41 Elementary Number Theory 92 41.1 Subgroups of the Integers . . . . . . . . . . . . . . . . . . . . 92 41.2 Greatest Common Divisors . . . . . . . . . . . . . . . . . . . . 92 41.3 The Euclidean Algorithm . . . . . . . . . . . . . . . . . . . . . 93 41.4 Prime Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . 96 41.5 The Fundamental Theorem of Arithmetic . . . . . . . . . . . . 97 4...

This paper describes a multi-material virtual prototyping (MMVP) system for modelling and digital fabrication of discrete and functionally graded multi-material objects for biomedical applications. The MMVP system consists of a DMMVP module, an FGMVP module and a virtual reality (VR) simulation module. The DMMVP module is used to model discrete multi-material (DMM) objects, while the FGMVP modu...

In order to improve the sensing performance for cognitive radio, this paper proposes a spectrum sensing method based on Gabor transform. Firstly, a continuous-time signal is transformed into a discrete-time signal, then, the discrete-time signal is converted into Gabor transform by over-sampling. Secondly, the Gabor transform coefficient of the discrete-time signal is obtained, and then a modul...

This paper presents a hardware module design for the forward Binary Discrete Cosine Transform (BinDCT) and its implementation on a field programmable gate array device. Different architectures of the BinDCT module were explored to ensure the maximum efficiency. The elaboration of these architectures included architectural design, timing and pipeline analysis, hardware description language model...

The aim of this paper is to present the BANCO project and its first results. ESTIA had not experimental setups to make work labs in the discrete-time control courses. It is why some Alecop setups have been improved to use them in these work labs. They were prepared to be used in the Control courses of the second and the third year. The made improvements concern especially an electronic module a...

let $r$ be a right artinian ring or a perfect commutative‎‎ring‎. ‎let $m$ be a noncosingular self-generator $sum$-lifting‎‎module‎. ‎then $m$ has a direct decomposition $m=oplus_{iin i} m_i$‎,‎where each $m_i$ is noetherian quasi-projective and each‎‎endomorphism ring $end(m_i)$ is local‎.

We consider the Whitehead problem for principal ideal domains of large size. It is proved, in ZFC, that some p.i.d.’s of size ≥ א2 have nonfree Whitehead modules even though they are not complete discrete valuation rings. A module M is a Whitehead module if ExtR(M,R) = 0. The second author proved that the problem of whether every Whitehead Z-module is free is independent of ZFC + GCH (cf. [5], ...

We extend the concept of amenability of a Banach algebra A to the case that there is an extra A -module structure on A, and show that when S is an inverse semigroup with subsemigroup E of idempotents, then A = l(S) as a Banach module over A= l(E) is module amenable iff S is amenable. When S is a discrete group, l(E) = C and this is just the celebrated Johnson’s theorem.

.Abstract The alternate use [l] of the discrete cosine transform (DCT) and the discrete sine transform (DST) can achieve higher data compression rates and less blocking effects in image processing. A parallel lattice structure that can dually generate the 1-D DCT and DST is proposed. This architecture is ideally suited for VLSI implementation because of its maldularity, regularity, and local in...