In this paper we introduce two Algorithms, the first Algorithms when it is odd order and how we calculate magic square and rotation for it. The second Algorithms when it be even order and how to find magic square and rotation for it.

In this paper we present a new method for solving fully fuzzy multi-objective linear programming problems and find the fuzzy optimal solution of it. Numerical examples are provided to illustrate the method.

Essential approaches involving photons are among the most common uses of parallel optical computation due to their recent invention, ease of production, and low cost. As a result, most researchers have concentrated their efforts on it. The Basic Arithmetic Unit BAU is built using a three-step approach that uses optical gates with three states to configure the circuitry for addition, subtraction, and multiplication. This is a new optical computing method based on the usage of a radix of (2): a binary number with a signed-digit (BSD) system that includes the numbers -1, 0, and 1. Light with horizontal polarization (LHP) (↔), light with no intensity (LNI) (⥀), and light with vertical polarization (LVP) (↨) is represen

The problem of non-Darcian-Bènard double diffusive magneto-Marangoni convection   is considered in a horizontal infinite two layer system. The system consists of a two-component fluid layer placed above a porous layer, saturated with the same fluid with a constant heat sources/sink in both the layers, in the presence of a vertical magnetic field.   The lower porous layer is bounded by rigid boundary, while the upper boundary of the fluid region is free with the presence of Marangoni effects.  The system of ordinary differential equations obtained after normal mode analysis is solved in a closed form for the eigenvalue and the Thermal Marangoni Number (TMN) for two cases of Thermal Boundary Combinations (TBC); th

In many applications such as production, planning, the decision maker is important in optimizing an objective function that has fuzzy ratio two functions which can be handed using fuzzy fractional programming problem technique. A special class of optimization technique named fuzzy fractional programming problem is considered in this work when the coefficients of objective function are fuzzy. New ranking function is proposed and used to convert the data of the fuzzy fractional programming problem from fuzzy number to crisp number so that the shortcoming when treating the original fuzzy problem can be avoided. Here a novel ranking function approach of ordinary fuzzy numbers is adopted for ranking of triangular fuzzy numbers with simpler an

In this paper we give many connections between essentially quasi-Dedekind (quasi-
Dedekind) modules and other modules such that Baer modules, retractable modules,
essentially retractable modules, compressible modules and essentially compressible
modules where an R-module M is called essentially quasi-Dedekind (resp. quasi-
Dedekind) if, Hom(M N ,M )  0 for all N ≤e M (resp. N ≤ M). Equivalently, a
module M is essentially quasi-Dedekind (resp. quasi-Dedekind) if, for each
f End (M) R  , Kerf ≤ e M implies f = 0 (resp. f  0 implies ker f  0 ).

With the increasing rate of unauthorized access and attacks, security of confidential data is of utmost importance. While Cryptography only encrypts the data, but as the communication takes place in presence of third parties, so the encrypted text can be decrypted and can easily be destroyed. Steganography, on the other hand, hides the confidential data in some cover source such that the existence of the data is also hidden which do not arouse suspicion regarding the communication taking place between two parties. This paper presents to provide the transfer of secret data embedded into master file (cover-image) to obtain new image (stego-image), which is practically indistinguishable from the original image, so that other than the indeed us

The aim of current study is estimate the ability of low cost adsorbents, which consist of extracted silica from rice husk ash in treatment of Industrial waste water that contains heavy metals (Cd, Co and Pb) with other pollutants by fixed filters technique with determine the best method for that, and study the effect of a number of variables and parameters. This study involved one waste water samples were collected from. State battery manufacturing company (SBMC) (before treatment unit) at 5th and 22th, of the January 2015. Adsorption tests showed that all tested adsorbent materials had a significant heavy metal removal efficiency. pH values showed a significant impact on adsorption process, but best removal efficiency occurred at pH 4.5

Let R be a ring with identity and M be a right unitary R-module. In this paper we
introduce the notion of strongly coretractable modules. Some basic properties of this
class of modules are investigated and some relationships between these modules and
other related concepts are introduced.