADI schemes for solving the nonlinear Poisson-Boltzmann equation

Weihua Geng, Shan Zhao (2013)

Molecular Based Mathematical Biology

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The Poisson-Boltzmann (PB) model is an effective approach for the electrostatics analysis of solvated biomolecules. The nonlinearity associated with the PB equation is critical when the underlying electrostatic potential is strong, but is extremely difficult to solve numerically. In this paper, we construct two operator splitting alternating direction implicit (ADI) schemes to efficiently and stably solve the nonlinear PB equation in a pseudo-transient continuation approach. The operator...

On the derivation and mathematical analysis of some quantum–mechanical models accounting for Fokker–Planck type dissipation: Phase space, Schrödinger and hydrodynamic descriptions

José Luis López, Jesús Montejo–Gámez (2013)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

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This paper is intended to provide the reader with a review of the authors’ latest results dealing with the modeling of quantum dissipation/diffusion effects at the level of Schrödinger systems, in connection with the corresponding phase space and fluid formulations of such kind of phenomena, especially in what concerns the role of the Fokker–Planck mechanism in the description of open quantum systems and the macroscopic dynamics associated with some viscous hydrodynamic models of Euler...

An inverse problem for adhesive contact and non-direct evaluation of material properties for nanomechanics applications

F.M. Borodich, B.A. Galanov, S.N. Gorb, M.Y. Prostov, Y.I. Prostov, M.M. Suarez-Alvarez (2012)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

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We show how the values of the effective elastic modulus of contacting solids and the work of adhesion, that are the crucial material parameters for application of theories of adhesive contact to nanomechanics, may be quantified from a single test using a non-direct approach (the Borodich-Galanov (BG) method). Usually these characteristics are not determined from the same test, e.g. often sharp pyramidal indenters are used to determine the elastic modulus from a nanoindentation test,...

Dimension Distortion by Sobolev Mappings in Foliated Metric Spaces

Zoltán M. Balogh, Jeremy T. Tyson, Kevin Wildrick (2013)

Analysis and Geometry in Metric Spaces

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We quantify the extent to which a supercritical Sobolev mapping can increase the dimension of subsets of its domain, in the setting of metric measure spaces supporting a Poincaré inequality. We show that the set of mappings that distort the dimensions of sets by the maximum possible amount is a prevalent subset of the relevant function space. For foliations of a metric space X defined by a David–Semmes regular mapping Π : X → W, we quantitatively estimate, in terms of Hausdorff dimension...