Structure of runoff. rainfall mathematical model comprises of separation base flow discharge and determining infiltration, effective rainfall and direct runoff. These processes are calculated by various methods. Instantaneous unit hydro graph which Nash model in its index sample has considered as a conceptual model, applied widely in runoff. Rainfall models. Here, the author produces a conceptual mathematical model with some proposed methods for determining separation processes of baseflow infiltration, effective rainfall runoff and direct runoff. Non. Linear mathematical optimization is used for calculation of the model's parameters. Performance results of the model prove the superiority of the proposed method over the other common ones. For doing the research, both methods of artificial neural networks and mathematical optimization of instataneous unit hydrograph are used, because the artificial neural network only, requires a lot of information and the results may not always be obtainable, but an artificial neural network. mathematical optimization combination makes possible a quick convergence and assured results.

In this paper, modified laplace homotopy perturbation method(LHPM) is implemented to give approximate and analytical solutions of nonlinear ordinary differential equation systems model for HIV infection . Mathematical models have proven valuable in understanding the dynamics of HIV infection. By comparing these models to data obtained from patients undergoing antiretroviral drug therapy, it has been possible to determine many quantitative features of the interaction between HIV, the virus that causes AIDS, and the cells that are infected by the virus. We apply modified LHPM by setting a perturbation parameter and an embedding parameter as the damping parameter. Fourth-order Runge-Kutta method (RK4) is used to evaluate the effectiveness of the proposed algorithm. When we do not know the exact solution of a given problem, generally we use the RK4 method for comparison since it is widely used and accepted. Comparison of the results with RK4 method is confirmed that modified LHPM performs with very high accuracy. Results show that modified LHPM is a very promising method for obtaining approximate solutions to the model for HIV. The results validate the accuracy and efficiency of the proposed method for the approximate solution of the HIV infection model.

Algebraic hyperstructures have many applications in various sciences. The main purpose of this paper is to provide a new application of weak hyperstructures in Chemistry. The Motivation for the study of hyperstructures comes from chemical reactions. By hyperstructures theory, we provide mathematical models for chemical reactions. We study chemical hyperstructures of standard reduction potentials for consecutive oxidation states of elements of Cm; Er; Pm; Mg; Tm; Au and Cf.

The survey of effective factors on rainfall-Runoff relations cause to improve Mathematical models to analysis that phenomena. For this reason, first of all at 80 experimental plots the correlation matrices among runoff coefficient and some other environmental factors conclude from the topography: plot's length and slop percentage, from the soil: clay, silt, sand all percentage, EC, pH, Strength coefficient, gravel percentage and sum of gravel and litter percentage and from the vegetation cover: canopy and organic matter have been surveyed. In the next step at 77 and after 75 plots two rainfall single events with duration of more than 24h and average intensity of 1.5 mm/h selected and mathematical model of accumulated infiltration with relation to plot's length based on regression prepared. After, the prepared model tested by a group of plots with equal condition except length and rainfall depth of 38.2 and 34.8mm. The result is that by increasing the plot's length the accumulated infiltration depth added but the intensity of effectiveness of plot's length on accumulated infiltration depth decrease with increasing length of plot and finally after nearly 22m length the variation of the curve of accumulated infiltration depth with plot's length roughly convert to a linear variation with light gradient.

This paper is aimed to develope a mathematical model for sustainable forest development by strategic landuse planning. Such plans are naturally multi purpose so that multi-criteria optimization is utilized for modeling. The objective functions are: Maximization of carbon sequestration, net present value of income, stand volume, employment generation and minimization of soil erosion. Lp-norm is used to aggregate the objectives. The model is implemented for Caspian forest in Ramsar. Sensitivity analysis is made by different norms and weights.

