The variational ITERATION method (VIM) was extended to find approximate solutions of fractional chemical engineering equations. The Lagrange multipliers of the VIM were not identified EXPLICITly. In this paper we improve the VIM by using concept of fixed point ITERATION method. Then this method was implemented for solving system of the time fractional chemical engineering equations. The obtained approximate solutions are compared with the numerical results in the literature to show the applicability, efficiency and accuracy of the method.

Sadi is the master of easy but difficult word in Persian literature. The reason of his easiness and difficulty may be highly related to his poetry form. One of the clear stylistic specifications in his lyric is the syntactic ITERATION directly related to the grammar in one hand, and eloquence on the other hand. Syntactic ITERATION in Sadi lyric is mainly seen in a parallel, allegoric and mac=tching form. In lingual aspect, the most important specification of these lines is the ITERATION of word especially pronoun, preposition, conjunction and prefix adjective. According to the loveliness of his lyrics, the dominant content in these lines is description of beloved, lover and their relation.It is tried in this research that the lines of syntactic ITERATION in his lyric are studied stylistically in three domains of eloquence, language and content.

In this paper, we report the application of two parameter coupled alternating group EXPLICIT (CAGE) ITERATION and Newton-CAGE ITERATION methods for the cubic spline solution of non-linear differential equation u" = f (r, u, u') subject to given natural boundary conditions. The error analysis for CAGE ITERATION method is discussed in details. We compared the results of proposed CAGE ITERATION method with the results of corresponding two parameter alternating group EXPLICIT (TAGE) ITERATION method to demonstrate computationally the efficiency of the proposed method.

The present paper discusses implicit memory (compared to EXPLICIT memory) as a new phenomenon in memory research. First, ideas about implicit memory are considered very briefly from historical point of view. Then, as in recent studies, two lines of research are discussed; i.e., subliminal stimuli and repetition priming studies. These studies, especially priming studies, show that EXPLICIT memory are affected differently by various variables. While EXPLICIT memory tests are affected by the levels-of-processing and the interval between encoding and retrieval stages (forgetting effect), implicit memory tests are not affected. On the other hand, while implicit memory tests are sensitive to modality and mood changes, manipulated both at encoding and at retrieval, memory tests are unaffected. The findings related to amnesic patients are impaired with respect to EXPLICIT memory and are intact with respect to implicit memory.There are two theoretical explanations for this double dissociation between EXPLICIT and implicit memory. The processing view suggests that there is a single and integrated memory system and the discrepancy between EXPLICIT and implicit memory are explained the different natures of relation between encoding and retrieval processes or procedures. The multiple memory systems view, which is more promising and supported by empirical evidence, claims that each of these two types of memory is supported by an independent and separate system(s). Although these systems interact with each other, they follow different rules, however.

For an asymptotically non-expansive self-mapping T, we will prove the strong convergence of {xn} defined by xn+1 = (1−an−bn)xn+anu+bnTnxn, xn+1 = anu+(1−an)Tnxn, whenever {bn}, {an}Ì (0,1) satisfy (C1) limn®¥ an=0, (C2) S¥n=0 =¥ (C3) limn®¥ Kn-1/an = 0 or (C4) S¥n=0 (kn-1)<+¥ application, we also establish the strong convergence of the viscosity approximation schemes with a contraction ¦ given by xn+1 = anf (xn) + (1 −an)Tnxn and xn+1 = (1 −an− bn)xn+an f(xn) +bnTnxn.

In [1], introduce a modified variational ITERATION method (MVIM) for a special kind of nonlinear differential equations. In this paper, we consider variational ITERATION method (VIM) and MVIM (introduced in [1]) to obtain exact solution to Fisher’s equation. It is shown in this paper the application of VIM to Fisher’s equation leads to calculation of unneeded terms and more time consumed in repeated calculations for series solutions. Therefore, we use MVIM for Fisher’s equation to overcome these disadvantages.

The variational ITERATION method (VIM) has been applied to solve many functional equations, so far. In this paper the problem of conversion of three radioactive materials has been studied. By mathematical modeling of the problem a system of ordinary differential equations has been derived. The variational ITERATION method is applied to obtain exact solution of this system of ordinary differential equations.