This paper presents a proposed neural network algorithm to solve the shortest path problem (SPP) for communication routing. The solution extends the traditional recurrent Hopfield architecture introducing the optimal routing for any request by choosing single and multi link path node-to-node traffic to minimize the loss. This suggested neural network algorithm implemented by using 20-nodes network example. The result shows that a clear convergence can be achieved by 95% valid convergence (about 361 optimal routes from 380-pairs). Additionally computation performance is also mentioned at the expense of slightly worse results.

Let M be an R-module, where R is a commutative ring with unity. A submodule N of M is called e-small (denoted by N e  M) if N + K = M, where K e  M implies K = M. We give many properties related with this type of submodules.

Field experiment conducted to measure vibrations on three axes longitudinal X, lateral Y and vertical Z on steering wheel, platform tractor and vertical vibration in seat tractor and seat effective amplitude transmissibility (SEAT) factor during operation tillage in silt clay loam soil with depth 18 cm in Baghdad. Split – split plot design under randomized complete block design with three replications least significant design 5 % used. Three factor were used in this experiment included two types of plows included chisel and disc plows which represented main plot, three tires inflation pressure was second factor included 1.1 ,1.8 and 2.7 bar, and three forward speeds of the tillage was third factor included 2.35 , 4.25 and 6.50 km/hr. Resu

Let R be associative; ring; with an identity and let D be unitary left R- module; . In this work we present semiannihilator; supplement submodule as a generalization of R-a- supplement submodule, Let U and V be submodules of an R-module D if D=U+V and whenever Y≤ V and D=U+Y, then annY≪R;. We also introduce the the concept of semiannihilator -supplemented ;modules and semiannihilator weak; supplemented modules, and we give some basic properties of this conseptes

Abstract

There have been a number of positive developments in inclusive education in many different countries, recognizing that all students, including those with disabilities, have a right to education. Around the world, educators, professionals, and parents are concerned about including children with disabilities in mainstream schools along with their peers. As a result of this trend, a number of factors are contributing, including the increasing importance of education in achieving social justice for pupils with special education needs; the right of individuals with disabilities to attend mainstream schools together with their typically developing peers; the benefit of equal opportunities for everyone in achie

Let R be a commutative ring with identity 1 and M be a unitary left R-module. A submodule N of an R-module M is said to be pure relative to submodule T of M (Simply T-pure) if for each ideal A of R, N?AM=AN+T?(N?AM). In this paper, the properties of the following concepts were studied: Pure essential submodules relative to submodule T of M (Simply T-pure essential),Pure closed submodules relative to submodule T of M (Simply T-pure closed) and relative pure complement submodule relative to submodule T of M (Simply T-pure complement) and T-purely extending. We prove that; Let M be a T-purely extending module and let N be a T-pure submodule of M. If M has the T-PIP, then N is T-purely extending.

In this paper by using δ-semi.open sets we introduced the concept of weakly δ-semi.normal and δ-semi.normal spaces . Many properties and results were investigated and studied. Also we present the notion of δ- semi.compact spaces and we were able to compare with it δ-semi.regular spaces

The importance of knowledge is represented in the use of various sources of information, the corresponding to the same level of importance is the use of modern means and technologies in the delivery and investment of these sources to the beneficiaries, among these means and technologies are the multimedia that deal with most of the human senses, but the most important of which is sight and hearing, if these are invested the means in the field of education will give many positive results, such as the speed of receiving information, its clarity, and its freedom from impurities and influences, as well as its stability in memory as it is based on nderstanding, not memorization. On this basis, the experience of supporting the education process

This paper proposes a completion that can allow fracturing four zones in a single trip in the well called “Y” (for confidential reasons) of the field named “X” (for confidential reasons). The steps to design a well completion for multiple fracturing are first to select the best completion method then the required equipment and the materials that it is made of. After that, the completion schematic must be drawn by using Power Draw in this case, and the summary installation procedures explained. The data used to design the completion are the well trajectory, the reservoir data (including temperature, pressure and fluid properties), the production and injection strategy. The results suggest that multi-stage hydraulic fracturing can