Most algorithms for computing local or global solutions of linear differential systems handle only the case of square systems. However, in many applications such as control theory, systems that appear are generally non-square. In this paper, we use a constructive algebraic analysis approach to reduce the integration of a rectangular linear ordinary differential system to that of a square system...

The design and implementation of a high-speed direct digital frequency synthesizer are presented. A modified Brent-Kung parallel adder is combined with pipelining technique to improve the speed of the system. A gated clock technique is proposed to reduce the number of registers in the phase accumulator design. The quarter wave symmetry technique is used to store only one quarter of the sine wav...

The distributional properties of the translation flow on unit square have been considered in different fields mathematics, including algebraic geometry and discrepancy theory. One method to quantify equidistribution is compare error between

Given the popularity of decimal arithmetic, hardware implementation of decimal operations has been a hot topic of research in recent decades. Besides the four basic operations, the square root can be implemented as an instruction directly in the hardware, which improves the performance of the decimal floating-point unit in the processors. Hardware implementation of decimal square rooters is usu...

Cytochrome P450 21-hydroxylase (P450c21) is a key enzyme for corticosteroidogenesis. To understand the regulatory mechanisms of cortisol production in fish, we have cloned a cDNA encoding P450c21, for the first time in non-mammalian vertebrates, from the head kidney of the eel (Anguilla japonica). The overall similarity of the deduced P450c21 sequence was modest (41-44% amino acid identity) bet...

Given a square matrix with elements in the group-ring of a group, one can consider the sequence formed by the trace (in the sense of the group-ring) of its powers. We prove that the corresponding generating series is an algebraic G-function (in the sense of Siegel) when the group is free of finite rank. Consequently, it follows that the norm of such elements is an exactly computable algebraic n...

The readers of this article should be familiar with modular arithmetic, and may also recall Sophie Germain's identity. This article deals with an application of the identity in solving the equation 3 + 4 = 5. A word about the identity As the name says, Sophie Germain's identity was rst discovered by Sophie Germain. It reads a 4 + 4b = a + 4ab + 4b 4ab = (a + 2b) 4ab = (a + 2ab+ 2b)(a 2ab+ 2b) ....

This work considers lattice walks restricted to the quarter plane, with steps taken from a set of cardinality three. We present a complete classification of the generating functions of these walks with respect to the classes algebraic, transcendental holonomic and non-holonomic. The principal results are a new algebraic class related to Kreweras’ walks; two new non-holonomic classes; and enumer...

In this paper, we prove some properties of algebraic cone metric spaces and introduce the notion of algebraic distance in an algebraic cone metric space. As an application, we obtain some famous fixed point results in the framework of this algebraic distance.