We consider the complexity of a Lenstra Lenstra Lovász lattice reduction algorithm ([LLL]) in which the vectors are allowed to be linearly dependent and in which one also asks for the matrix of the transformation from the given generators to the reduced basis. The main problem will be to show that the entries of the transformation matrix remain bounded through the algorithm, with a reasonable b...

with x an n-dimensional vector, A a constant square matrix of order n, and Q a square matrix of order n, quasiperiodic in time t. We say that a change of variables x = P(t)y is a Lyapunov-Perron (LP) transformation if P(t) is nonsingular and P(t), P−1(t), and Ṗ (t) are bounded for all t ∈R. Moreover, if P , P−1, and Ṗ are quasiperiodic in time t, we refer to x = P(t)y as a quasiperiodic LP tran...

The singular value decomposition (SVD) technique is extended to incorporate the additive components for approximation of a rectangular matrix by the outer products of vectors. While dual vectors of the regular SVD can be expressed one via linear transformation of the other, the modified SVD corresponds to the general linear transformation with the additive part. The method obtained can be relat...

We study the optical properties of a two-axis galvanometric optical scanner constituted by a pair of rotating planar mirrors, focusing our attention on the transformation induced on the polarization state of the input beam. We obtain the matrix that defines the transformation of the propagation direction of the beam and the Jones matrix that defines the transformation of the polarization state....

The influence of aluminium on the microstructure of austempered ductile cast iron (ADI) has been studied. The presence of well distributed graphite in the matrix, and a relatively high volume fraction of retained austenite are responsible for the good mechanical properties of the Aluminium alloyed austempered ductile irons including excellent wear resistance, higher resistance to thermal shock,...

We present a new method of Speaker Adapted Training (SAT) that is more robust, faster, and results in lower error rate than the previous methods. The method, called Inverse Transform SAT (ITSAT) is based on removing the differences between speakers before training, rather than modeling the differences during training. We develop several methods to avoid the problems associated with inverting th...

Superelastic NiTi (51.0 at.% Ni) specimens reinforced with 0, 10 and 20 vol.% TiC particles were deformed under uniaxial compression while neutron diffraction spectra were collected. The experiments yielded in-situ measurements of the thermoelastic stress-induced transformation. The evolution of austenite/martensite phase fractions and of elastic strains in the reinforcing TiC particles and the...

In this paper, the generalized learning vector quantization (GLVQ) algorithm is applied to design a handwritten Chinese character recognition system. The system proposed herein consists of two modules, feature transformation and recognizer. The feature transformation module is designed to extract discriminative features to enhance the recognition performance. The initial feature transformation ...

*Correspondence: [email protected] 1Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia 2Department of Mathematics, Aligarh Muslim University, Aligarh, 202 002, India Abstract In this paper, we characterize the matrix classes ( 1, p(F)) (1≤ p <∞), where p(F) is some Fibonacci di...

We have transformed the scalar wave equation into a matrix eigenvalue equation, the diagonalization of which gives the guided modes and a discrete representation of the radiation modes. The method is simple and can be used for arbitrary refractive index profdes. I