Abstract:
We introduce the concept of almost semiprime submodules of unitary modules over a commutative ring with nonzero identity. We investigate some basic properties of almost semiprime and weakly semiprime submodules and give some characterizations of them, especially for (finitely generated faithful) multiplication modules. 1. Introduction Throughout this paper, all rings are commutative rings with identity and all modules are unitary. Various generalizations of prime (primary) ideals are studied in [1–8]. The class of prime submodules of modules as a generalization of the class of prime ideals has been studied by many authors; see, for example, [9, 10]. Then many generalizations of prime submodules were studied such as weakly prime (primary) [11], almost prime (primary) [12], 2-absorbing [13], classical prime (primary) [14, 15], and semiprime submodules [16]. In this paper, we study weakly semiprime and almost semiprime submodules as the generalizations of semiprime submodules. Weakly semiprime submodules have been already studied in [17]. Here we first define the notion almost semiprime submodules and get a number of propensities of almost semiprime and weakly semiprime submodules. Also, we give some characterizations of such submodules in multiplication modules. Now we define the concepts that we will use. For any two submodules and of an -module , the residual of by is defined as the set which is clearly an ideal of . In particular, the ideal is called the annihilator of . Let be a submodule of and let be an ideal of ; the residual submodule of by is defined as . These two residual ideals and submodules were proved to be useful in studying many concepts of modules; see, for example, [18, 19]. A proper submodule of an -module is a prime submodule if, whenever for and , or . An -module is called a prime module if its zero submodule is a prime submodule. A proper submodule of an -module is called weakly prime (weakly primary) if , where and ; then or ( or ). A proper submodule of an -module is called almost prime (almost primary) if, whenever for and , or ( or ). A proper ideal of a commutative ring is called semiprime if , where and ; then . A proper submodule of an -module is called semiprime if, whenever , , and such that , . An -module is called a second module provided that, for every element , the -endomorphism of produced by multiplication by is either surjective or zero; this implies that is a prime ideal of and is said to be -second [20]. An -module is called a multiplication module provided that, for every submodule of , there exists an ideal of

Abstract:
Let $G$ be a group with identity $e$, and let $R$ be a $G$-graded commutative ring, and let $M$ be a graded $R$-module. In this paper we characterize graded weak multiplication modules.

Abstract:
Introduction: Most women experience the premenstrual syndrome at their reproductive age. This is a periodic occurrence (event) that happens during the luteal phase of mentyral cycle and includes the combination of physical, psychological and behavioral changes that interfere with familial communication and social activities. In this regard, different methods have been suggested and one of them is traditional use of medicinal herbs. This study was carried out to detect the effect of fennel on the premenstrual syndrome in students of Shahrekord University of medical sciences in 2008. Methods: In this single blind clinical trial, sixty students with premenstrual syndrome were randomly assigned to either the fennel extract or placebo groups. Data collection was done via DRSP questionnaire and the severity of premenstrual syndrome was detected in two cycles before the intervention and it was compared with after the intervention conditions. To analyze the data, we used SPSS and P<0.05 was considered as significant. Results: There were no significant differences between the mean scores of premenstrual syndrome in the two groups before the treatment (100.38±33.43 in fennel group VS 104.30 ±19.50 in placebo group), but after the treatment, there was a significant difference between two groups [(64.40±29.3 in fennel group VS 79.10±28.11 in placebo group), P=0.01]. Conclusion: Fennel extract is probably effective in the treatment of premenstrual syndrome. We suggest fennel extracts for the treatment of PMS.

Abstract:
Let $ R $ be a commutative ring with non-zero identity. We define a proper submodule $ N $ of an $ R $-module $ M $ to be weakly prime if $ 0 ot = rmin N $( $ rin R, min M $) implies $ min N $ or $ rMsubseteq N $. A number of results concerning weakly prime submodules are given. For example, we give three other characterizations of weakly prime submodules.

Abstract:
Introduction: Nowadays using plant extracts as antimicrobial additives has got an important role in maintaining the quality of food products. Garlic is one of the plants the antimicrobial effect of which has been proved by biochemical investigation. The aim of this study was to assess the effect of different concentrations of garlic powder extract and garlic tablet extract on Salmonella typhimurium and Shigella dysenteric in the same conditions. Methods: To do this investigation fresh garlic from Hamadan and garlic tablets from Kowsar Pharmacy Company were provided. Minimum Inhibitory Concentration (MIC) and Minimum Bactericidal Concentration (MBC) of garlic Powder extract and garlic tablet extract on the growth of two micro-organisms were tested through tube standard method. Results: The MIC of garlic Powder extract on the tested microorganisms was 12.5 mg/ml and the MBC was 25 mg/ml while the MIC of garlic tablet extract was 40mg/ml and the MBC was 80 mg/ml. According to these results the inhibitory effect of the extract of the garlic (GP >) on both bacteria was similar but the inhibitory effect of the garlic powder was much more than that of garlic tablet (3.28 times) either on Salmonella or Shigella. Conclusion: Noticing the findings of the present study and other related reports in this field the application of this extract in food preservative systems is useful for inhibiting food contaminations

Abstract:
Analysis and interpretation of spatial variability of soils properties is a keystone in site-specific management. The objectives of this study were to evaluate two different Artificial Neural Network (ANN) structures as single hidden-layer and multiple hidden-layer for estimation of spatial variability of some soil chemical properties. Soil samples were collected at approximately 60x60 m grids at 0-30 cm depth and coordinates of each of the 100 points were recorded with GPS. ANN models, applicable to each of these soils and consisting of two input parameters (X and Y coordinate system) were developed. The whole data is composed of 100 data points, which separated into two parts randomly: A training set consisting of 80% data points and a validation or testing set consisting of 20% data points. Generally, approximately the study highlights the superiority of the multiple hidden layers ANN model over single hidden layer ANN models (except Ca), for determining soil properties compacted to a given state.