We present an analytic study of the finite size effects in Sine–Gordon model, based on the semiclassical quantization of an appropriate kink background defined on a cylindrical geometry. The quasi–periodic kink is realized as an elliptic function with its real period related to the size of the system. The stability equation for the small quantum fluctuations around this classical background is ...

We calculate the three-point functions in the sine-Liouville theory explicitly. The same calculation was done in the (unpublished) work of Fateev, Zamolodchikov and Zamolodchikov to check the conjectured duality between the sine-Liouville and the SL(2,R)/U(1) coset CFTs. The evaluation of correlators boils down to that of a free-field theory with a certain number of insertion of screening opera...

This article pushes the role of sine and cosine functions beyond traditional purpose determining sides a right triangle, into realm lengths any triangle with practically same ease. Extended are formulated dependent on two angles (instead one) — sin*(α,γ) cos*(α,γ)—that allow (via direct application) computation shorter scalene as resul...

We refine a formula on values of multiple sine functions at division points. As applications we prove a formula on a sum of reciprocal trigonometric values, and obtain multiple modularity of a three variable modular function, which concerns a generalization of the Dedekind η function.

This paper is associated with implementation of Sine & Cosine using Volder’s CORDIC Algorithm. CORDIC algorithm based Systems are used for fast and silicon area efficient computation of the sine and cosine functions. The algorithmic approach for the CORDIC algorithm implementation is presented here. Summary of CORDIC synthesis results based on Actel and XILINX FPGAs is given. Finally applicatio...

A new process to produce orientation-patterned gallium phosphide (OP-GaP) on GaAs with almost perfectly parallel domain boundaries is presented. Taking advantage of the chemical selectivity between phosphides and arsenides, OP-GaP processed into suspended shallow-ridge waveguides. Efficient second-harmonic generation from telecom wavelengths achieved in both Type-I Type-II polarisation configur...

An efficient approach for solving stochastic optimal control problems is to employ dynamic programming (DP). For continuous-valued nonlinear systems, the corresponding DP recursion generally cannot be solved in closed form. Thus, a typical approach is to discretize the DP value functions in order to be able to carry out the calculation. Especially for multidimensional systems, either a large nu...

We show that high-dimensional analogues of the sine function (more precisely, the d-dimensional polar sine and the d-th root of the d-dimensional hypersine) satisfy a simplex-type inequality in a real preHilbert space H. Adopting the language of Deza and Rosenberg, we say that these d-dimensional sine functions are d-semimetrics. We also establish geometric identities for both the d-dimensional...

The problem of semi-cardinal spline interpolation was solved by Schoenberg exploiting the piecewise polynomial form of the splines. In the present paper, we propose a new construction for the Lagrange functions of semi-cardinal spline interpolation , based on a radial basis and Fourier transform approach. This approach suggests a way of extending semi-cardinal interpolation to polyharmonic spli...