జర్నల్ ఆఫ్ అప్లైడ్ & కంప్యూటేషనల్ మ్యాథమెటిక్స్

In this paper, we consider a type of space fractional advection-dispersion equation, which is obtained from the classical advection-diffusion equation by replacing the spatial derivatives with a generalized derivative of fractional order. Firstly, we utilize the modified weighted and shifted Grunwald difference operators to approximate the Riemann-Liouville fractional derivatives and present the finite volume method. Specifically, we discuss the Crank-Nicolson scheme and solve it in matrix form. Secondly, we prove that the scheme is unconditionally stable and convergent with the accuracy of O(τ2 + h2). Furthermore, we apply an extrapolation method to improve the convergence order, which can be O(τ4 + h4). Finally, two numerical examples are given to show the effectiveness of the numerical method, and the results are in excellent agreement with the theoretical analysis.

The invasive species model describes the connections between three species: People, trees and rats. In 2008, Basener, Brooks, Radin and Wiandt presented an article in that, they created a mathematical model for such dynamical system. In this work we changed the model and investigated the equilibrium points and stability of the invasive species model with harvesting. We have shown that the system has a conditionally stable equilibrium point, in this case the three populations live together. We made numerical simulations, too, and saw the amount of the rats decrease because of the harvesting.

Purpose: The paper aims to find the convergence control parameter region for an unsteady three dimensional Navier-Stokes equations of flow between two parallel disks by using Homotopy Analysis Method. Findings: The region and value of the convergence control parameter has been found.

Most of rural population in developing countries depends on the biomass energy for cooking and heating purposes. Women in this sector spend large part of their daily time in the kitchen cooking the food and suffering from the contaminants emitted from the biomass cook stoves. This study focuses on the numerical modeling of indoor air pollutant in a single room Nepali kitchen by solving the Navier-Stokes equations to analyze velocity profile and temperature distribution throughout different sections of the kitchen to depicted the pollutant paths. The study explored the fluid flow profile, temperature profile based on the changing parameters such as inlet velocity, number and position of ventilation proper positioning of the ventilation to minimize the effect of pollutant to the person working in the kitchen.

The investigation has been carried out to view the effect of rainfall in soils. The non-uniformly motion has been considered. The raindrop affects the soil dynamics and generates fracture. The Pressure head analysis, water content distribution, raindrop affect with various time domains has been done with Matlab. A proper case study has been done by taking sandy loam. Total head, effect on concentration, velocity profile (fluid motion in soil) can be viewed. The run off rate has also been calculated for different rainfall. The estimated analysis of rainfall on infiltration process has been shown graphically as well as in table.

Systematization of knowledge about multiple regression: the withdrawal of the regression equation 1) Through a system of normal equations and 2) Matrix method; solution 1) Using packet analysis EXCEL, 2) Matrix calculator and "matrix arithmetic"; 3) Solution in MATLAB as the normal equations, and directly – matrix method; controversy about the statistical reliability - University of Vladivostok against the University of Indiana; graphical and tabular analysis of residues; concluded by differentiating the normal equations; Study regression with z-statistics and graphs standard normal probability.

The main aim of the present paper is to introduce the concept of lacunary almost statistical convergence and strongly almost convergence of the generalized difference sequences of Fuzzy numbers. We also investigate their some basic topological properties.

A steady-state three-dimensional mathematical model for the dispersion of pollutants from a continuously emitting ground point source in moderated winds is formulated by considering the eddy diffusivity as a power law profile of vertical height. The advection along the mean wind and the diffusion in crosswind and vertical directions was accounted. The closed form analytical solution of the proposed problem has obtained using the methods of Laplace and Fourier transforms. The analytical model is compared with data collected from nine experiments conducted at Inshas, Cairo (Egypt). The model shows a best agreement between observed and calculated concentration.

The magnetohydrodynamic (MHD) stability of oscillating fluid with longitudinal magnetic field has been discussed. The problem is formulated and the (MHD) basic equations are solved. By using the computer procedure from different values of the acting magnetic field the stable and unstable regions are identified. This phenomenon is interest, academically and during the geological drilling in the crust of the earth as we have superposed gas-oil layer mixture fluids. A general eigenvalue relation is derived studied analytically and results are confirmed numerically. The oscillating liquid has stabilizing tendency, in the absence of the effect of the electromagnetic field in the liquid and gas cylinder region, so the model is only subject to the capillary force. It has been found that the model is unstable in the region 0 < x < 1, while it is stable in the region 1 ≤ x < ∞ where x is the longitudinal dimensionless wave number. This means that the model is just unstable in small domains of axisymmetric perturbation but it stables in all domains. For very high intensity of magnetic field the model is completely stable for all values of wavelengths. The capillary force is destabilizing only in a small axisymmetric domain while it is stabilizing in all other axisymmetric perturbations. The stability behavior of the model comes after destabilizing behavior of the model when it be reduced and suppressed.

We give in this work the sufficient conditions on the positive solutions of the difference equation 8 1 1 n n n n x x x x α − + = + , n=0,1,…., where α ≥ 0 and s > 0 with arbitrary positive initials x-1; x0 to be bounded and the equilibrium point to be globally asymptotically stable. Finally we present the condition for which every positive solution converges to a prime two periodic solution. We have given a non-oscillatory positive solution which converges to the equilibrium point.

In this paper we propose two problems which related to fractional Brownian motion. First problem- simultaneous estimation of two parameters-Hurst exponent and the volatility, that describes this random process. Numerical tests for the simulated fBm provided an efficient method. Second problem- approximation of the increments of observed time series with power function by increments from the fractional Brownian motion. Approximation and estimation have shown on the example of real data- daily deposit interest rates.

