The well-studied methods of current source density analysis use the Laplacian transform to identify locations and relative magnitudes of current sources and sinks. The method is typically used in reduced one-dimensional form for electrophysiological measures, due to technical limitations. The present paper outlines a two-dimensional method in which simultaneous samples are recorded from multipl...

We introduce a curvature function for planar graphs to study the connection of curvature and geometric and spectral properties of the graph. We show that non-positive curvature implies that the graph is infinite, locally similar to a tessellation and admits no cut locus. For negative curvature we prove empty interior of minimal bigons and explicit bounds for the growth of distance balls and Che...

In this paper, we construct a new model based on the coupling of thermoelasticity, plasma, and microelongation effect under volumetric absorption laser pulse. Three different thermoelasticity theories are applied to in 2D thermoelastic semiconducting medium whose properties temperature-dependent. The surface is exposed radiation having spatial temporal Gaussian distributions; addition, consider...

Alternative specifications of univariate asymmetric Laplace models are described and investigated. A more general mixture model is then introduced. Bivariate extensions of these models are discussed in some detail, with particular emphasis on associated parameter estimation strategies. Multivariate versions of the models are briefly introduced.

1. L. Fejer, Neue Eigenschaften der Mittelwerte bei den Fourierreihen, J. London Math. Soc. vol. 8 (1933) pp. 53-62. 2. M. S. Robertson, On the coefficients of a typically-real function, Bull. Amer. Math. Soc. vol. 41 (1935) pp. 565-572. 3. W. Rogosinski, Uber positive harmonische Enlwicklungen und typischreelle Potenzreihen, Math. Z. vol. 35 (1932) pp. 93-121. 4. W. T. Scott and H. S. Wall, Th...

Given a divergence operator δ on a probability space such that the law of δ(h) is infinitely divisible with characteristic exponent h 7→ − 2 ∫ ∞ 0 htdt, or ∫ ∞ 0 (e − ih(t)− 1)dt, h ∈ L(R+), (0.1) we derive a family of Laplace transform identities for the derivative ∂E[eλδ(u)]/∂λ when u is a non-necessarily adapted process. These expressions are based on intrinsic geometric tools such as the Ca...

So-called sparse estimators arise in the context of model fitting, when one a priori assumes that only a few (unknown) model parameters deviate from zero. Sparsity constraints can be useful when the estimation problem is under-determined, i.e. when number of model parameters is much higher than the number of data points. Typically, such constraints are enforced by minimizing the L1 norm, which ...

We develop the theory of transient electrophoresis a weakly charged, infinitely long cylindrical colloidal particle under an application transverse or tangential step electric field. Transient electrophoretic mobility approaches steady with time. derive closed-form expressions for cylinder without involving numerical inverse Laplace transformations and corresponding time-dependent Henry functio...

It is well known that the Green function of the standard discrete Laplacian on l2(Zd), ∆stψ(n) = (2d) −1 ∑ |n−m|=1 ψ(m), exhibits a pathological behavior in dimension d ≥ 3. In particular, the estimate 〈δ0|(∆st − E − i0)δn〉 = O(|n|− d−1 2 ) fails for 0 < |E| < 1 − 2/d. This fact complicates the study of the scattering theory of discrete Schrödinger operators. Molchanov and Vainberg suggested th...

This paper is concerned with the asymptotic behavior of the trav-eling wave fronts in Lotka-Volterra competition system. By Laplacian transform, we prove that the traveling wave fronts of the system grow exponentially when the traveling coordinate tends to negative infinity.