In this paper, we show that B-spline quarks and the associated quarklets fit into theory of biorthogonal multiwavelets. Quark vectors are used to define sequences subspaces [Formula: see text] which fulfill almost all conditions a multiresolution analysis. Under some special on parameters, they even satisfy those properties. Moreover, prove possess modulation matrices perfect reconstruction con...

An efficient algorithm for the multiplication in GF (2) was introduced by Mastrovito. The space complexity of the Mastrovito multiplier for the irreducible trinomial x +x+1 was given as m − 1 XOR and m AND gates. In this paper, we describe an architecture based on a new formulation of the multiplication matrix, and show that the Mastrovito multiplier for the generating trinomial x + x + 1, wher...

Digital signal processors (DSPs) are very important in various engineering disciplines. Fast multiplication is very important in DSPs for convolution, Fourier transforms, etc. A fast method for multiplication based on ancient Indian Vedic mathematics is proposed in this paper. The whole of Vedic mathematics is based on 16 sutras (word formulae) and manifests a unified structure of mathematics. ...

The theory of M-ideals and multiplier mappings of Banach spaces naturally generalizes to left (or right) M-ideals and multiplier mappings of operator spaces. These subspaces and mappings are intrinsically characterized in terms of the matrix norms. In turn this is used to prove that the algebra of left adjointable mappings of a dual operator space X is a von Neumann algebra. If in addition X is...

This paper considers a robust control synthesis problem for uncertain linear systems to meet design specifications given in terms of multiple frequency domain inequalities in (semi)finite ranges. In this paper, we restrict our attention to static (gain feedback) controllers. We will develop a new multiplier method that allows for reduction of synthesis conditions to linear matrix inequality pro...

The theory of M-ideals and multiplier mappings of Banach spaces naturally generalizes to left (or right) M-ideals and multiplier mappings of operator spaces. These subspaces and mappings are intrinsically characterized in terms of the matrix norms. In turn this is used to prove that the algebra of left adjointable mappings of a dual operator space X is a von Neumann algebra. If in addition X is...

In this paper we describe a neural network-based method aimed at automatically calibrating the detector module contained in a scanner for a highresolution positron emission tomography (PET) system for small animals. The detector module is composed of crystal elements, arranged in a regular matrix and sensitive to gamma rays emitted by a radioactive source. The crystal matrix is optically couple...

We introduce implementations of arithmetic operators based on the binary stored-carry-or-borrow (BSCB) representation. Several BSCB arithmetic elements, including full-adder, ripple-carry adder, and carry-lookahead adder are presented, followed by detailed design of an array multiplier. In the latter design, the conventional initial AND matrix is transformed and expressed with a redundant radix...

We present a vector-by-matrix multiplier architecture incorporating the high potential of optical computing within electronics. This architecture stems from advances in optical switching technology, optical communication, and laser on silicon, and overcomes previous bottlenecks implied by the speed of transferring information to the optical vector-by-matrix multiplier. Based on this architectur...