In this paper, we first characterize the convex L-subgroup of an L-ordered group by means of four kinds of cut sets of an L-subset. Then we consider the homomorphic preimages and the product of convex L-subgroups. After that, we introduce an L-convex structure constructed by convex L-subgroups. Furthermore, the notion of the degree to which an L-subset of an L-ordered group is a convex L-subgroup is proposed and characterized. An L-fuzzy convex structure which results from convex L-subgroup degree is imported naturally, and its L-fuzzy convexity preserving mappings investigated.

Sample size calculations are now mandatory for many research protocols and it is a main question before accomplishing a research. This paper outlines the ways of calculating sample sizes in clinical trial studies with two groups: binary, ordered categorical, and continuous outcomes. In each section a table for calculating sample size and working examples are given.

The notion of a G-semigroup was introduced by Sen [8] in 1981. We can see that any semigroup can be considered as a G-semigroup. The aim of this article is to study the concept of (0-)minimal and max- imal ordered bi-ideals in ordered G-semigroups, and give some charac- terizations of (0-)minimal and maximal ordered bi-ideals in ordered G- semigroups analogous to the characterizations of (0-) minimal and maxi- mal ordered bi-ideals in ordered semigroups considered by Iampan [5].

In this paper, we introduce the concept of Krasner hyperring (R,+,.) together with a suitable partial order relation £. Also, we con-sider some Krasner hyperrings and dene a binary relation on them which become ordered Krasner hyperrings. By using the notion of pseudoorder on an ordered Krasner hyperring (R,+,.,£), we obtain an ordered ring. Moreover, we give some results on ordered Krasner hyperrings.

Let S be an ordered semi group. A fuzzy subset of S is an arbitrary mapping from S into [0,1], where [0,1] is the usual interval of real numbers. In this paper, the concept of fuzzy generalized bi-ideals of an ordered semi group S is introduced. Regular ordered semi groups are characterized by means of fuzzy left ideals, fuzzy right ideals and fuzzy (generalized) bi-ideals. Finally, two main theorems which characterize regular ordered semi groups and intraregular ordered semi groups in terms of fuzzy left ideals, fuzzy right ideals, fuzzy bi-ideals or fuzzy quasi-ideals are given. The paper shows that one can pass from results in terms of fuzzy subsets in semi groups to ordered semi groups. The corresponding results of unordered semi groups are also obtained.

When the density current smashes into the lower dense fluid mass a plunge region will occur. Since the plunge depth bounds between density current and ambient fluid, determining of this point is important. In this research, the hydraulic parameters of density current and bed slope of stagnant fluid were investigated. To achieve the purpose of this research a physical model was built in the hydraulic laboratory of Shahid Chamran University (SCU) and various experiments were performed. In the experiments, the plunge depth at the different discharge of density current and density difference 6, 9, 13 and 16 kg/m3 at three slopes 8, 12 and 16% was measured. Then using Flow-3D under RNG turbulence model, plunge depth was simulated for the same experimental condition. The comparison of results obtained showed that the predicted plunge depth with Flow-3D under RNG turbulence model had a high and satisfactory accuracy. Finding showed that for the 8% bed slope, the results of RNG turbulence model 14% was more than experimental data. While, for the entire slope, the results of RNG turbulence model was predicted 10.5% in average more than measured data. Generally, the statistical investigations showed that the RNG turbulence model with satisfactory precision estimated the plunge point depth.