The paper extends homogeneous functional calculus on vector lattices. It is shown that the function of elements of a relatively uniformly complete vector lattice can naturally be defined if the positively homogeneous function is defined on some conic set and is continuous on some closed convex subcone. An interplay between Minkowski duality and homogeneous functional calculus leads to the envel...

We have successfully generated vector beams with higher-order polarization states using photonic-crystal lasers. We have analyzed and designed lattice structures that provide cavity modes with different symmetries. Fabricated devices based on these lattice structures produced doughnut-shaped vector beams, with symmetries corresponding to the cavity modes. Our study enables the systematic analys...

Introduction. We propose to investigate here the consequences of the identity of each pair chosen from three important generalizations of the relation of betweenness on a line, namely, algebraic betweenness [l, p. 27 J, metric betweenness [3, p. 36], and lattice betweenness [7, Part I I ] . We shall also find an interpretation of metric betweenness in the Banach space of all continuous function...

This paper is the extension of two-stage vector quantization–(spherical) lattice vector quantization (VQ–(S)LVQ) recently introduced by Pan and Fischer [1]. First, according to high resolution quantization theory, generalized vector quantization–lattice vector quantization (G-VQ–LVQ) is formulated in order to release the constraint of the spherical boundary for the second-stage lattice vector q...

We study ”nearly orthogonal” lattice bases, or bases where the angle between any basis vector and the linear subspace spanned by the other basis vectors is greater than π 3 radians. We show that a nearly orthogonal lattice basis always contains a shortest lattice vector. Moreover, if the lengths of the basis vectors are “nearly equal”, then the basis is the unique nearly orthogonal lattice basi...

AbstructWe present several results regarding the properties of a random vector, uniformly distributed over a lattice cell. This random vector is the quantization noise of a lattice quantizer at high resolution, or the noise of a dithered lattice quantizer at all distortion levels. We find that for the optimal lattice quantizers this noise is wide-sense-stationary and white. Any desirable noise ...

W e present several results regarding the propert ies of a random vector, uniformly distributed over a lattice cell. This random vector is the quantization noise of a lattice quantizer at high resolution, or the noise of a dithered lattice quantizer at all distortion levels. W e find that for the optimal lattice quantizers this noise is wide-sense-stat ionary and white. Any desirable noise spec...

As the digital information must be stored and recovered in an effective ways, it is necessary to compress data in image coding, wavelet transform and lattice vector quantization are adopted in this paper to improve the compression effective of image coding. We first propose the two dimensional spatial wavelet decomposition of image, and then we present lattice Vector Quantization coding scheme ...