We consider the broken ray transform on Riemann surfaces in the presence of an obstacle. If the surface has nonpositive curvature and the obstacle is strictly convex, we show that a function is determined by its integrals over broken geodesic rays that reflect on the boundary of the obstacle. Our proof is based on a Pestov identity with boundary terms, and it involves Jacobi fields on broken ra...

We determine the trace function representation, or equivalently, the Fourier spectral sequences of binary Jacobi sequences of period pq, where p and q are two distinct odd primes. This includes the twin-prime sequences of period p(p + 2) whenever both p and p + 2 are primes, corresponding to cyclic Hadamard difference sets. c © 2008 Elsevier B.V. All rights reserved.

Let G (α,β) λ be the eigenfunctions of the Dunkl–Cherednik operator T on R. In this paper we express the product G (α,β) λ (x)G (α,β) λ (y) as an integral in terms of G (α,β) λ (z) with an explicit kernel. In general this kernel is not positive. Furthermore, by taking the so–called rational limit, we recover the product formula of M. Rösler for the Dunkl kernel. We then define and study a convo...

The aim of this paper is to prove new uncertainty principles for an integral operator T with a bounded kernel for which there is a Plancherel theorem. The first of these results is an extension of Faris’s local uncertainty principle which states that if a nonzero function f ∈ L(R, μ) is highly localized near a single point then T (f) cannot be concentrated in a set of finite measure. The second...

The one-dimensional Dunkl operator Dk with a non-negative parameter k, is considered under an arbitrary nonlocal boundary value condition. The right inverse operator of Dk, satisfying this condition is studied. An operational calculus of Mikusiński type is developed. In the frames of this operational calculi an extension of the Heaviside algorithm for solution of nonlocal Cauchy boundary value ...

A stochastic Ramsey model is studied with the Cobb-Douglas production function maximizing the expected discounted utility of consumption. We transformed the Hamilton-Jacobi-Bellman (HJB) equation associated with the stochastic Ramsey model so as to transform the dimension of the state space by changing the variables. By the viscosity solution method, we established the existence of viscosity so...

Mammography is the only effective and viable technique to detect breast cancer especially in the case of minimal tumors. About 30% to 50% of breast cancers demonstrate deposits of calcium called micro calcifications. Our method proposes an approach for detecting microcalcification in mammograms based on combined feature set with Support Vector Machine (SVM) classifier. The diagonal matrix ̳S‘ o...

The discrete Laguerre transform (DLT) belongs to the family of unitary transforms known as Gauss-Jacobi transforms. Using classical methodology, the DLT is derived from the orthonormal set of Laguerre functions. By examining the basis vectors of the transform matrix, the types of signals that can be best represented by the DLT are determined. Simulation results are used to compare the DLT's e e...