Background and objective One of the most important goals of the crisis management headquarters is the proper preparation and distribution of food to the affected people during a disaster. Due to the limitations related to shelf life and storage of perishable food products, operational costs, and transportation, their distribution is challenging. In this study, we aim to develop a mathematical model using integer linear programming for the optimization of cold food supply chain during disasters.  Method This study uses an operational research approach. A two-objective mixed integer linear programming model was designed for a cold, stable and multi-level supply chain in the food industry in the conditions of uncertainty and crisis. In this programming model, the economic order quantity (EOQ) performance optimization method was used to determine the optimal order point. The presented model was solved based on the real data obtained from the crisis management headquarters in Iran and implemented as a pilot for 16 supply centers, 5 distribution channels, and 35 crisis management headquarters with two LP-metric and augmented epsilon constraint (AEC) methods. Results The findings of testing research hypotheses using one-way analysis of variance showed that the use of mathematical models had a positive and significant effect on the optimization of the cold food supply chain during disasters. In this regard, there was no significant difference between LP-metric and AEC methods (P>0.05). Also, the use of mathematical models had a positive and significant effect on improving the quality of food industry. Optimizing the supply chain by the mathematical model has a positive and significant effect on the performance of food industries. The optimal order point in the chain model had a EOQ of 3436 units. Conclusion By using the presented mathematical model, it is possible to optimize the management process of the cold food supply chain during disasters. It has a higher performance compared to traditional approaches. It is expected that by using the presented mathematical model, relief operations and food distribution during disasters can be facilitated and optimized.

Meandering rivers are among the most dynamic features on earth's surface. A meandering river exhibits progressive change in position as it migrates across its floodplain. The planform dynamics of meandering rivers result from the interactions among flow, sediment transport, and evolving channel morphology that collectively scale with planform curvature. The view that planform curvature has a major influence on the rate and character of meander migration is supported by field observations and theoretical considerations. Morphological river changes (bed topography and/or plane-shape changes) occur as result of natural and/or of human interventions so that alluvial meandering streams strive to achieve an equilibrium configuration. As documented by many experimental and theoretical works the plane shape of a meander wave is the result of the complex interplay flow pattern-bed deformation bank erosion. The geometric shape of the meander wave gives rise to a complicated flow field which, in turn, modifies the bed topography and reshapes the meander wave through the bank erosion. In fact, in nature, different meandering streams exhibit different geometric characteristics so that the stream conditions may vary from one meander loop to another. Thus, many laboratory and field studies, apart numerical researches show that the evolution of a meander wave is mainly governed by the bed deformation that drives the erosion process at the channel banks. Particularly, outer-banks are considerably vulnerable to erosion processes. On the other side, the evaluation of the bank erosion and the consequent migration of meandering rivers are fundamental, both because of hazards associated with them and because of their effects in riparian ecosystem dynamics. The modeling of meandering-river migration requires the simulation of the following processes: hydrodynamics, sediment transport, bed morphodynamics, and bank erosion. Furthermore, in this paper plane form of a meander wave was determined by the mathematical model. Under the conditions prevailing in natural streams, the channel centerlines follow sine-generated curves, with an assumed steady-state turbulent and subcritical flow, of large width-to-depth ratio and small Froude number. The plane deformation of the channel was caused by the action on the banks of the convective vertically-averaged meandering flow. It has to be pointed out and as it is well known that, the regime development of the flow width goes much faster than that of the channel slope. Therefore, in this model the regime development of slope (i. e., the loop expansion), a nearly constant flow width was assumed, which can be identified as the regime width. Accordingly, in this article, the flow width (with as the flow depth) was assumed to be constant along the channel length. Since the width-to-depth ratio was large, the effect of the cross-circulation was negligible. In overall, the channel deformation, as the result of both channel down valley migration and lateral expansion, is entirely due to the action of the convective vertically-averaged meandering flow. The growth (expansion and expansion) of meander loops is attributed to the regime-trend the loops continually grow in their amplitude (i. e., their length increases) and thus the channel slope progressively decreases to the regime state. This model was able to predict the migration and expansion of meander loops. The following computational procedure was adopted to determine the migration and expansion speed of the meander loop under various values of the deflection angle along the channel centerline. (1) Set regime channel conditions, (2) Compute of meandering channel lengths, (3) Calculate regime slope, (4) Compute water depth, (5) Compute the average specific volumetric sediment transport rate (sediment transport is assumed to be the only bed-load in this article), (6) Compute the angle between the streamline and the coordinate line, (7) Compute the migration speed of meander loops and (8) Compute the expansion speed of meander Loops. The model was then applied to a sine-generated meandering channel and the migration and expansion component of bank speed deformation was calculated. Modeling results showed that, for small deflection angle migration was the main deformation in the meandering channels, on the other hand, for large deflection angles both migration and expansion became smaller in the meandering channels. Furthermore the effect of deflection angle along the channel centerline and channel-averaged specific volumetric sediment transport rate, have been proposed by model. The result showed that the specific volumetric sediment transport rate had significant effect on channel migration and expansion rates.