The aim of this paper is to introduces and study the concept of CSO-compact space via the notation of simply-open sets as well as to investigate their relationship to some well known classes of topological spaces and give some of his properties.

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

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.

In the present paper, a simply* compact spaces was introduced it defined over simply*- open set previous knowledge and we study the relation between the simply* separation axioms and the compactness, in addition to introduce a new types of functions known as 𝛼𝑆 𝑀∗ _irresolte , 𝛼𝑆 𝑀∗ __𝑐𝑜𝑛𝑡𝑖𝑛𝑢𝑜𝑢𝑠 and 𝑅 𝑆 𝑀∗ _ continuous, which are defined between two topological spaces.

Most of the Weibull models studied in the literature were appropriate for modelling a continuous random variable which assumes the variable takes on real values over the interval [0,∞]. One of the new studies in statistics is when the variables take on discrete values. The idea was first introduced by Nakagawa and Osaki, as they introduced discrete Weibull distribution with two shape parameters q and β where      0 < q < 1 and b > 0. Weibull models for modelling discrete random variables assume only non-negative integer values. Such models are useful for modelling for example; the number of cycles to failure when components are subjected to cyclical loading. Discrete Weibull models can be obta

Many codiskcyclic operators on infinite-dimensional separable Hilbert space do not satisfy the criterion of codiskcyclic operators. In this paper, a kind of codiskcyclic operators satisfying the criterion has been characterized, the equivalence between them has been discussed and the class of codiskcyclic operators satisfying their direct summand is codiskcyclic. Finally, this kind of operators is used to prove that every codiskcyclic operator satisfies the criterion if the general kernel is dense in the space.

Flow of water under concrete dams generates uplift pressure under the dam, which may cause the dam to function improperly, in addition to the exit gradient that may cause piping if exceeded a safe value. Cutoff walls usually used to minimize the effect of flow under dams. It is required to
1)minimize the flow quantity to conserve water in the reservoir, it is also required to
2)minimize the uplift pressure under the dam to maintain stability of the dam, and it is required to

3) minimize the exit gradient to prevent quick condition to occur at the toe of the dam where piping may occur and may cause erosion of the soil. Varying the angle of cutoff walls affects its influence on the factors aforementioned that are required to