We exhibit sharp upper bounds for the probability distribution of the distance from a system of multivariate polynomial equations to the strata of all systems having a critical zero of given corank. We also prove sharp upper bounds for the probability distribution of the condition number of singular systems of multivariate polynomial equations. We finally state a new and sharp technique of the ...

In this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. We utilize spectral-collocation method combining with a product integration technique in order to discretize the terms involving spatial fractional order derivatives that leads to a simple evaluation of the related terms. By using Bernstein polynomial basis, the problem is transformed in...

The work aims at investigating the techno-economic performance of a biodiesel micro combined heat and power (CHP) system for residential applications. CHP unit is based on direct-injection compression ignition engine providing 6.7 kWel 11.3 kWth. A 0D model developed validated to characterise behaviour biodiesel-fired full partial load in terms efficiency, fuel consumption, emissions. Furthermo...

Daniel Abramovitch Hewlett-Packard Laboratories 1501 Page Mill Road, M/S 2U-10 Palo Alto, CA 94304 Abstract– This paper describes the PES Pareto Method, a useful tool for identifying and eliminating key contributors to uncertainty in the Position Error Signal (PES) of a magnetic disk drive[1, 2, 3]. Once identified and ranked according to their overall effect on PES, the top–ranking sources can...

Complete discrimination system for polynomial and direct integral method were discussed systematically. In particularly, we pointed out some mistaken viewpoints. Combining with complete discrimination system for polynomial, direct integral method was developed to become a powerful method and was applied to a lot of nonlinear mathematical physics equations. All single traveling wave solutions to...

We consider real trigonometric polynomial Bernoulli equations of the form A(θ)y′=B1(θ)+Bn(θ)yn where n≥2, with A,B1,Bn being polynomials degree at most μ≥1 in variables θ and Bn(θ)≢0. also A(θ)yn−1y′=B0(θ)+Bn(θ)yn A,B0,Bn variable For first equation, we show that when n≥4, it has 3 solutions n is even 5 odd. second n≥3, odd even. provide two types mentioned above maximum number achieved. The pr...

Abstract— A new polynomial method to solve Volterra–Fredholm Integral equations is presented in this work. The method is based upon Shifted Legendre Polynomials. The properties of Shifted Legendre Polynomials and together with Gaussian integration formula are presented and are utilized to reduce the computation of Volterra–Fredholm Integral equations to a system of algebraic equations. Some num...