cu2o nanoparticles were synthesized by thermal treatment in liquid paraffin without any inert gas protection using nano structures of schiff base copper (ii) complex (1) as precursor. liquid paraffin was used as solvent and reductant. span 80 was applied to control the morphology of cuprous oxide nanoparticles. the nano structure of the complex was characterized by x-ray diffraction measurement...

Theorem 1. 1) Under local changes of the fields u = u(w) the coefficient g(u) in the bracket (2) transforms like a bilinear form (a tensor with upper indices); if det g 6= 0, then the expression b k (u) = gΓ j sk transforms in such a way that the Γjsk are the Christoffel tymbols of a differential-geometric connection. 2) In order that the bracket (2) be skew-symmetric it is necessary and suffic...

Laplace transform is a very powerful mathematical tool applied in various areas of engineering and science. With the increasing complexity of engineering problems, Laplace transforms help in solving complex problems with a very simple approach just like the applications of transfer functions to solve ordinary differential equations. This paper will discuss the applications of Laplace transforms...

In the paper the question is a q-Fourier transform of a q-Gaussian a q ′ -Gaussian (with some q ′ ) up to a constant factor is analyzed for the whole range of q ∈ (−∞, 3). This question is connected with applicability of Fq-transform in the study of limit processes in nonextensive statistical mechanics. We derive some functional-differential equations for the q-Fourier transform of q-Gaussians....

In this section we propose a hybrid Gibbs and variational inference for our differential topic models. The idea is to first lower bound the model likelihood with variational inference [1], so that it is conjugated to the prior, then use a Gibbs style sampler for this bound. In this method we will use the usual Chinese restaurant representation of the PYP so that the combinatorial term ( mikw ti...

The purpose of the present paper is to initiate a systematic study of the relation of the boundary values for hyperbolic-dissipative systems of partial differential equations. We introduce a general framework for explicitly deriving the boundary kernel for the Dirichlet-Neumann map. We first use the Laplace and Fourier transforms, and the stability consideration to derive the Master Relationshi...

Fractional Fourier transforms (FrFT) are a natural one-parameter family of unitary transforms that have the ordinary Fourier transform embedded as a special case. In this paper, following the efforts of several authors, we explore the theory and applications of FrFT, from the standpoints of both quantum mechanics and analysis. These include the phase plane interpretation of FrFT, FrFT’s role in...

W derive an analytical expression for the cumulative distribution function of travel time for a vehicle traversing a freeway link of arbitrary length. The vehicle’s speed is assumed to be modulated by a random environment that can be modeled as a stochastic process. We first present a partial differential equation (PDE) describing the travel time distribution and obtain a solution in terms of L...

In this paper, we propose the use of partial differential equation (PDE) based novel PDE transforms for determining jump discontinuity locations in piecewise smooth data containting potential isolated jump discontinuities. The PDE transform method involves evolving coupled PDEs under different time scales to extract edge information. Multiscale edge detection is done by varying the parameters a...

Abstract. In this paper we consider the Laplace transforms of some random series, in particular, the random series derived as the squared L2 norm of a Gaussian stochastic process. Except for some special cases, closed form expressions for Laplace transforms are, in general, rarely obtained. It is the purpose of this paper to show that for many Gaussian random processes the Laplace transform can...