The cohesive crack model has demonstrated its accuracy in the simulation of crack growth phenomena in concrete structures. Moreover, the Boundary Element Method (BEM) is recognised as a robust and efficient numerical technique for addressing fracture problems. In this context, the present study aims at coupling the cohesive crack model to a BEM formulation to simulate the mechanical behaviour of cracked concrete structure. The cohesive cracks are modelled mechanically through the sub-region BEM approach. Because the tractions values along the fractured interfaces depend on the crack opening displacements, this problem is solved in the context of nonlinear solutions. The nonlinear system of equations is solved using the Tangent Operator (TO) technique, in which tangent prevision and tangent correction steps are required. Such scheme assures better convergence and accuracy than the classical Newton approach. The determination of the TO terms is the main contribution of this study. To validate the proposed formulation, it was applied in the simulation of crack growth in concrete structures. The results achieved were compared to numerical and experimental responses available in the literature. Apart from the strong agreement among the results obtained, faster convergence was verified using TO instead of the classical scheme.

The article proposes some analytical considerations about the 3d algebra, and the possibilities of an extension in 3d of some standard 2d analytical functions. It takes also in consideration some problems about the derivative and the integrals.

Even apart from the instability due to speculation, there is the instability due to the characteristic of human nature that a large proportion of our positive activities depend on spontaneous optimism rather than mathematical expectations, whether moral or hedonistic or economic. Most, probably, of our decisions to do something positive, the full consequences of which will be drawn out over many days to come, can only be taken as the result of animal spirits—a spontaneous urge to action rather than inaction, and not as the outcome of a weighted average of quantitative benefits multiplied by quantitative probabilities.

Physical and numerical descriptions related to the heat transfer phenomenon inside the multilayer nanomaterial of thin film are determined. The mathematical model, of a multilayer of thin film of tin dioxide that deposits on a composite substrate of Silicon Dioxide/Silicon, is studied and solved by two numerical techniques, by taking into account the variability of the thermal conductivity. The two main interests in this study are the determination of the value of the applied maximum temperature on the multilayer nanomaterial, and the analysis, of the effect of the porosity medium that exists between certain layers, on the heat transfer. In plus, in order to determine our system physical parameters, the influence of the thickness of the thin deposit film is studied and the numerical model, which estimates these values in the heterojunction device, is analyzed.

Duality assertions are very important in optimization from the theoretical as well as from the numerical point of view. So this paper presents duality of multiobjective rough convex programming problems in rough environment when the multiobjective function is deterministic and roughness is in feasible region. Also it discussed the duality when roughness in multiobjective function and the feasible region is deterministic. The concepts and some theorems of duality in the rough environment are discussed. Also, the procedure of solution of these kind of problems described.

In this paper we study the Diophantine equation 1+5x2=3yn.

Combined heat and mass transfer on mixed convection non-similar flow of electrically conducting nanofluid along a permeable vertical plate in the presence of thermal radiation is investigated. The governing partial differential equations of the problem are transformed into a system of non linear ordinary differential equations by applying the Sparrow–Quack–Boerner local non-similarity method (LNM). Furthermore, the obtained equations are solved numerically by employing the Fourth or fifth order Runge Kutta Fehlberg method with conjunction to shooting technique. The profiles of flow and heat transfer are verified by using five types of nanofluids of which metallic or nonmetallic nanoparticles, namely Copper (Cu), Alumina (Al2O3), Copper oxide (CuO), silver (Ag) and Titanium (TiO2) with a water-based fluid. Rosseland approximation model on black body is used to represent the radiative heat transfer. Effects of thermal radiation, buoyancy force parameters and volume fraction of nanofluid on the velocity and temperature profiles in the presence of suction/injection are depicted graphically. Comparisons with previously published works are performed, and excellent agreement between the results is obtained. The conclusion is that the flow fields is affected by these parameters.

Ant Colony Optimization is a new meta-heuristic technique used for solving different combinatorial optimization problems. ACO is based on the behaviors of ant colony and this method has strong robustness as well as good distributed calculative mechanism. ACO has very good search capability for optimization problems. Travelling salesman problem is one of the most famous combinatorial optimization problems. In this paper we applied the ant colony optimization technique for symmetric travelling salesperson problem. Analysis are shown that the ant select the rich pheromone distribution edge for finding out the best path.

Einstein was convinced that solutions to the epistemological problems of quantum theory could be found in a grand unified field theory. Hidden variable theory considers the behavior of a system in terms of parameters that have been inaccessible to experiment, while such variables later become manifest through applications of new experimental technologies. Jacobson Resonance theory may satisfy Einstein’s conclusory belief that an attempt must be made to find a purely algebraic theory for the description of reality. The hidden variable required to explain the disparate elements in both general relativity and quantum theory may well be the biological model. Only a biological system can amplify the weak triggers of gravitons by a factor of 1040; to reveal the effect of a single system on a coordinated multifactorial complex array of total systems, through electrophysiological changes, e.g., from nonionizing radiant energy in the PicoTesla range and even weaker, down to an attogauss. The equation, Mc2=BvLq has yielded basis for inertial electromagnetic induction, connecting the phonon field and photons, and space and matter. It explains the associated conjunction of natural phenomena through a string theory analog, wherein the plethora of subatomic particles are but different vibrational states of strings. Unification comes simply from the harmonies and grand orchestrations of nature, and may well include spin-2 gravitons (gravity waves). It appears logical to extrapolate the generic formulation as: 2 2 2 . . 1 → → → − − ∂ ∂ = ∇    −    ∮ x∮ J c mcL dL j S L v r q v c Selected experimental outcomes are referenced for empirical support of said hypothesis.