We use the biorthogonal multiwavelets related by differentiation constructed in previous work to construct compactly supported biorthogonal multiwavelet bases for the space of vector fields on the upper half plane R+ such that the reconstruction wavelets are divergence-free and have vanishing normal components on the boundary of R+. Such wavelets are suitable to study the Navier–Stokes equation...

Let Tq+1 be the q + 1-regular tree and let G be a group of autormophisms acting transitively on the vertices and on the boundary of Tq+1. We give an upper bound for the growth of cocycles with values in any unitary representation of the group G. This bound is optimal by projecting the Haagerup cocycle onto the subspace of the kernel of the divergence. We also obtain a description of functions c...

We develop the energy norm a-posteriori error analysis of exactly divergence-free discontinuous RTk/Qk Galerkin methods for the incompressible Navier-Stokes equations with small data. We derive upper and local lower bounds for the velocity-pressure error measured in terms of the natural energy norm of the discretization. Numerical examples illustrate the performance of the error estimator withi...

‎In this paper‎, ‎we study the Neumann boundary value problem of a class of nonlinear divergence type diffusion equations‎. ‎By a priori estimates‎, ‎difference and variation techniques‎, ‎we establish the existence and uniqueness of weak solutions of this problem.

In this paper we introduce a nonextensive quantum information theoretic measure which may be defined between any arbitrary number of density matrices, and we analyze its fundamental properties in the spectral graph-theoretic framework. Unlike other entropic measures, the proposed quantum divergence is symmetric, matrix-convex, theoretically upper-bounded, and has the advantage of being generali...

various molecular techniques are available to make differences and to study the genetic divergences among species and populations, of which the most efficient ones are pcr-based markers. one of these methods, molecular fingerprinting, enables the distinction of closely related populations. issr-primers are universal primers that can be used for such studies. the utility of these primers was tes...

This paper presents a numerical analysis for the time-implicit approximation of Boltzmann equation based on moment system in velocity dependence and discontinuous Galerkin finite-element (DGFE) time position dependence. The implicit nature DGFE method provides robust algorithm solutions equation. closure relation systems derives from minimization suitable φ -divergence. We present sufficient co...

Mahalanobis’ D-square (D2) statistics was applied to assess diversity in the 9 genotypes collectedof semi-arid region of India (7 genotypes from Gujarat and Rajasthan for normal toxic and two fromOrissa csmcri’s plantation of non toxic nature. These genotypes were grouped into five. Cluster I andIII had two genotypes, cluster II had three genotypes and cluster VI and V contributed as solitaryge...

We present new excess risk bounds for randomized and deterministic estimators for general unbounded loss functions including log loss and squared loss. Our bounds are expressed in terms of the information complexity and hold under the recently introduced v-central condition, allowing for high-probability bounds, and its weakening, the v-pseudoprobability convexity condition, allowing for bounds...