We consider an alloy type potential on an infinite metric graph. We assume a covering condition on the single site potentials. For random Schrödingers operator associated with the alloy type potential restricted to finite volume subgraphs we prove a Wegner estimate which reproduces the modulus of continuity of the single site distribution measure. The Wegner constant is independent of the energy.

Recently Sarkar (DCC 2014) has proposed a new attack on small decryption exponent when RSA Modulus is of the form N = pq for r ≥ 2. This variant is known as Prime Power RSA. The work of Sarkar improves the result of May (PKC 2004) when r ≤ 5. In this paper, we improve the existing results for r = 3, 4. We also study partial key exposure attack on Prime Power RSA. Our result improves the work of...

In this paper, we derive a generalized multiplicative Hardy-LittlewoodPolya type inequality, as well as several related additive inequalities, for functions of operators in Hilbert spaces. In addition, we find the modulus of continuity of a function of an operator on a class of elements defined with the help of another function of the operator. We then apply the results to solve the following p...

We consider the Harnack inequality for harmonic functions with respect to three types of infinite-dimensional operators. For the infinite dimensional Laplacian, we show no Harnack inequality is possible. We also show that the Harnack inequality fails for a large class of Ornstein-Uhlenbeck processes, although functions that are harmonic with respect to these processes do satisfy an a priori mod...

where B is a Gaussian field on [0, 1] × S1 whose behavior in time is that of fractional Brownian motion (fBm) with any parameter H ∈ (0, 1), and whose behavior in space is homogeneous, and can be completely arbitrary within that restriction. By “regularity theory” for a Gaussian field Y we mean a characterization of almostsure modulus of continuity for Y that can be written using information ab...

We prove Gaussian estimates from above of the fundamental solutions to a class of ultraparabolic equations. These estimates are independent of the modulus of continuity of the coefficients and generalize the classical upper bounds by Aronson for uniformly parabolic equations.  2003 Elsevier Science (USA). All rights reserved.

In this paper we study the following modified quasi-geostrophic equation ∂tθ + u · ∇θ + ν|D| θ = 0, u = |D|Rθ with ν > 0 and 0 < α < 1. This equation was firstly introduced by Constantin-Iyer-Wu in [10]. Here, we first prove the local existence result of smooth solutions by using the energy method and the regularization effect of the transport equation with fractional diffusion, and then throug...

This work aims at explaining the syntactical properties of continuous normalization, as introduced in proof theory by Mints, and further studied by Ruckert, Buchholz and Schwichtenberg. In an extension of the untyped coinductive λ-calculus by void constructors (so-called repetition rules), a primitive recursive normalization function is defined. Compared with other formulations of continuous no...

We review several competing chaining methods to estimate the supremum, the diameter of the range or the modulus of continuity of a stochastic process in terms of tail bounds of their two-dimensional distributions. Then we show how they can be applied to obtain upper bounds for the growth of bounded sets under the action of a stochastic flow.

In this paper we give a detailed description of the random wavelet series representation of real-valued linear fractional stable sheet introduced in [3]. By using this representation, in the case where the sample paths are continuous, an anisotropic uniform and quasi-optimal modulus of continuity of these paths is obtained as well as an upper bound for their behavior at infinity and around the ...