In this paper, we have analyzed a MATHEMATICAL MODEL for the study of interaction between tumor cells and oncolytic viruses. The MODEL is analyzed using stability theory of differential equations. We gain some conditions for global stability of trivial and interior equilibrium point.

This paper presents an exact MODEL for the resource investment problem with generalized precedence relations in which the minimum or maximum time lags between a pair of activities may vary depending on the chosen modes. All resources considered are renewable. The objective is to determine a mode and a start time for each activity so that all constraints are obeyed and the resource investment cost is minimized. Project scheduling of this type occurs in many fields for instance, construction industries. The proposed MODEL has been inspired by the packing problems. In spite of the fact that it needs a feasible solution to start for conventional MODELs, the new MODEL has no need for a feasible solution to startup with. Computational results with a set of 60 test problems have been reported and the efficiency of the proposed MODEL has been analyzed.

According to cancer’ s global statistics, there will be 27. 5 million new cases of cancer each year by 2040, therefore, it is crucial to achieve a deeper understanding of the cancer progression mechanisems and immune system functions in response to it. Nowadays, computational MODELs are widely used to capture dynamics of the tumor-immune system (TIS). The proposed MODEL on this manuscript is on the basis of the ordinary differential equations which mechanistically MODELs the interactions of tumor cells, CTLs, NKs and MDSCs. CTLs and NK cells are the most important cells of adaptive and innate immune system, respectively that encounter with tumor cells, while MDSCs as immature immune cells suppress the immune responses in the inflammatory environments. Due to the error of the in-vivo/in-vitro experiments, vagueness, imprecise information, incomplete data and natural variability of the tumor-immune system emerges between different individuals, the kinetic parameters of computational MODELs are uncertain that this uncertainty can be captured by fuzzy sets. Hence, we assign fuzzy numbers with triangular membership functions instead of crisp numbers to some kinetic parameters of the tumor– immune system MODEL. In fact, the uncertainty in the kinetic parameters of the ordinary differential equations affects the dynamic of the system species. In this essay, for the first time, a fuzzy number has been used to MODEL the uncertainty of the parameters of the ODE MODEL. Our data reveals that increasing/decreasing the uncertainty region of the MODEL's fuzzy parameters increases/decreases the uncertainty region of dynamics of species. Furtheremore, the simulations of the MODEL in the crisp setting of parameters show that the repition of 5-FU treatment for inhibition of MDSCs dramatically inhibits tumor cells and eradicate tumor.

With increasing competition in the business world and the emergence and development of new technologies, many companies have turned to integrated production and distribution for timely production and delivery at the lowest cost of production and distribution and with the least delay in delivery. By increasing human population and the increase in greenhouse gas emissions and industrial waste, in recent years the pressures of global environmental organizations have prompted private and public organizations to take action to reduce environmental pollutants. This paper presents a nonlinear mixed integer MODEL for the production and distribution of goods with specified shipping capacity and specific delivery time for customers. The proposed MODEL is applicable to flexible production systems; it also provides routing for the means of transportation of products, as well as the reduction of emissions from production and distribution. The MODEL is presented, and then by MATHEMATICAL linearization is transformed into a mixed integer linear MODEL. The data of a furniture company is used to solve the linear MODEL, and then the linear MODEL with the company data is solved by CPLEX software. The numerical results show that as costs increase, delays are reduced and consequently, customer satisfaction increases, and as costs increase the air pollution decreases.

One of the most important parameters in designing grout mixtures is to determine type and size of the existing particles in the grout admixtures which are directly related to the size, shape and geometric configurations of the soil particles to be grouted. Generally, the ratio of the smallest soil particles to the largest cement particles in the grout admixtures is defined as the groutability ratio. To date, groutability ratios are mainly determined via experimental results and/or empirical equations. However, in order to properly analyze soil groutability, it is important to develop analytical methods to account for the most effective and determinative parameters. In this paper, a new MATHEMATICAL approach is developed to compute the effective voids diameter and also to determine the smallest effective diameter of voids that may exist among soil particles which can be used to classify the quality of grouting performance.

A novel MATHEMATICAL MODEL has been developed to aid the formulation of emulsion explosives. This MATHEMATICAL MODEL calculated heat of explosion, oxygen balance and raw material cost as a function of explosive ingredients, and the solution of the MATHEMATICAL MODEL was obtained by a MS Excel program. The effects of the different content of NH4NO3, NaNO3, H2O, and span-80 and composite fuel oil on the heat of explosion and the specific volume of emulsion explosive were discussed based on the proposed MATHEMATICAL MODEL. The results show that (1) with the increasing of the content of NH4NO3, the heat of explosion and the specific volume increase. (2) The better content of NaNO3, H2O and Span-80 in the formulation of emulsion explosive are 7%~9%, 9%~10%, 1.5%~2% respectively, and this formulation results in an oxygen balance of zero or close to zero.

In this paper, a new competitive location problem for a chain is considered. The owner of the chain can offer a variety of products. The objective of the MODEL is to determine both the location of new facilities and the optimal product type for each opened facility. The patronizing behavior of the customers is based on Hu rule and the location of new facilities is selected from a set of potential sites. As a result, the proposed MODEL is a nonlinear integer programming problem and for solving it, the problem is reformulated as a mixed integer linear programming one. Therefore, a standard optimization solver can be used for obtaining the optimal solutions to small-and medium-size problems. To cope with large-size problems, we develop two methods: 1) a heuristic method for a special case and 2) a hybrid heuristic- re y algorithm for general cases. By using the proposed MODEL, it is numerically shown that in multi-product industries in which the owner of the facilities is able to offer different types of products, in addition to the optimal location, it is necessary to determine the best products. At the end, a real-world case study for locating a new bakery is presented.

Regarding the importance of competitive advantages among the transportation systems, improving the costumer’ ssatisfaction is an important factor in attracting them to these systems. In this research, we focus on the effects of constructingnew stations on users and a new MATHEMATICAL MODEL is proposed for this problem. In the proposed MODEL, two simultaneous effects on customers by constructing new stations are investigated. One effect is the improvementof the demand access to the railway network and the other one is related to the increase in the travelling time forcustomers sitting in the train. As the first effect, the less the customer’ s distance to the stations, the more attractiveto use this system and the second effect concerns the increased in the traveling time in new stops which may resultto customer’ s dissatisfaction. The proposed MATHEMATICAL MODEL achieves the time optimality, furthermore; it maximizesthe covered population to locate the stations. For locating the optimal site for new stations, we need to applythe population usage information. The proposed MODEL is examined on the Mashhad’ s subway as a case study and theresults are reported.

In Iran, oil products are the most valuable export, 30% of which (Crude Oil) is used domestically every year. Countries like Iran depend heavily on oil revenues. One of the main sectors for consumption of crude oil in Iran is the transportation Industry. This paper aims to measure and estimate fuel productivity in land transportation in Iran using available data from 1973-2003. The function of fuel productivity is estimated using time series analysis, and the co integration with stationary variables have been accounted and analyzed. At this stage, initially the co-integration variables of the MODEL are known, and then, the structure of the MODEL and the number of optimal orders are identified. The next step however, determines the number of co-integration vectors of the MODEL which eventually with some restrictions estimate the fuel productivity function within the land transportation sectors e.g. rail and road.