This paper presents a connection between qualitative matrix theory and linear complementarity problems (LCPs). An LCP is said to be sign-solvable if the set of the sign patterns of the solutions is uniquely determined by the sign patterns of the given coefficients. We provide a characterization for sign-solvable LCPs such that the coefficient matrix has nonzero diagonals, which can be tested in...

Lieb and Seiringer stated in their reformulation of the BessisMoussa-Villani conjecture that all coefficients of the polynomial p(t) = tr[(A+ B)] are nonnegative whenever A and B are any two positive semidefinite matrices of the same size. We will show that for all m ∈ N the coefficient of t in p(t) is nonnegative, using a connection to sums of Hermitian squares of non-commutative polynomials w...

We define a cotriple (co)homology of crossed modules with coefficients in a π1-module. We prove its general properties, including the connection with the existing cotriple theories on crossed modules. We establish the relationship with the (co)homology of the classifying space of a crossed module and with the cohomology of groups with operators. An example and an application are given.

We establish a connection between (degenerate) nonsymmetric Macdonald polynomials and standard bases and dual standard bases of maximal parabolic modules of affine Hecke algebras. Along the way we prove a (weak) polynomiality result for coefficients of symmetric and nonsymmetric Macdonald polynomials.

We study some problems of the parameter inference which are in connection with wide sense stationary long memory processes. Here we present the asymptotic behaviour of the corelation matrix and the limit distributions of the LSE for the regression coefficients in some types of linear models with singular Gaussian and non-Gaussian errors.

We present some results on the mathematical analysis of kinetic equations for modelling transport processes in semiconductors. We focus our attention on the connection between the kinetic models and the fluids ones based on driftdiffusion or hydrodynamic equations. Asymptotic analysis gives hydrodynamic coefficients in, terms of microscopic quantities and allows to derive accurate boundary cond...

Abstract: The moment-rotation model is the main study of semi-rigid connection, moreover, the sensitivity coefficients of parameters on semi-rigid connection are the precondition of a moment-rotation model. There are two issues in the current research: the defective models would be obtained without considering the correlation among the parameters of the structure; for the higher precision sensi...

We first study some properties of images of commuting differential operators of polynomial algebras of order one with constant leading coefficients. We then propose what we call the image conjecture on these differential operators and show that the Jacobian conjecture [BCW], [E] (hence also the Dixmier conjecture [D]) and the vanishing conjecture [Z3] of differential operators with constant coe...

Isothermal mutual diffusion coefficients (D) have been measured for binary aqueous solutions of sodium alkylsulfonates at 25 degrees C. The diffusion coefficient values drop as the concentration of micelles in the system increases. As the length of the hydrocarbon chain increases, the observed drop in D becomes increasingly sharp and shifts to lower concentrations. When the micellization proces...

Pseudodifferential operators are formal Laurent series in the formal inverse ∂−1 of the derivative operator ∂ whose coefficients are holomorphic functions. Given a pseudodifferential operator, the corresponding formal power series can be obtained by using some constant multiples of its coefficients. The space of pseudodifferential operators is a noncommutative algebra over C and therefore has a...