مجله بین المللی محاسبات و مدل سازی ریاضی
سال یکم شماره 4 (Autumn 2011)

The Scaling Law for the Discrete Kinetic Growth Percolation Model The critical exponent of the total number of finite clusters α is calculated directly without using scaling hypothesis both below and above the percolation threshold pc based on a kinetic growth percolation model in two and three dimensions. Simultaneously, we can calculate other critical exponents β and γ, and show that the scaling law α + 2β +γ = 2 has been held in the simulation result above the percolation threshold pc.

The unsteady flow of a visco-elastic Maxwell fluid through a rectilinear pipe having its cross-section as a parallelogram under the influence of a axial pressure gradient (I) varying linearly with time, and (II) decreasing exponentially with time has been discussed in the present paper. Variables separable and Laplace transform methods have been used to solve the problem.

In this paper, we have outlined the surrogate management framework for optimization of expensive functions. An initial simple iterative method which we call the “Strawman” method illustrates how surrogates can be incorporated into optimization to stand in for the most expensive function. These ideas are made rigorous by incorporating them into the framework of pattern search methods. The SMF algorithm is presented, including mesh definition, and choice of polling points. In summarizing the ideas of surrogate-based optimization, we enrich this paper with an admittedly simplistic analogy which helps to compare optimization strategies.

Two parties that conduct a business transaction through the internet do not see each other personally nor do they exchange any document neither any money hand-to-hand currency. Electronic payment is a way by which the two parties transfer the money through the internet. Therefore integrity of payment and order information of online purchase is an important concern. With online purchase the customer and merchant cannot be assumed to be completely honest or they can act to change either payment information or the order information. Pateria, Singh and Raghuwanshi proposed a new protocol model based on tree entities customer, merchant and the payment authority that can verify each other. Unfortunately, this protocol is not secure. In this paper, a new protocol is proposed based on elliptic curve Diffie-Hellman key agreement protocol which is secure. The security of our protocol depends on ECDLP and since the ECC is a suitable public key cryptosystem, this protocol can be replaced with another protocol.

Resource allocation and optimal leveling are among the top challenges in project management. This paper presents a DEA-based procedure for determining an optimal level of inputs to produce a fixed level of outputs. To achieve this goal, we assume that the levels of outputs can be forecasted in the next season and the procedure will determine optimal level of inputs for all DMUs. Such as some of them can only take integer values. So, after this design for the value of inputs and outputs all DMUs are placed on the optimal level. An illustrative example is used to show the applicability of the proposed method.

There are situations that Decision Making Units (DMU’s) have uncertain information and their inputs and outputs cannot alter redially. To this end, this paper combines the rough set theorem (RST) and Data Envelopment Analysis (DEA) and proposes a non-redial Rough-DEA (RDEA) model so called additive rough-DEA model and illustrates the proposed model by a numerical example.

New statistic based models provide a wide area of prediction equipments for different science areas. Among these fields biology have just entered the contest of interdisciplinary sciences. Drug discovery is a long and expensive process which could be decreased with theoretical approaches. In this study, 500 reported assayed anti cancer molecules were extracted from Science Direct articles, sketched, optimized with AM1 basis set with Gaussian, and analyzed for their bioactivities with PASS. Molecular and physicochemical descriptors such as MW, H Donor/Acceptor, LogP, Parachor, and etc of 15 screened compounds were calculated with Dragon and applied for Stepwise Multi Linear Regression process within SPSS. Calculations present that H Donor, H Acceptor, Polarizability, and Refractivity descriptors are the most impacting factors on emergence of antineoplastic activity with higher than 91% accuracy. A valid model is achieved which will be utilized for future molecule discovery and prediction.

In this paper we study Multiple periodic solutions for a class of non-autonomous and convex Hamiltonian systems and we investigate use some properties of Ekeland index.