In this paper, we introduced module that satisfying strongly -condition modules and strongly -type modules as generalizations of t-extending. A module  is said strongly -condition if for every submodule of  has a complement which is fully invariant direct summand. A module   is said to be strongly -type modules if every t-closed submodule has a complement which is a fully invariant direct summand. Many characterizations for modules with strongly -condition for strongly -type module are given. Also many connections between these types of module and some related types of modules are investigated.

In this paper, the series solutions of a non-linear delay integral equations are considered by a modified approach of homotopy analysis method (MAHAM). We split the function   into infinite sums. The outcomes of the illustrated examples are included to confirm the accuracy and efficiency of the MAHAM. The exact solution can be obtained using special values of the convergence parameter.

This paper deals with an analytical study of the flow of an incompressible generalized Burgers’ fluid (GBF) in an annular pipe. We discussed in this problem the flow induced by an impulsive pressure gradient and compare the results with flow due to a constant pressure gradient. Analytic solutions for velocity is earned by using discrete Laplace transform (DLT) of the sequential fractional derivatives (FD) and finite Hankel transform (FHT). The influences of different parameters are analyzed on a velocity distribution characteristics and a comparison between two cases is also presented, and discussed in details. Eventually, the figures are plotted to exhibit these effects.

Nowadays, a very widespread of smartphones, especially Android smartphones, is observed. This is due to presence of many companies that produce Android based phones and provide them to consumers at reasonable prices with good specifications. The actual benefit of smartphones lies in creating communication between people through the exchange of messages, photos, videos, or other types of files. Usually, this communication is through the existence of an access point through which smartphones can connect to the Internet. However, the availability of the Internet is not guaranteed in all places and at all times, such as in crowded places, remote areas, natural disasters, or interruption of the Internet connection for any reason. To create a

The heat and mass transfer coefficients of the indirect contact closed circuit cooling tower, ICCCCT, were investigated experimentally. Different experiments were conducted involving the controlling parameters such as air velocity, spray water to air mass flow rate ratio, spray water flow rate, ambient air wet bulb temperature and the provided heat load to investigate their effects on the performance of the ICCCCT. Also the effect of using packing on the performance of the ICCCCT was investigated. It was noticed that these parameters affect the tower performance and the use of packing materials is a good approach to enhance the performance for different operational conditions. Correlations for mass and heat transfer coefficients are pres

In this paper, we introduce and study a new concept (up to our knowledge) named CL-duo modules, which is bigger than that of duo modules, and smaller than weak duo module which is given by Ozcan and Harmanci. Several properties are investigated. Also we consider some characterizations of CL-duo modules. Moreover, many relationships are given for this class of modules with other related classes of modules such as weak duo modules, P-duo modules.

The purpose of this paper is to introduce and study the concepts of fuzzy generalized open sets, fuzzy generalized closed sets, generalized continuous fuzzy proper functions and prove results about these concepts.

Let R be a commutative ring with unity 1 6= 0, and let M be a unitary left module over R. In this paper we introduce the notion of epiform∗ modules. Various properties of this class of modules are given and some relationships between these modules and other related modules are introduced.

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