x T t  . A nontrivial solution of Equation (1) is called oscillatory if it has arbitrarily large zeros, otherwise it is said to be nonoscillatory. Equation (1) is said to be oscillatory if all of it’s nontrivial solutions are oscillatory. Recently, Meng and Xu [6] studied Equation (1) and obtained some sufficient conditions for oscillation of the Equation (1), we list the main results of [6] a...

1. The B.W.K. Method. The B.W.K. procedure1 was discovered in connection with problems of wave mechanics, where Planck's constant h was treated as a very small quantity, and functions could be expanded in series of powers of h. The first terms of the expansion correspond to classical mechanics (completed with some quantum conditions) and higher terms represent typical wave-mechanical effects. O...

A constructive version of a theorem of Thue is used to provide representations of certain integers as x2 −Dy2, where D = 2, 3, 5, 6, 7.

We calculate the low-energy parameter S in QCD, which is also known as L10, and the pion decay constant fπ using inhomogeneous Bethe-Salpeter equation in improved ladder approximation. To extract these quantities we calculate the “V − A” two-point function, ΠV V (q 2) − ΠAA(q 2), in space-like region. We obtain S = 0.43 ∼ 0.48, which is about 30% larger than the experimental value. The calculat...

A nonlinear stochastic integral equation of the Hammerstein type in the form x(t; c) = h(t; co) + f k(t, s; co)f (s, x(s; co)) dy (s) is studied where t E S, a v-finite measure space with certain properties, co E Q, the supporting set of a probability measure space (Q, A, P), and the integral is a Bochner integral. A random solution of the equation is defined to be a second order vector-valued ...

Existence of positive solutions for the nonlinear fractional differential equation Dsu(x) = f (x,u(x)), 0 < s < 1, has been studied (S. Zhang, J. Math. Anal. Appl. 252 (2000) 804–812), where Ds denotes Riemann–Liouville fractional derivative. In the present work we study existence of positive solutions in case of the nonlinear fractional differential equation: L(D)u= f (x,u), u(0)= 0, 0 < x < 1...

We consider the Benjamin-Bona-Mahony (BBM) equation on the one dimensional torus T = R/(2πZ). We prove a Unique Continuation Property (UCP) for small data in H(T) with nonnegative zero means. Next we extend the UCP to certain BBM-like equations, including the equal width wave equation and the KdV-BBM equation. Applications to the stabilization of the above equations are given. In particular, we...

in this research, papaya slices with dimensions of 0.5×2×5 cm3 were dried at 45 °c using a cabinet dryer in which drying air velocity and relative humidity were 0.9 m/s and 30%, respectively. the moisture diffusion coefficient of papaya was determined in this drying condition. mass transfer equation with its boundary conditions was solved based on finite difference method. finally, coefficient ...

in this paper, an iterative method is proposed for solving matrix equation $sum_{j=1}^s a_jx_jb_j = e$. this method is based on the global least squares (gl-lsqr) method for solving the linear system of equations with the multiple right hand sides. for applying the gl-lsqr algorithm to solve the above matrix equation, a new linear operator, its adjoint and a new inner product are dened. it is ...

We study the long-time stability of soliton solutions to the Korteweg-deVries equation. We consider solutions u to the KdV with initial data in Hs, 0 ≤ s < 1, that are initially close in Hs norm to a soliton. We prove that the possible orbital instability of these ground states is at most polynomial in time. This is an analogue to the Hs orbital instability result of [7], and obtains the same m...