PRINCE is a lightweight block cipher proposed by Borghoff et al. at Asiacrypt 2012. Due to its originality, novel design and low number of rounds, it has already attracted the attention of a large number of cryptanalysts. Several results on reduced versions have been published to date; the best one is an attack on 8 rounds out of the total number of 12. In this paper we improve this result by t...

in this article, a mathematical model describing the growth orterminating myelogenous leukemia blood cancer's cells against naive t-celland eective t-cell population of body, presented by fractional dierentialequations. we use this model to analyze the stability of the dynamics, whichoccur in the local interaction of eector-immune cell and tumor cells. wewill also investigate the optima...

in this paper, we present the numerical solution of ordinary dierential equations (or sdes), from each order especially second-order with time-varying and gaussian random coecients. we indicate a complete analysis for second-order equations in special case of scalar linear second-order equations (damped harmonic oscillators with additive or multi- plicative noises). making stochastic dierent...

So far, many methods have been presented to solve the rst-order di erential equations. But, not many studies have been conducted for numerical solution of high-order fuzzy di erential equations. In this research, First, the equation by reducing time, we transform the rst-order equation. Then we have applied Adams-Bashforth multi-step methods for the initial approximation of one order di erentia...

in this study we produced a new method for solving regular dierential equations with step size h and taylor series. this method analyzes a regular dierential equation with initial values and step size h. this types of equations include quadratic and cubic homogenous equations with constant coecients and cubic and second- level equations.

in this paper, the dierential transform method (dtm) is applied to the fisherequation. this method can be used to obtain the exact solutions of fisherequation. finally, we give some examples to illustrate the suciency of themethod for solving such nonlinear partial dierential equations. these resultsshow that this technique is easy to apply.

here, a new method called aboodh transform homotopy perturbation method(athpm) is used to solve nonlinear partial dierential equations, we presenta reliable combination of homotopy perturbation method and aboodh transformto investigate some nonlinear partial dierential equations. the nonlinearterms can be handled by the use of homotopy perturbation method. the resultsshow the eciency of this...

this paper describes an approximating solution, based on lagrange interpolation and spline functions, to treat functional integral equations of fredholm type and volterra type. this method can be extended to functional dierential and integro-dierential equations. for showing eciency of the method we give some numerical examples.

in this study, a new and ecient approach is presented for numerical solution offredholm integro-dierential equations (fides) of the second kind on unbounded domainwith degenerate kernel based on operational matrices with respect to generalized laguerrepolynomials(glps). properties of these polynomials and operational matrices of integration,dierentiation are introduced and are ultilized to r...

in this paper a numerical method for solving forth order fuzzy dierentialequations under generalized differentiability is proposed. this method is basedon the interpolating a solution by piecewise polynomial of degree 8 in the rangeof solution . we investigate the existence and uniqueness of solutions. finally anumerical example is presented to illustrate the accuracy of the new technique.