Applied Mathematics

Fully developed laminar mixed convection of permeable couple stress fluid in a vertical channel has been investigated analytically in the presence of heat generation or absorption. Uniform wall temperatures with asymmetric and symmetric heating have been considered. An analytical solution has been developed by using perturbation technique. Results are depicted graphically on the flow for different values of couple stress parameter, porous parameter, mixed convection parameter and heat generation or absorption coefficient. The results show that the flow reversal occurs near the walls of the channel for sufficiently large value of the ratio of Grashof number and Reynolds number.

In this paper we have investigated the steady plane Couette flow of viscous incompressible fluid between two porous parallel plates through porous medium with magnetic field. We have studied the velocity, average velocity, shearing stress, skin frictions, the volumetric flow, drag coefficients and stream lines.

Unsteady MHD flow through porous medium past an impulsively started inclined plate with variable temperature and mass diffusion in the presence of Hall current is studied here. The fluid considered is gray, absorbing-emitting radiation but a non-scattering medium. The Governing equations involved in the present analysis are solved by the Laplace-transform technique. The velocity profile is discussed with the help of graphs drawn for different parameters like thermal Grashof number, mass Grashof Number, Prandtl number, Hall current parameter, permeability parameter, magnetic field parameter and Schmidt number, and the numerical values of skin-friction have been tabulated

A parametric mean length is defined as the quantity , Where This being the useful mean length of codewords weighted by utilities,  Lower and upper bounds for are derived in terms of ‘useful’ information measure.

Akaike information criterion, AIC is widely used for model selection. The AIC as the estimator of asymptotically unbias for the second term Kullbake-Leibler risk considers the divergency between true model and offered models. The AIC, is an inconsistent estimator. In this article the proposed approach the problem the inconsistency of AIC, it is the use of consistent offered information criterion, called M1IC (Masumeh information criterion). At the end of these two information criteria of model selection of classic and linear models have been considered by the simulation of Monte-Carlo.

In this article, the phenomenon of fingero-imbibition in a particular displacement method concerning two immiscible fluids through a dipping homogeneous porous media with a magnetic field effect has been discussed analytically under certain conditions. This phenomenon provides a nonlinear partial differential equation as a governing equation, which can be solved by Homotopy Perturbation Sumudu transform method (HPSTM). The numerical and graphical results are discussed using MATLAB.

In this paper fuzzy soft connectedness on fuzzy soft topological spaces are defined. Some related properties regarding the newly defined concepts are proved.

In this work, the Adomian decomposition (ADM) and Picards Iterative Methods were used to solve nonlinear ordinary differential equations analytically and numerically using the Trapezoidal rule approach, and the results are compared for accuracy and rate of convergence. Though a little modification by the use of contraction principle was made to the Picard Iteration Method in order to accelerate the convergence of the method it was found out that the ADM converges faster than the Picard’s method.

The proof will demonstrate the non-existence of a 3x3 magic square of squares. I remember reading a Scientific America article and at the bottom of the article was the link to an article which described this problem. To me it seemed bizarre that a problem that had such a clear start point and was based on a concept so simple to understand could have no proof. I decided then that I would prove that such a square could never exist. I was inspired that the problem had been unresolved such it was first asked in 1984 and that it could be dated back to great mathematicians such as Leonhard Euler. Like many people interested in maths I am in awe of much of the the work that Leonhard Euler did so to be able to solve a problem whose roots can be traced back to him was exciting. People have been working with magic squares for centuries and yet nobody has presented a proof showing why a 3x3 magic square comprised entirely of square numbers cannot exist. I decided that night that I would provide such a proof. I was unaware how complex the problem was and how complex the tools I would need to solve the problem were but it was the start of the most wonderful journey that I wish I could relive. For hundreds of years people have been constructing magic squares. The definition of a magic square which I will refer to extensively throughout this proof states the following. The sum of all the elements in the rows, columns and diagonals must be equal. Each element must be unique in any square and must be a natural number. Therefore when I say something has been proven false through the defintion of a magic square this is the definition I am referrring to. Well reading an article in Scientific America I came across something that rather astounded me. The article claimed that no one had found an example of a 3x3 magic square that contains only magic square numbers. Furthermore no onw has proven that such a square cannot exist. This type of problem can be traced back all the way to Leonhard Euler who is the first person known to construct a 4x4 magic square of squares. I have always been fascinated in mathematical mysteries as the world is written in the mathematics to understand mathematics is to understand the world. Therefore by proving something in maths I am making the world a little more interesting. In the proof that follows I will show why a 3x3 magic square of squares can never exist. I will do this in 10 parts. The first part will be a general proof as to why the lowest element must be the middle or the corner for any magic square of squares to exist. I will then show that the lowest element can never occupy the middle or the corner of any square without violating the definition of what a magic square is.

Traditional economic production / order quantity (EPQ/EOQ) models make various simplifying assumptions in order to arrive at a closed form solution for the optimal lotsize in a production facility. The assumption of fixed unit cost in EOQ / EPQ models has also been tackled by many researchers. For example, Cheng (1991) formulated a problem where production cost is affected by both the product’s demand and the process reliability. Lee (1994), by formulating the unit cost on a function of the order quantity, took the economies of scale into account. Quality level of the product and specifications of the adopted manufacturing process also affect the unit product’s cost. Therefore, in this paper we consider a profit maximizing firm who wants to jointly determine the optimal lotsizing, pricing and marketing decisions along with manufacturing requirements in terms of flexibility and reliability of the process. The objective is to determine the optimal order lotsize to maximize the total profit by employing the type of fuzzy numbers which are triangular. We propose two fuzzy inventory model in which first model with fuzzy reliability level and second model with fuzzy reliability level and second model with fuzzy reliability and fuzzy economic production quantity (EPQ) is presented. For ech case we employ the signed distance, a ranking method for fuzzy numbers, to find the estimate of total profit per unit time in the fuzzy sense and then derive the corresponding optimal lotsize. Numerical examples are provided to illustrate the results of proposed models.