The primary aim of this paper, is to introduce the rough probability from topological view. We used the Gm-topological spaces which result from the digraph on the stochastic approximation spaces to upper and lower distribution functions, the upper and lower mathematical expectations, the upper and lower variances, the upper and lower standard deviation and the upper and lower r th moment. Different levels for those concepts are introduced, also we introduced some results based upon those concepts.

This paper aims to decide the best parameter estimation methods for the parameters of the Gumbel type-I distribution under the type-II censorship scheme. For this purpose, classical and Bayesian parameter estimation procedures are considered. The maximum likelihood estimators are used for the classical parameter estimation procedure. The asymptotic distributions of these estimators are also derived. It is not possible to obtain explicit solutions of Bayesian estimators. Therefore, Markov Chain Monte Carlo, and Lindley techniques are taken into account to estimate the unknown parameters. In Bayesian analysis, it is very important to determine an appropriate combination of a prior distribution and a loss function. Therefore, two different

The aim of this research is to prove the idea of maximum m_X-N-open set, m-N-extremally disconnected with respect to t and provide some definitions by utilizing the idea of m_X-N-open sets. Some properties of these sets are studied.

We consider the problem of calibrating range measurements of a Light Detection and Ranging (lidar) sensor that is dealing with the sensor nonlinearity and heteroskedastic, range-dependent, measurement error. We solved the calibration problem without using additional hardware, but rather exploiting assumptions on the environment surrounding the sensor during the calibration procedure. More specifically we consider the assumption of calibrating the sensor by placing it in an environment so that its measurements lie in a 2D plane that is parallel to the ground. Then, its measurements come from fixed objects that develop orthogonally w.r.t. the ground, so that they may be considered as fixed points in an inertial reference frame. Moreov

      In this article, we introduce a new type of soft spaces namely, soft  spaces as   a generalization of soft paces. Also, we study the weak forms of soft  spaces, namely, soft  spaces, soft  spaces, soft  space, and soft  spaces. The characterizations and fundamental properties related to these types of soft spaces and the relationships among them are also discussed.

The current research deals with studying the aesthetics of symbolic values in the design of internal spaces and their connotations through their existence as a material value, as well as the symbolic meanings and their connotations that touch the spiritual and emotional side of the human being as an intangible value, and the research included four chapters, so the research problem was embodied by the following question (What is the role of values Symbolism and aesthetics in the design of interior spaces)? Therefore, the aim was to clarify the role of symbolic values and their aesthetics in the design of internal spaces. The first chapter included the importance of research, the need for it, the limits of the research and its terminology.

This paper considers a new Double Integral transform called Double Sumudu-Elzaki transform DSET. The combining of the DSET with a semi-analytical method, namely the variational iteration method DSETVIM, to arrive numerical solution of nonlinear PDEs of Fractional Order derivatives. The proposed dual method property decreases the number of calculations required, so combining these two methods leads to calculating the solution's speed. The suggested technique is tested on four problems. The results demonstrated that solving these types of equations using the DSETVIM was more advantageous and efficient

Background: This study aims to investigate the effect of fixed orthodontic appliances and/or antihypertensive drugs on the weight of experimental rats. Materials and Methods: Thir-ty-six male Wistar albino rats were subjected to a split-mouth design study, in which an orthodontic appliance was inserted in one side to move the first molar mesially for 2 weeks while the other side acted as a control to tooth movement. The rats were allocated into three groups: group A (n = 12), without any pharmacological treatment; group B (n = 12), subcu-taneous injection of bisoprolol fumarate (5 mg/kg) daily; and group C (n = 12), subcutaneous injection of valsartan (10 mg/kg) daily. A fixed orthodontic appliance with a closing coil spring delivering 5

With the development of information technology and means for information transfer it has become necessary to protect sensitive information. The current research presents a method to protect secret colored images which includes three phases: The first phase calculates hash value using one of hash functions to ensure that no tampering with or updating the contents of the secret image. The second phase is encrypting image and embedding it randomly into appropriate cover image using Random Least Significant Bit (RLSB) technique. Random hiding provides protection of information embedded inside cover image for inability to predict the hiding positions, as well as the difficult of determining the concealment positions through the analysis of im