This paper is concerned with introducing and studying the first new approximation operators using mixed degree system and second new approximation operators using mixed degree system which are the core concept in this paper. In addition, the approximations of graphs using the operators first lower and first upper are accurate then the approximations obtained by using the operators second lower and second upper sincefirst accuracy less then second accuracy. For this reason, we study in detail the properties of second lower and second upper in this paper. Furthermore, we summarize the results for the properties of approximation operators second lower and second upper when the graph G is arbitrary, serial 1, serial 2, reflexive, symmetric, tra

In this paper, point estimation for parameter ? of Maxwell-Boltzmann distribution has been investigated by using simulation technique, to estimate the parameter by two sections methods; the first section includes Non-Bayesian estimation methods, such as (Maximum Likelihood estimator method, and Moment estimator method), while the second section includes standard Bayesian estimation method, using two different priors (Inverse Chi-Square and Jeffrey) such as (standard Bayes estimator, and Bayes estimator based on Jeffrey's prior). Comparisons among these methods were made by employing mean square error measure. Simulation technique for different sample sizes has been used to compare between these methods.

Methods of estimating statistical distribution have attracted many researchers when it comes to fitting a specific distribution to data. However, when the data belong to more than one component, a popular distribution cannot be fitted to such data. To tackle this issue, mixture models are fitted by choosing the correct number of components that represent the data. This can be obvious in lifetime processes that are involved in a wide range of engineering applications as well as biological systems. In this paper, we introduce an application of estimating a finite mixture of Inverse Rayleigh distribution by the use of the Bayesian framework when considering the model as Markov chain Monte Carlo (MCMC). We employed the Gibbs sampler and

One of the main causes for concern is the widespread presence of pharmaceuticals in the environment, which may be harmful to living things. They are often referred to as emerging chemical pollutants in water bodies because they are either still unregulated or undergoing regulation. Pharmaceutical pollution of the environment may have detrimental effects on ecosystem viability, human health, and water quality. In this study, the amount of remaining pharmaceutical compounds in environmental waters was determined using a straightforward review. Pharmaceutical production and consumption have increased due to medical advancements, leading to concerns about their environmental impact and potential harm to living things due to their increa

The present study aim at preparing frusemide in liquid form suitable for oral use. This is achieved through preparing different liquid forms of frusemide. The frusemide liquid is prepared in the following forms: oral solution, syrup and elixir with intensity of 1, 0.4 and 0.8% weight /volume respectively and in combination with potassium carbonate, polysorbate 80, alcohol and phosphate buffer solution of pH8 to dissolve the frusemide in the above mentioned forms. The different forms of the prepared medicine have been stored in glass bottles that can provide protection against light and at 40, 50, 60⁰C for four months. Besides the pH has been checked to decide the period of validity. The results show that the expiration date of

Background: The present study was carried out to compare shear bond strength of sapphire bracket bonded to zirconium surface after using different methods of surface conditioning and assessment of the adhesive remnant index. Materials and methods: The sample composed of 40 zirconium specimens divided into four groups; the first group was the control, the second group was conditioned by sandblast with aluminum oxide particle 50 μm, the third and fourth group was treated by (Nd: YAG) laser (1064nm)(0.888 Watt for 5 seconds) for the 1st laser group and (0.444 Watt for 10 seconds) for the 2nd laser group. All samples were coated by z-prime plus primer. A central incisor sapphire bracket was bonded to all samples with light cure adhesive res

One of the unique properties of laser heating applications is its powerful ability for precise pouring of energy on the needed regions in heat treatment applications. The rapid rise in temperature at the irradiated region produces a high temperature gradient, which contributes in phase metallurgical changes, inside the volume of the irradiated material. This article presents a comprehensive numerical work for a model based on experimentally laser heated AISI 1110 steel samples. The numerical investigation is based on the finite element method (FEM) taking in consideration the temperature dependent material properties to predict the temperature distribution within the irradiated material volume. The finite element analysis (FEA) was carried

Using the Internet, nothing is secure and as we are in need of means of protecting our data, the use of passwords has become important in the electronic world. To ensure that there is no hacking and to protect the database that contains important information such as the ID card and banking information, the proposed system stores the username after hashing it using the 256 hash algorithm and strong passwords are saved to repel attackers using one of two methods: -The first method is to add a random salt to the password using the CSPRNG algorithm, then hash it using hash 256 and store it on the website. -The second method is to use the PBKDF2 algorithm, which salts the passwords and extends them (deriving the password) before being ha

Most heuristic search method's performances are dependent on parameter choices. These parameter settings govern how new candidate solutions are generated and then applied by the algorithm. They essentially play a key role in determining the quality of the solution obtained and the efficiency of the search. Their fine-tuning techniques are still an on-going research area. Differential Evolution (DE) algorithm is a very powerful optimization method and has become popular in many fields. Based on the prolonged research work on DE, it is now arguably one of the most outstanding stochastic optimization algorithms for real-parameter optimization. One reason for its popularity is its widely appreciated property of having only a small number of par

The electronic characteristics, including the density of state and bond length, in addition to the spectroscopic properties such as IR spectrum and Raman scattering, as a function of the frequency of Sn₁₀O₁₆, C₂₄O_6, and hybrid junction (Sn₁₀O₁₆/C₂₄O₆) were studied. The methodology uses DFT for all electron levels with the hybrid function B3-LYP (Becke level, 3-parameters, Lee–Yang-Parr), with 6-311G (p,d)  basis set, and Stuttgart/Dresden (SDD) basis set, using Gaussian 09 theoretical calculations. The geometrical structures were calculated by Gaussian view 05 as a supplementary program. The band gap was calculated and compared to the measured valu