A perfect sequence has the optimal periodic autocorrelation function where all out-of-phase values are zero, and an orthogonal set has orthogonality that the periodic correlation function for any pair of distinct sequences in the set takes zero at the zero shift. The real-valued perfect sequences of period N = 2 are derived from a real-valued Huffman sequence of length 2 + 1 with ν ≥ n whose ou...

The main objective of this project is to design the full-rate Space-Time-Frequency Trellis code (STFTC), which is based on Quasi-Orthogonal designs for Multiple-Input Multiple-Output (MIMO) Orthogonal Frequency Division Multiplexing (OFDM) systems. The proposed Quasi-Orthogonal Space-TimeFrequency Trellis code combines set partitioning and the structure of quasi-orthogonal space-frequency desig...

The concept of a linear ordered orthogonal array is introduced, and its equivalent geometrical configuration is determined when its strength is 3 and 4. Existence of such geometrical configurations is investigated. They are also useful in the study of (T, M, S)-nets.

Given a convex region in the plane, and a sweep-line as a tool, what is best way to reduce the region to a single point by a sequence of sweeps? The problem of sweeping points by orthogonal sweeps was first studied in [2]. Here we consider the following slanted variant of sweeping recently introduced in [1]: In a single sweep, the sweep-line is placed at a start position somewhere in the plane,...

This paper presents a method for solving the problem of global illumination for general environments, using projection of the radiance function on a set of orthonormal basis functions. Wavelet scaling functions form this basis set. The highlights of the paper are : it (i) points out the di culty associated with the straightforward projection of the integral operator associated with the radiance...

It was already known that there exists a family of continuum many pairwise orthogonal elements of R. A family F ⊆ R \ 0 of pairwise orthogonal sequences is orthogonally complete or a maximal orthogonal family iff the only element of R orthogonal to every element of F is 0, the constant 0 sequence. It is somewhat surprising that Kunen’s perfect set of orthogonal elements is maximal (a fact first...

Saccharomyces cerevisiae (baker’s yeast) can exhibit sustained oscillations during the operation in a continuous bioreactor that adversely affects its stability and productivity. Because of heterogeneous nature of cell populations, the cell population balance equation (PBE) can be used to capture the dynamic behavior of such cultures. In this work, an unstructured-segregated model is used f...

two latin squares of order $n$ are orthogonal if in their superposition, each of the$n^{2}$ ordered pairs of symbols occurs exactly once. colbourn, zhang and zhu, in a seriesof papers, determined the integers $r$ for which there exist a pair of latin squares oforder $n$ having exactly $r$ different ordered pairs in their superposition. dukes andhowell defined the same problem for latin squares ...

A l-norm penalized orthogonal forward regression (l-POFR) algorithm is proposed based on the concept of leaveone-out mean square error (LOOMSE). Firstly, a new l-norm penalized cost function is defined in the constructed orthogonal space, and each orthogonal basis is associated with an individually tunable regularization parameter. Secondly, due to orthogonal computation, the LOOMSE can be anal...