The purpose of this paper is to investigate the properties spectral and tiling subsets cyclic groups, with an eye towards set conjecture in one dimension, which states that a bounded measurable subset $\mathbb{R}$ accepts orthogonal basis exponentials if only it tiles by translations. This strongly connected its discrete counterpart, namely every finite group, tile. tools presented herein are r...

The problem of searching a polygonal region for an unpredictably moving intruder by a set of stationary guards, each carrying an orientable laser, is known as the Searchlight Scheduling Problem. Determining the computational complexity of deciding if the polygon can be searched by a given set of guards is a long-standing open problem. Here we propose a generalization called the Partial Searchli...

Light transport in a strongly scattering, strongly anisotropic material is studied experimentally using both static and time-resolved techniques. Both the static and the dynamic results are well characterized by a diffusion equation with an anisotropic diffusion tensor and a scalar absorption term. Light diffuses 4.0 times faster along the uniaxial axis of the material compared with diffusion i...

Orthogonal metric space is a considerable generalization of usual obtained by establishing perpendicular relation on set. Very recently, the notions orthogonality set and are described notable fixed point theorems given in orthogonal spaces. Some for generalizations contraction principle via altering distance functions spaces presented proved this paper. Furthermore, an example to clarify these...

In this paper, a method for parameterizing orthogonal wavelet transforms is presented. The parameter space is given by the rotation angles of the orthogonal 2 2 rotations used in the lattice filters realizing the stages of the wavelet transform. Different properties of orthogonal wavelet transforms can be expressed in this parameter space. Then, the parameter space is restricted to the set of r...

This paper addresses a mathematically sound technique for the orthogonal matrix optimization problem that has broad applications in recent signal processing problems including the independent component analysis. We propose Dual Cayley parametrization technique that can decompose a slightly restricted version of the original problem into a pair of simple constraint-free optimization problems. Th...

This paper examines optical CDMA (OCDMA) communication techniques with optical orthogonal codes. These optical orthogonal codes (OOC) set are constructed by using difference set methods. Simulations that show OOC reduce interference due to other users and channel noise. Probability of error can be reduce by selection of proper weight (w), length (n) & cardinality(C) of OOC.

In this paper, a novel method for constructing complementary sequence set with zero correlation zone (ZCZ) is presented by interleaving and combining three orthogonal matrices. The constructed set can be divided into multiple sequence groups and each sequence group can be further divided into multiple sequence subgroups. In addition to ZCZ properties of sequences from the same sequence subgroup...