In this article, we will show the complex inversion formula for the inversion of the L2-transform and also some applications of the L2, and Post Widder transforms for solving singular integral equation with trigonometric kernel. Finally, we obtained analytic solution for a partial differential equation with non-constant coefficients.

A set of parametric equations of an algebraic curve or surface is called normal, if all the points of the curve or the surface can be given by the parametric equations. In this paper, we present a method to decide whether a set of parametric equations is normal. In addition, we give some simple criteria for a set of parametric equations to be normal. As an application, we present a method to fi...

We have developed a theoretical description of how of an asteroid’s polarizationphase curve will be affected by the removal of the dust from the surface due to a sizedependent phenomenon such as radiation pressure-driven escape of levitated particles. We test our calculations against new observations of four small (D ≈ 1 km) nearEarth asteroids [(85236), (142348), (162900) and 2006 SZ217] obtai...

MOS varactors are used extensively as tunable elements in the tank circuits of RF voltage-controlled oscillators (VCOs) based on submicrometer CMOS technologies. MOS varactor topologies include conventional D=S=B connected, inversion-mode (I-MOS), and accumulation-mode (A-MOS) structures. When incorporated into the VCO tank circuit, the large-signal swing of the VCO output oscillation modulates...

This contribution describes how an elliptic curve cryptosystem can be implemented on very low cost microprocessors with reasonable performance. We focus in this paper on the Intel 8051 family of microcontrollers popular in smart cards and other cost-sensitive devices. The implementation is based on the use of the finite fieldGF ((2− 17)) which is particularly suited for low end 8-bit processors...

We describe e cient formulas for computing pairings on ordinary elliptic curves over prime elds. First, we generalize lazy reduction techniques, previously considered only for arithmetic in quadratic extensions, to the whole pairing computation, including towering and curve arithmetic. Second, we introduce a new compressed squaring formula for cyclotomic subgroups and a new technique to avoid p...

Because of the distortions of geometrical optics, .image curves< and, the outlines of the objects that generate them need not have the same topology. New image loops appear when the object curve touches the caustic of the family of (imaginary) rays emitted by the observing eye. Such disruption may be elliptic (loop born from an isolated point) or hyperbolic (loop pinched off from an already exi...

The computation of P over elliptic curves is the dominant operation. It depends on the representation of the scalar . The binary method is the standard unsigned method that is used to compute the elliptic curve point . Researchers found that it is not the most efficient way for implementing elliptic curve computations. Other recoding methods such as CR, NAF, and MOF were presented in order to e...

Considering non-negative characteristic of the particle size distribution (PSD), based on trust-regionreflective Newton method, two non-negative regularization methods of truncated singular value decomposition (TSVD) and Tikhonov (TIK) for photon correlation spectroscopy (PCS) are proposed in this paper. Combining two regularization parameter criterions of GCV and L-curve, two non-negative regu...

For a hyperelliptic curve of genus g, it is well known that the symmetric products of g points on the curve are expressed in terms of their Abel–Jacobi image by the hyperelliptic sigma function (Jacobi inversion formulae). Matsutani and Previato gave a natural generalization of the formulae to the more general algebraic curves defined by y = f(x), which are special cases of (n, s) curves, and d...