In this paper we shall characterize Sobolev spaces of an arbitrary order of smoothness using nonstationary tight wavelet frames for L2(R). In particular, we show that a Sobolev space of an arbitrary fixed order of smoothness can be characterized in terms of the weighted `2-norm of the analysis wavelet coefficient sequences using a fixed compactly supported nonstationary tight wavelet frame in L...

for arbitrary time t and arbitrary λ > 0, where ψ is a smooth bump function supported in [−2, 2] if λ < 1 and supported in [1, 2] if λ ≥ 1. This generalizes previous results in [MT]. We also prove pointwise estimates for the gradient of these convolution kernels. As a corollary, we reprove basic multiplier estimates from [HS] and [V1] and derive Sobolev estimates for the solutions to the wave e...

This paper deals with free vibration analysis of thick Laminated curved panels with finite length, based on the three-dimensional elasticity theory. Because of using two-dimensional generalized differential quadrature method, the present approach makes possible vibration analysis of cylindrical panels with two opposite axial edges simply supported and arbitrary boundary conditions including Fre...

Permutation is widely used in cryptographic algorithms. However, it is not well-supported in existing instruction sets. In this paper, two instructions, PPERM3R and GRP, are proposed for efficient software implementation of arbitrary permutations. The PPERM3R instruction can be used for dynamically specified permutations; the GRP instruction can be used to do arbitrary n-bit permutations with u...

We prove some new evaluations for multiple polylogarithms of arbitrary depth. The simplest of our results is a multiple zeta evaluation one order of complexity beyond the well-known Broadhurst-Zagier formula. Other results we provide settle three of the remaining outstanding conjectures of Borwein, Bradley, and Broadhurst [4]. A complete treatment of a certain arbitrary depth class of periodic ...

We provide several machine-independent characterizations of deterministic complexity classes in the model of computation proposed by L. Blum, M. Shub and S. Smale. We provide a characterization of partial recursive functions over any arbitrary structure. We show that polynomial time over an arbitrary structure can be characterized in terms of ∗These authors has been supported City University of...