Results 1 - 10 of 894
Results 1 - 10 of 894. Search took: 0.023 seconds
|Sort by: date | relevance|
[en] The ensemble of antagonistic matrices is introduced and studied. In antagonistic matrices the entries and are real and have opposite signs, or are both zero, and the diagonal is zero. This generalization of antisymmetric matrices is suggested by the linearized dynamics of competitive species in ecology. (paper)
[en] Decomposition of unipotents gives short polynomial expressions of the conjugates of elementary generators as products of elementaries. It turns out that with some minor twist the decomposition of unipotents can be read backwards to give very short polynomial expressions of the elementary generators themselves in terms of elementary conjugates of an arbitrary matrix and its inverse. For absolute elementary subgroups of classical groups this was recently observed by Raimund Preusser. I discuss various generalizations of these results for exceptional groups, specifically those of types E6 and E7, and also mention further possible generalizations and applications.
[en] The kinematics of an inelastic solid established in terms of Laplace stretch and its rate are decomposed into one stretch that describes an elastic response, another stretch that describes an inelastic response, and their rates. These kinematics are a direct consequence of Laplace stretch belonging to the group of all real, , upper-triangular matrices with positive diagonal elements. The Laplace stretch follows from a Gram–Schmidt decomposition of the deformation gradient.
[en] We show that if a set of four mutually unbiased bases (MUBs) in exists and contains the identity, then any other basis in the set contains at most two product states and at the same time has Schmidt rank at least three. Here both the product states and the Schmidt rank are defined over the bipartite space . We also investigate the connection of the Sinkhorn normal form of unitary matrices to the fact that there is at least one vector unbiased to any two orthonormal bases in any dimension. (paper)
[en] In a low energy approximation of the massless Yukawa theory (Nelson model) we derive a Faddeev–Kulish type formula for the scattering matrix of N electrons and reformulate it in LSZ terms. To this end, we perform a decomposition of the infrared finite Dollard modifier into clouds of real and virtual photons, whose infrared divergencies mutually cancel. We point out that in the original work of Faddeev and Kulish the clouds of real photons are omitted, and consequently their wave-operators are ill-defined on the Fock space of free electrons. To support our observations, we compare our final LSZ expression for with a rigorous non-perturbative construction due to Pizzo. While our discussion contains some heuristic steps, they can be formulated as clear-cut mathematical conjectures.
[en] Highlights: • Very high-order spatial discretisations in electrochemical simulations are tested. • Asymmetric 4-to7-point approximations enable to use grids with less than 15 points. • Brute force resolution of the resulting problem is competitive in all cases studied. • Comparison between LU and QR decompositions and sparse matrix methods is performed. • Easy-to-implement, C++ example programs are provided. The use of very high order spatial discretisation in digital simulation of electrochemical experiments is assessed, considering up to asymmetric 8-point approximations for the derivatives. A wide range of conditions are examined, including several mechanisms and electrodes and potential-step and potential-sweep experiments. In all cases it is found that asymmetric multi-point approximations in combination with exponentially expanding grids provides very accurate results and with very reduced number of grid points (<15). Consequently, the direct (‘brute force’) resolution of the finite-difference equation system by standard matrix techniques becomes a competitive and more general alternative to specialised methods like the Thomas algorithm.
[en] Using an approach proposed by Lunin in 1989, upper bounds are found for the norms of large submatrices of a fixed -matrix which defines an operator from into with unit norm. Bibliography: 15 titles.
[en] An inclusion of purely dilatational eigenstrain in an infinitely extended isotropic elastic matrix, independently of its shape, causes a deviatoric stress field around it. The present paper analyses the energy and volume changes due to the formation of a circular inhomogeneity in a deviatoric stress field coming from a circular inclusion of dilatational eigenstrain. It is found that the elastic stress inside the inhomogeneity remains deviatoric and the inhomogeneity formation does not change the volume of the inclusion-matrix system; it is argued that the same occurs for any inclusion shape and non-uniform eigenstrain. The elastic energy changes occurring in the domains occupied by matrix, inhomogeneity, and inclusion are calculated, and its dependence on the elastic properties and geometrical parameters of inhomogeneity and matrix is numerically investigated. Strengthening effects of the matrix-inhomogeneity system are examined by means of the energy force and expanding moment acting on the inhomogeneity.
[en] Highlights: • The amplitude–frequency response is presented by the multiple scale method. • The gap between negative and positive bifurcation points can be enhanced by parametric load. • The nonlocal continuum theory can present a more proper model. In the present work, the nonlinear vibration of a carbon nanotube which is subjected to the external parametric excitation is studied. By the nonlocal continuum theory and nonlinear von Kármán beam theory, the governing equation of the carbon nanotube is derived with the consideration of the large deformation. The principle parametric resonance of the nanotube is discussed and the approximation explicit solution is presented by the multiple scale method. Numerical calculations are performed. It can be observed that when the mode number is 1, the stable region can be significantly changed by the parametric excitation, length-to-diameter ratio and matrix stiffness. This phenomenon becomes different to appear if the mode number increases. Moreover, the small scale effects have great influences on the positive bifurcation point for the short carbon nanotube, and the nonlocal continuum theory can present the proper model.
[en] We complete the understanding of the question of the essential self-adjoitness and non-essential self-adjointness of the discrete Laplacian acting on 1-forms. We also discuss the notion of completeness. Moreover, we study the relationship between the adjacency matrix of the line graph and the discrete Laplacian acting on 1-forms. Thanks to it, we exhibit a condition that ensures that the adjacency matrix on line graph is bounded from below and not essentially self-adjoint.