Generalised definitions of exponential, trigonometric sine and cosine and hyperbolic sine and cosine functions are given. In the lowest order, these functions correspond to ordinary exponential, trigonometric sine etc. Some of the properties of the generalised functions are discussed. Importance of these functions and their possible applications are also considered. PACS No.: 02.30.Hq, 02.30.Gp...

Generalised definitions of exponential, trigonometric sine and cosine and hyperbolic sine and cosine functions are given. In the lowest order, these functions correspond to ordinary exponential, trigonometric sine etc. Some of the properties of the generalised functions are discussed. Importance of these functions and their possible applications are also considered. PACS No.: 02.30.Hq, 02.30.Gp...

The sine-Gordon equation has hyperelliptic al function solutions over a hyperelliptic Jacobian for y = f(x) of arbitrary genus g. This article gives an extension of the sine-Gordon equation to that over subvarieties of the hyperelliptic Jacobian. We also obtain the condition that the sine-Gordon equation in a proper subvariety of the Jacobian is defined.

Although turtles (order Testudines) constitute one of the major reptile groups, their phylogenetic relationships remain largely unresolved. Hence, we attempted to elucidate their phylogeny using the SINE (short interspersed repetitive element) method, in which the sharing of a SINE at orthologous loci is indicative of synapomorphy. First, a detailed characterization of the tortoise polIII/SINE ...

This paper describes the design and implementation of a ROM-Less Direct Digital Frequency Synthesizer (DDS) using Bezier curve approximation. With Bezier curve approximation, phase values between 0 to π are mapped to sine amplitudes. Then, half wave symmetry of sine wave is exploited to construct full sine wave. The proposed approximation introduces maximum error of 7.9×10, which is equivalent ...

The relationship between the soliton dynamics provided by the classical sine-Gordon and massive Thirring models is exhibited. Solitons are characterized as classical relativistic particles through the consideration of their associated canonical realizations of the Poincare group. It is shown that the soliton in the massive Thirring model determines two different kinds of relativistic particles ...

Scleroderma renal crisis has been documented as the presenting manifestation of systemic sclerosis sine scleroderma in pregnancy only once in the literature. Unfortunately, since scleroderma renal crisis in sine scleroderma pregnant patients is so rare, that patient expired. We present a case of a sine scleroderma pregnant patient with an initial manifestation of scleroderma renal crisis surviv...