The aim of this paper is to consider the optimal, from the viewpoint of a state estimation accuracy, measurement location problem in linear distributed-parameter systems with white Gaussian noises. In contrary to earlier works the proposed approach consists of two steps. Namely, to find closed form solution for the optimal measurement weighting function (MWF), assuming measurements continuous i...

We study an implicit inhomogeneous linear differential-difference equation in the module of formal generalized functions over a commutative ring. prove well-posedness and find fundamental solution. obtain representation unique solution to form convolution given function. also consider second order differential arbitrary

We develop a green light source with low spatial coherence via intracavity frequency doubling of a solid-state degenerate laser. The second-harmonic emission supports many more transverse modes than the fundamental emission, and exhibits lower spatial coherence. A strong suppression of speckle formation is demonstrated for both fundamental and second-harmonic beams. Using the green emission for...

Effective techniques to reduce graphene oxide are in demand owing to the multitude of potential applications of this two-dimensional material. A very promising green method to do so is by exposure to ultraviolet irradiation. Unfortunately, the dynamics behind this reduction remain unclear. Here we perform a series of transient absorption experiments in an effort to develop and understand this p...

in this paper, based on sinh-cosh method and sinh-gordon expansion method,families of solutions of (2+1)-dimensional breaking soliton equation are obtained.these solutions include jacobi elliptic function solution, soliton solution,trigonometric function solution.

We present the first numerical approximation of the scalar Schwarzschild Green function in the time domain, which reveals several universal features of wave propagation in black hole spacetimes. We demonstrate the trapping of energy near the photon sphere and confirm its exponential decay. The trapped wavefront passes through caustics resulting in echoes that propagate to infinity. The arrival ...

In this paper, the meshless integral method based on the regularized boundary integral equation [1] has been extended to analyze the large deformation of elastoplastic materials. The updated Lagrangian governing integral equation is obtained from the weak form of elastoplasticity based on Green-Naghdi’s theory over a local sub-domain, and the moving least-squares approximation is used for meshl...

In this research, firms aim at maximizing two purposes of social welfare (environment) and profitability in the supply chain system. It is assumed that there are two supply chains, a green and an ordinary, each consists of a manufacturer and a supplier; in which the manufacturer generates profit through franchises. The green and the ordinary manufacturers form a cartel on the market of a certai...