Based on analysis of basic cubic spline interpolation, the clamped cubic spline interpolation is generalized in this paper. The methods are presented on the condition that the first derivative and second derivative of arbitrary node are given. The Clamped spline and Curvature-adjusted cubic spline are also generalized. The methods are presented on the condition that the first derivatives of arb...

Two computational methods for pruning a reassigned spectrogram to show only quasisinusoidal components, or only impulses, or both, are presented mathematically and provided with step-by-step algorithms. Both methods compute the second-order mixed partial derivative of the short-time Fourier transform phase, and rely on the conditions that components and impulses are each well-represented by rea...

A non associative, noncommutative algebra is defined that may be interpreted as a set of vector modules over a noncommutative surface of rotation. Two of these vector modules are identified with the analogues of the tangent and cotangent spaces in noncommutative geometry, via the definition of an exterior derivative. This derivative reduces to the standard exterior derivative in the commutative...

The 2D gravity described by the action which is an arbitrary function of the scalar curvature f(R) is considered. The classical vacuum solutions are analyzed. The one-loop renormalizability is studied. For the function f = R lnR the model coupled with scalar (conformal) matter is exactly integrated and is shown to describe a black hole of the 2D dilaton gravity type. The influence of one-loop q...

Two spectrophotometric methods are described and applied to resolve ternary mixtures of the corticosteroid hydrocortisone (HYD) and the antibiotics nystatin (NYS) and oxytetracycline (OXY). The simultaneous determination of these three compounds was firstly accomplished by a derivative method using the “ratio spectrum-zero crossing derivative” and then by multivariate methods partial least squa...

We consider the canonical quantization of a generalized two-dimensional massive fermion theory containing higher odd-order derivatives. The requirements of Lorentz invariance, hermiticity of the Hamiltonian and absence of tachyon excitations suffice to fix the mass term, which contains a derivative coupling. We show that the basic quantum excitations of a higher-derivative theory of order 2N + ...

We compute the anomalous dimensions of BMN operators with two covariant derivative impurities at the planar level up to first order in the effective coupling λ′. The result equals those for two scalar impurities as well as for mixed scalar and vector impurities given in the literature. Though the results are the same, the computation is very different from the scalar case. This is basically due...

Reverse engineering of program code is the process of constructing a higher level abstraction of an implementation in order to facilitate the understanding of a system that may be in a \legacy" or \geriatric" state. Changing architectures and improvements in programming methods, including formal methods in software development and object-oriented programming , have prompted a need to reverse en...

It is attempted to extend a two-step without memory method to it's with memory. Then, a new two-step derivative free class of without memory methods, requiring three function evaluations per step, is suggested by using a convenient weight function for solving nonlinear equations. Eventually, we obtain a new class of methods by employing a self-accelerating parameter calculated in each iterative...