The problem of water wave scattering by a semi-infin ite floating dock on the free surface of an ocean with variable bottom topography is considered using linear theory. By employing a perturbation analysis and using Green's integral theorem, the analytical expression for the first order reflection coefficient is obtained in terms of a computable integral involving the bottom shape function. Al...

Melnikov’s method is applied to the planar double pendulum proving it to be a chaotic system. The parameter space of the double pendulum is discussed, and the integrable cases are identified. In the neighborhood of the integrable case of two uncoupled pendulums Melnikov’s integral is evaluated using residue calculus. In the two limiting cases of one pendulum becoming a rotator or an oscillator,...

We evaluate partition functions of matrix models which are given by topologically twisted and dimensionally reduced actions of d = 4 N = 1 super Yang-Mills theories with classical (semi-)simple gauge groups, SO(2N), SO(2N + 1) and USp(2N). The integrals reduce to those over the maximal tori by semi-classical approximation which is exact in reduced models. We carry out residue calculus by develo...

Cauchy principal value is a standard method applied in mathematical applications by which an improper, and possibly divergent, integral is measured in a balanced way around singularities or at infinity. On the other hand, entropy prediction of systems behavior from a thermodynamic perspective commonly involves contour integrals. With the aim of facilitating the calculus of such integrals in thi...

Background: Enterococci are important gram-positive bacteria causing dental calculus in human beings; however, the role of these bacteria in oral cavity is unclear. The aim of this study was to investigate the presence of Enterococcal Surface Protein (esp) gene in Enterococcus faecalis isolated from dental calculus in the city of Sari, Iran. Materials and Methods: In the present study, 207 den...

background: pistachio is one of the main nutrients, not only as a strategic crop but also as a main type of nut, in iranians’ food cycle. the aim of this study was to measure the relative safety of iranian pistachio based on the standard pesticide’s residue limits, which should be monitored and assessed in the cultivation of pistachio in order to confirm its public health. methods: fifty sample...

There are more advanced methods, especially Cauchy's residue calculus using complex variable theory, but a typical calculus course mentions only these two methods. Students quickly learn from experience that Archimedes really was a genius, but for practical purposes the Fundamental Theorem is the way to go. But there is a third method, which is quite elementary although not well known. It is de...

On a compact manifold with boundary, consider the realization B of an elliptic, possibly pseudodifferential, boundary value problem having a spectral cut (a ray free of eigenvalues), say R − . In the first part of the paper we define and discuss in detail the operator logB; its residue (generalizing the Wodzicki residue) is essentially proportional to the zeta function value at zero, ζ(B, 0), a...

background and aims. previous researches, conducted mostly on extracted teeth, have shown that efficacy of calculus removal decreases with increasing pocket depth, but there is still a lack of clinical studies concerning the correlation be-tween residual calculus and varying pocket depths. the objective of the present clinical study was to assess the efficiency of mechanical tooth depuration by...