Plant photosynthesis is considered to consist of photochemical reactions originating from 2 separate pigment systems. Fractionation of the 2 photochemical systems has been demonstrated only recently by detergent treatment of spinach chloroplasts followed by di fferential centri ftugation ( 1, 9). This study shows that the light and heavy fractions obtained by either digitonin or Triton X-100 tr...

in this paper, a new and ecient approach based on operational matrices with respect to the gener-alized laguerre polynomials for numerical approximation of the linear ordinary dierential equations(odes) with variable coecients is introduced. explicit formulae which express the generalized la-guerre expansion coecients for the moments of the derivatives of any dierentiable function in terms...

KLEIN is a family of lightweight block ciphers which proposed at RFIDSec 2011 by Gong et. al. It has a 64-bit state and 64, 80 or 96-bit key size which introduce its version. It uses 16 same 4-bit Sboxes combined with two AES’s MixColumn transformations for each round. This approach allows compact implementations of KLEIN in both low-end software and hardware. Such an innovative combination att...

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...

This paper deals with development and analysis of a fully discrete nite element method for a nonlinear di erential system for describing an air water system in groundwater hydrol ogy The nonlinear system is written in a fractional ow formulation i e in terms of a saturation and a global pressure The saturation equation is approximated by a nite element method while the pressure equation is trea...

Stochastic di erential games are considered in a non-Markovian setting. Typically, in stochastic di erential games the modulating process of the di usion equation describing the state ow is taken to be Markovian. Then Nash equilibria or other types of solution such as Pareto equilibria are constructed using Hamilton-Jacobi-Bellman (HJB) equations. But in a non-Markovian setting the HJB method i...

in this paper, the reduced dierential transform method is investigated fora nonlinear partial dierential equation modeling nematic liquid crystals, itis called the hunter-saxton equation. the main advantage of this methodis that it can be applied directly to nonlinear dierential equations withoutrequiring linearization, discretization, or perturbation. it is a semi analytical-numerical metho...

in this paper an approximate analytical solution of the fractional zakharov-kuznetsov equations will be obtained with the help of the reduced differential transform method (rdtm). it is in-dicated that the solutions obtained by the rdtm are reliable and present an effective method for strongly nonlinear fractional partial differential equations.

the purpose of this paper is to study the fuzzy fractional differentialequations. we prove that fuzzy fractional differential equation isequivalent to the fuzzy integral equation and then using this equivalenceexistence and uniqueness result is establish. fuzzy derivative is considerin the goetschel-voxman sense and fractional derivative is consider in theriemann liouville sense. at the end, we...