The new approach of the generalized (G'/G)-expansion method is an effective and powerful mathematical tool in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in science, engineering and mathematical physics. In this article, the new approach of the generalized (G'/G)-expansion method is applied to construct traveling wave solutions of the Kadomtsev-Petviashvili-B...

A new generalized inversion for square matrices based on projections is introduced. It includes as special cases known generalized inverses such as the Moore-Penrose and the Drazin inverses. When associated with a regular matrix pencil, it can be expressed by a contour integral formula and can be used, in particular, to write down an explicit representation of the solutions of linear differenti...

We propose an adaptive reversible data hiding method with superior visual quality and capacity in which an adaptive generalized difference expansion (AGDE) method is applied to an integer-to-integer subband transform (I2I-ST). I2I-ST performs the reversible subband transform and the AGDE method is a state-of-the-art method of reversible data hiding. The results of experiments we performed objec...

ABSTRACT Exact solutions of nonlinear evolution equations (NLEEs) play a vital role to reveal the internal mechanism of complex physical phenomena. In this work, the exact traveling wave solutions of the Boussinesq equation is studied by using the new generalized (G'/G)-expansion method. Abundant traveling wave solutions with arbitrary parameters are successfully obtained by this method and the...

ABSTRACT: We investigate the mechanism of spin gap formation in a two-dimensional model relevant to Mott insulators such as CaV4O9. From the perturbation expansion and quantum Monte Carlo calculations, the origin of the spin gap is ascribed to the four-site plaquette singlet in contrast to the dimer gap established in the generalized dimerized Heisenberg model. We investigate the mechanism of s...

In memoriam Csörgő Sándor, dear friend and great scholar Keywords: Bessel function of first kind J ν (z) Bounds for J ν (z) Positive zeros j ν,s of J ν (z) Generalized Kapteyn expansion Kapteyn series a b s t r a c t A new inequality is derived for the Bessel function of the first kind J ν (z), ν ∈ R, and a discussion of the consequent convergence is given for the generalized Kapteyn-type expan...

We study a generalization of the notion of Gaussian free field (GFF). Although the extension seems minor, we first show that a generalized GFF does not satisfy the spatial Markov property, unless it is a classical GFF. In stochastic homogenization, the scaling limit of the corrector is a possibly generalized GFF described in terms of an “effective fluctuation tensor” that we denote by Q. We pro...

In this paper,the traditional G′/G-expansion method is improved and a generalized G′/G-expansion method is proposed to seek exact solutions of nonlinear evolution equations.And we choose Benjamin-Bona-Mahony equation,(2+1) dimensional generalized Zakharov-Kuznetsov equation and variant Bousinessq equations to illustrate the validity and advantages of the proposed method.It is shown that the pro...

Based on computerized symbolic computation and a new general ansatz,an extended Riccati equation rational expansion method is presented to construct multiple exact solutions for nonlinear evolution equations and implemented in a computer algebraic system.The validity and reliability of the method are tested by its application to four nonlinear evolution equations arising in physics,namely,gener...

In this research, a numerical method by piecewise approximated method for solving fuzzy differential equations is introduced. In this method, the solution by piecewise fuzzy polynomial is present. The base of this method is using fuzzy Taylor expansion on initial value of fuzzy differential equations. The existence, uniqueness and convergence of the approximate solution are investigated. To sho...