We study long-range correlation functions of the rectangular Ising lattice with cyclic boundary conditions. Specifically, we consider the situation in which two spins are on the same column, and at least one spin is on or near free boundaries. The low-temperature series expansions of the correlation functions are presented when the spin-spin couplings are the same in both directions. The exact ...

In 1978, Rivest, Adleman and Dertouzos asked for algebraic systems for which useful privacy homomorphisms exist. To date, the only acknownledged result is noise based encryption combined with bootstrapping. Before that, there were several failed attempts. We prove that fully homomorphic schemes are impossible for several algebraic structures. Then we develop a characterisation of all fully homo...

Synthetic oligonucleotides are used to regulate gene expression through different mechanisms. Chemical modifications of the backbone of the nucleic acid and/or of the 2' moiety of the ribose can increase nuclease stability and/or binding affinity of oligonucleotides to target molecules. Here we report that transfection of 2'-F-modified phosphorothioate oligonucleotides into cells can reduce the...

In this paper, we consider the (3 + 1)-dimensional fractional-stochastic quantum Zakharov–Kuznetsov equation (FSQZKE) with M-truncated derivative. To find novel trigonometric, hyperbolic, elliptic, and rational fractional solutions, two techniques are used: Jacobi elliptic function approach modified F-expansion method. We also expand on a few earlier findings. The extended has practical applica...

the drawing of frequency-path (f-p) models of optical beams is an approach for nonlinearity analysis in nano-metrology systems and sensors based on the laser interferometers. in this paper, the frequency-path models of four nano-metrology laser interferometry systems are designed, analyzed and simulated, including conventional and modified two- and three-longitudinal-mode laser interferometers....

An algorithm for the evaluation of the complex exponential function is proposed which is quasi-linear in time and linear in space. This algorithm is based on a modified binary splitting method for the hypergeometric series and a modified Karatsuba method for the fast evaluation of the exponential function. The time complexity of this algorithm is equal to that of the ordinary algorithm for the ...

We present a detailed comparison of the efficiency and accuracy of the secondand third-order split operator methods, a time dependent modified Cayley method, and the Chebychev polynomial expansion method for solving the time dependent Schrodinger equation in the onedimensional double well potential energy function. We also examine the efficiency and accuracy of the split operator and modified C...

The NNM (Nonlinear normal modes) have recently been investigated with the method of strained coordinates for spring mass models with some springs with piecewise linear stiffness. The N d.o.f. case and the mathematical validity of the method for large time were rigorously proved. The time validity is related to the nature of contact. For grazing contact, this method and also the multiscale expan...