Emission of compressional acoustic waves at the second harmonic frequency (second harmonic generation, SHG) is possible from rough surfaces undergoing oscillatory shear in liquids. This nonlinear response is a consequence of the inertial term in the Navier-Stokes equation. On a corrugated surface, the streamlines of the sheared liquid are not strictly parallel to the surface, leading to variati...

In this paper, a numerical method based on the hybrid of the quasilinearization method (QLM) and the collocation method is suggested for solving wellknown nonlinear Lane-Emden-type equations as singular initial value problems, which model many phenomena in mathematical physics and astrophysics. First, by using the QLM method, the nonlinear ordinary differential equation is converted into a sequ...

Based on congruences mod p and on properties of Bernoulli polynomials and Bernoulli numbers, several conditions are derived for x, k > 2 to satisfy the Diophantine equation 1k + 2k H-\(x 1 )* = xk . It is proved that ord2(x 3) = orà2k + 3 and that x cannot be divisible by any regular prime. Furthermore, by using the results of experiments with the above conditions on an SGI workstation it is pr...

Let p be a fixed odd prime number. Throughout this paper, Zp, Qp, and Cp will denote the ring of p-adic rational integers, the field of p-adic rational numbers, and the completion of algebraic closure of Qp, respectively. The p-adic norm is normalized so that |p|p 1/p. Let N be the set of natural numbers and Z N ∪ {0}. Let UD Zp be the space of uniformly differentiable functions on Zp. For f ∈ ...

We exploit the fact that the classical Bernoulli systems are con-tractive iterated function systems (IFS) of affine type to prove a number of properties of the infinite Bernoulli convolution measures ν λ. We develop and use a new duality notion for affine IFSs. This duality is based on a natural transfer operator R W , and on an associated random walk process Px. We show that the absolute-squar...

We study the corrector equation in stochastic homogenization for a simplified Bernoulli percolation model on Z, d > 2. The model is obtained from the classical {0, 1}-Bernoulli bond percolation by conditioning all bonds parallel to the first coordinate direction to be open. As a main result we prove (in fact for a slightly more general model) that stationary correctors exist and that all finite...

Let F be a C3 diffeomorphism on a Banach space B. F has a homoclinic tube asymptotic to an invariant manifold. Around the homoclinic tube, Bernoulli shift dynamics of submanifolds is established through shadowing lemma. This work removes an uncheckable condition of Silnikov [Equation (11), page 625 of L. P. Silnikov, Soviet Math. Dokl., vol.9, no.3, (1968), 624628]. Also, the result of Silnikov...

We obtain some well-known expansions for the Lerch transcendent and the Hurwitz zeta function using elementary Fourier analytic methods. These Fourier series can be used to analytically continue the functions and prove the classical functional equations, which arise from the relations satisfied by the Fourier conjugate and flat Fourier series. In particular, the functional equation for the Riem...

We exploit the fact that the classical Bernoulli systems are con-tractive iterated function systems (IFS) of affine type to prove a number of properties of the infinite Bernoulli convolution measures ν λ. We develop and use a new duality notion for affine IFSs. This duality is based on a natural transfer operator R W , and on an associated random walk process Px. We show that the absolute-squar...

Abstract. In this paper, we set up the dynamic frictionless Euler Bernoulli equation with Signorini contact conditions along the length of a thin beam and consider how to solve this equation. The existence of solutions is shown, based on a penalty method. Using energy conservation in the penalty method, we bound the integral of contact forces over time and space. Hölder continuity of the fundam...