Application of Fibonacci sine and cosine function to a nonlinear differential-difference equation

A new approach is constructed to obtain exact travelling wave solutions for a differential-difference equation by means of the property of the symmetrical Fibonacci sine and cosine function. As its illustration, some explicit and exact travelling wave solutions of Hybrid lattice, discretized mKdV lattice and modified Volterra lattice are obtained by computing the solutions of a lattice introduced by Wadati.     

Clusters of bound particles in the derivative δ-function Bose gas

In this paper we discuss a novel procedure for constructing clusters of bound particles in the case of a quantum integrable derivative δ-function Bose gas in one dimension. It is shown that clusters of bound particles can be constructed for this Bose gas for some special values of the coupling constant, by taking the quasi-momenta associated with the corresponding Bethe state to be equidistant points on a single circle in the complex momentum plane. We also establish a connection between these special values of the coupling constant and some fractions belonging to the Farey sequences in number theory. This connection leads to a classification of the clusters of bound particles associated with the derivative δ-function Bose gas and allows us to study various properties of these clusters like their size and their stability under the variation of the coupling constant.     

Off-diagonal Bethe ansatz solution of the XXX spin chain with arbitrary boundary conditions

Employing the off-diagonal Bethe ansatz method proposed recently by the present authors, we exactly diagonalize the XXX spin chain with arbitrary boundary fields. By constructing a functional relation between the eigenvalues of the transfer matrix and the quantum determinant, the associated T–Q$T\text{–}Q$ relation and the Bethe ansatz equations are derived.     

Controllability for a class of second-order evolution differential inclusions without compactness

In this paper, we discuss the existence and controllability for a class of second-order evolution differential inclusions without compactness in Banach spaces. By applying the technique of weak topology and Glicksberg–Ky Fan fixed point theorem, we prove our main results without the hypotheses of compactness on the operator generated by the linear part and any conditions on the multivalued nonlinearity expressed in terms of measures of noncompactness. Further, we extend our study to existence and controllability of second-order evolution differential inclusions with nonlocal conditions and impulses. Finally, an example is given for the illustration of the obtained theoretical results.     

Interference suppression for the LTE uplink

Interference cancellation is expected to have significant importance for next-generation wireless communication systems due to various co-channel deployment scenarios and denser frequency reuse. In this study, an interference cancellation receiver that exploits the unique characteristics of single-carrier frequency-division multiple access based systems is proposed. The proposed receiver suppresses the co-channel dominant interference by blanking frequency-domain samples where the desired and interfering signals overlap. In order to improve the performance, demodulation and regeneration stages can be introduced and repeated multiple times. Further enhancement is possible by initially accommodating a group of reliable symbols before the iterations. The simulation results indicate that proposed methods work particularly well for low overlap ratios compared to interference coordination and no cancellation schemes.     

Discrete breathers in nonlinear Schrödinger hypercubic lattices with arbitrary power nonlinearity

We study two specific features of onsite breathers in Nonlinear Schrödinger systems on d-dimensional cubic lattices with arbitrary power nonlinearity (i.e., arbitrary nonlinear exponent, n): their wavefunctions and energies close to the anti-continuum limit-small hopping limit-and their excitation thresholds. Exact results are systematically compared to the predictions of the so-called exponential ansatz (EA) and to the solution of the single nonlinear impurity model (SNI), where all nonlinearities of the lattice but the central one, where the breather is located, have been removed. In 1D, the exponential ansatz is more accurate than the SNI solution close to the anti-continuum limit, while the opposite result holds in higher dimensions. The excitation thresholds predicted by the SNI solution are in excellent agreement with the exact results but cannot be obtained analytically except in 1D. An EA approach to the SNI problem provides an approximate analytical solution that is asymptotically exact as n tends to infinity. But the EA result degrades as the dimension, d, increases. This is in contrast to the exact SNI solution which improves as n and/or d increase. Finally, in our investigation of the SNI problem we also prove a conjecture by Bustamante and Molina [C.A. Bustamante, M.I. Molina, Phys. Rev. B 62 (23) (2000) 15287] that the limiting value of the bound state energy is universal when n tends to infinity.     

Three formulas for eigenfunctions of integrable Schrödinger operators

We give three formulas for meromorphic eigenfunctions (scatteringstates) of Sutherlandsintegrable N-body Schrödinger operators and their generalizations.The first is an explicit computation of the Etingof–Kirillov tracesof intertwining operators, the second an integral representationof hypergeometric type, and the third is a formula of Bethe ansatz type.The last two formulas are degenerations of elliptic formulasobtained previously in connection with theKnizhnik–Zamolodchikov–Bernardequation. The Bethe ansatz formulas in the elliptic case are reviewed and discussed in more detail here: Eigenfunctionsare parametrized by a Hermite–Bethe variety, a generalizationof the spectral variety of the Lamé operator.We also give the q-deformed version of ourfirst formula. In the scalar slN case, this gives common eigenfunctionsof the commuting Macdonald–Rujsenaars difference operators.     

Fast algorithms for discrete polynomial transforms

Consider the Vandermonde-like matrix , where the polynomials satisfy a three-term recurrence relation. If are the Chebyshev polynomials , then coincides with . This paper presents a new fast algorithm for the computation of the matrix-vector product in arithmetical operations. The algorithm divides into a fast transform which replaces with and a subsequent fast cosine transform. The first and central part of the algorithm is realized by a straightforward cascade summation based on properties of associated polynomials and by fast polynomial multiplications. Numerical tests demonstrate that our fast polynomial transform realizes with almost the same precision as the Clenshaw algorithm, but is much faster for .

     

Direction-Dependent Free Energy Singularity of the Antiferroelectric Asymmetric Six-Vertex Model

The transition from the ordered commensurate phase to the incommensurate Gaussian phase of the antiferroelectric asymmetric six-vertex model is investigated by keeping the temperature constant below the roughening point and varying the external fields (h, v). In the (h, v) plane, the phase boundary is approached along straight lines v = k h, where (h, v) measures the displacement from the phase boundary. It is found that the free energy singularity displays the exponent 3/2 typical of the Pokrovski–Talapov transition f const(h)^3/2 for any direction other than the tangential one. In the latter case f shows a discontinuity in the third derivative.