Let R be a ring with 1 and W is a left Module over R. A Submodule D of an R-Module W is small in W(D ≪ W) if whenever a Submodule V of W s.t W = D + V then V = W. A proper Submodule Y of an R-Module W is semismall in W(Y ≪_S W) if Y = 0 or Y/F ≪ W/F ∀ nonzero Submodules F of Y. A Submodule U of an R-Module E is essentially semismall(U ≪es E), if for every non zero semismall Submodule V of E, V∩U ≠ 0. An R-Module E is essentially semismall quasi-Dedekind(ESSQD) if Hom(E/W, E) = 0 ∀ W ≪es E. A ring R is ESSQD if R is an ESSQD R-Module. An R-Module E is a scalar R-Module if, ∀ , ∃ s.t V(e) = ze ∀ . In this paper, we study the relationship between ESSQD Modules with scalar and multiplication Modules. We show that

In this paper, a Cholera epidemic model is proposed and studied analytically as well as numerically. It is assumed that the disease is transmitted by contact with Vibrio cholerae and infected person according to dose-response function. However, the saturated treatment function is used to describe the recovery process. Moreover, the vaccine against the disease is assumed to be utterly ineffective. The existence, uniqueness and boundedness of the solution of the proposed model are discussed. All possible equilibrium points and the basic reproduction number are determined. The local stability and persistence conditions are established. Lyapunov method and the second additive compound matrix are used to study the global stability of the system.

This study has contributed to understanding a delayed prey-predator system involving cannibalism. The system is assumed to use the Holling type II functional response to describe the consuming process and incorporates the predator’s refuge against the cannibalism process. The characteristics of the solution are discussed. All potential equilibrium points have been identified. All equilibrium points’ local stability analyses for all time delay values are investigated. The system exhibits a Hopf bifurcation at the coexistence equilibrium, which is further demonstrated. The center manifold and normal form theorems for functional differential equations are then used to establish the direction of Hopf bifurcation and the stability of the per

This work aims to see the positive association rules and negative association rules in the Apriori algorithm by using cosine correlation analysis. The default and the modified Association Rule Mining algorithm are implemented against the mushroom database to find out the difference of the results. The experimental results showed that the modified Association Rule Mining algorithm could generate negative association rules. The addition of cosine correlation analysis returns a smaller amount of association rules than the amounts of the default Association Rule Mining algorithm. From the top ten association rules, it can be seen that there are different rules between the default and the modified Apriori algorithm. The difference of the obta

This research presents experimental and theoretical investigation of 15 reinforced concrete spliced and nonspliced girder models. Splices of hooked dowels and cast in place joints, with or without strengthening steel plates were used. Post-tensioning had been used to enhance the splice strength for some spliced girders. The ANSYS computer program was used for analyzing the spliced and non-spliced girders. A nonlinear three dimensional element was used to represent all test girders. The experimental results have shown that for a single span girder using steel plate connectors in the splice zone has given a sufficient continuity to resist flexural stresses in this region. The experimental results have shown that the deflection of hooked do

  A new hetrocyclic liquid crystal compounds containing 1,3,4-oxadiazole with different substituted in para position (Bromo, Chloro, Nitro and Methyl) were synthesized and characterized by melting points, FTIR Spectroscopy and 1HNMR spectroscopy for [Cl-SR6] and [NO2-SR6] compounds. The liquid crystalline properties of the synthesized compounds were studied by using hot-stage polarizing optical microscopy (POM), so they determined the transition enthalpies and entropies by using differential scanning calorimetery (DSC). All of the compounds show mesomorphic properties. The compounds [Br-SR6], [Cl-SR6] and [NO2SR6] exhibit an enantiotropic dimorphism smectic (Sm) phase, while the compounds [MeSR6] showed nematic (N) phase throw cooli

Uncompleted Personality and it’s relation with Some Variables of the University Students

Geographic information system (GIS) is utilized in a variety of tasks such as, resource management, urban planning, emergency planning in case of accident, and rapid response etc. The aim of this study is to produce a digital map with the aid of GIS and a survey data. A survey data is conducted with Total Station technique on sanitary planning positions. The campus of Baghdad University is chosen to test the execution and accuracy of the results for sewer manholes locations. During the field survey, Total Station (Nikon Nivo) is used to identify the 3-D coordinates for each location. Finally, Geographical Information System (GIS) are utilized to present the digital map of the network sewer pipe line to the end users. Although Geographic Inf