The Lenstra, Lenstra, and Lovász (abbreviated as LLL) basis reduction algorithm computes a basis of a lattice consisting of short, and near orthogonal vectors. The quality of an LLL reduced basis is expressed by three fundamental inequalities, and it is natural to ask, whether these have a common generalization. In this note we find unifying inequalities. Our main result is Theorem 1. Let b1, ....

Abstract—We present a general theory of entanglementassisted quantum convolutional coding. The codes have a convolutional or memory structure, they assume that the sender and receiver share noiseless entanglement prior to quantum communication, and they are not restricted to possess the CalderbankShor-Steane structure as in previous work. We provide two significant advances for quantum convolut...

Introduction We have all heard the old joke of school being all about the three “R’s”, Reading ‘Ritin and ‘Rithmatik, but because of increasing class sizes and reported lack of instruction time, writing has been passed over for the more “important” subjects. The advent of computers and the increasing ease of word processing have given teachers the ultimate excuse, but most beginning composition...

Constrained orthogonal polynomials have been recently introduced in the study of the HohenbergKohn functional to provide basis functions satisfying particle number conservation for an expansion of the particle density. More generally, we define block orthogonal (BO) polynomials which are orthogonal, with respect to a first Euclidean inner product, to a given i-dimensional subspace Ei of polynom...

In order to compute orthogonal eigenvectors of a symmetric tridiagonal matrix without Gram-Schmidt orthogonalization, the MRRR algorithm finds a shifted LDL factorization (representation) for each eigenvalue such that the local eigenvalue is a singleton, that is defined to high relative accuracy and has a large relative gap. MRRR’s representation tree describes how, by successive shifting and r...

 Abstract—This paper proposes new adaptive tree search detection with variable path expansion based on Gram-Schmidt (GS) orthogonalization (GSO) in MIMO systems. We adopt the GSO procedure to reduce the channel matrix instead of the QR-decomposition in the conventional QRM-MLD. This detection scheme combined the GSO reduction with the M-algorithm, what we call GSM-MLD, can achieve near-ML perf...

Workers' remittances represent up to 47 percent of gross domestic product in some Asian countries. Also, workers' the region were estimated reach $256 billion out $483 received by developing However, growth effect remittance Asia has, over years, remained an open empirical question. To this end, study examines impact and its interactive effects with financial development institutional quality o...

A monocular visual servoing scheme for constrained robots is considered in this chapter. Inspired by the Orthogonalization Principle (OP) introduced by Suguru Arimoto in the context of robot force control, a Visual Orthogonalization Principle (VOP) is proposed and a novel control scheme for adaptive image-based visual servoing is presented. The scheme guarantees a global exponential convergence...

We introduce a computationally efficient FFT-based algorithm for the design of OFDM/ OQAM pulse shaping filters of arbitrary length and with arbitrary overlapping factors. The basic idea of our approach is to start from an arbitrary initial (nonorthogonal) filter and to perform an orthogonalization which yields an ISIand ICI-free pulse shaping filter. The orthogonalization is performed in the d...

In phase-shifting interferometry with unknown phase shifts, a normalization and orthogonalization phase-shifting algorithm (NOPSA) is proposed to achieve phase retrieval. The background of interferogram is eliminated through using the orthogonality of complex sinusoidal function; and the influence of phase shifts deviation on accuracy of phase retrieval is avoided through both normalization and...