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Due to its importance in physics and applied mathematics, the non-linear Sturm-Liouville problems
witnessed massive attention since 1960. A powerful Mathematical technique called the Newton-Kantorovich
method is applied in this work to one of the non-linear Sturm-Liouville problems. To the best of the authors’
knowledge, this technique of Newton-Kantorovich has never been applied before to solve the non-linear
Sturm-Liouville problems under consideration. Accordingly, the purpose of this work is to show that this
important specific kind of non-linear Sturm-Liouville differential equations problems can be solved by
applying the well-known Newton-Kantorovich method. Also, to show the efficiency of appl

The goal of this work is demonstrating, through the gradient observation of a   of type linear ( -systems), the possibility for reducing the effect of any disturbances (pollution, radiation, infection, etc.) asymptotically, by a suitable choice of related actuators of these systems. Thus, a class of  ( -system) was developed based on finite time  ( -system). Furthermore, definitions and some properties of this concept -system and asymptotically gradient controllable system ( -controllable) were stated and studied. More precisely, asymptotically gradient efficient actuators ensuring the weak asymptotically gradient compensation system ( -system) of known or unknown disturbances are examined. Consequently, under convenient hypo

The integral transformations is a complicated function from a function space into a simple function in transformed space. Where the function being characterized easily and manipulated through integration in transformed function space. The two parametric form of SEE transformation and its basic characteristics have been demonstrated in this study. The transformed function of a few fundamental functions along with its time derivative rule is shown. It has been demonstrated how two parametric SEE transformations can be used to solve linear differential equations. This research provides a solution to population growth rate equation. One can contrast these outcomes with different Laplace type transformations

    In this paper generalized spline method is used for solving linear system of fractional integro-differential equation approximately. The suggested method reduces the system to system of  linear algebraic equations. Different orders of fractional derivative for test example is given in this paper to show the accuracy and applicability of the presented method.

In this paper, three main generators are discussed: Linear generator, Geffe generator and Bruer generator. The Geffe and Bruer generators are improved and then calculate the Autocorrelation postulate of randomness test for each generator and compare the obtained result. These properties can be measured deterministically and then compared to statistical expectations using a chi-square test.

Background: Prophylaxis methods are used to mechanically remove plaque and stain from tooth surfaces; such methods give rise to loss of superficial structure and roughen the surface of composites as a result of their abrasive action. This study was done to assess the effect of three polishing systems on surface texture of new anterior composites after storage in artificial saliva. Materials and methods: A total of 40 Giomer and Tetric®N-Ceram composite discs of 12 mm internal diameter and 3mm height were prepared using a specially designed cylindrical mold and were stored in artificial saliva for one month and then samples were divided into four groups according to surface treatment: Group A (control group):10 specimens received no surfa

Background: This in vitro study was carried out to evaluate the effect of various endodontic irrigants (sodium hypochlorite, ethylene diaminetetracetic acid and normal saline) on sealing ability of (Biodentine, mineral trioxide aggregate, and amalgam) used to repair furcal perforations. Material and methods: One hundred and twenty extracted human molars with divergent roots were used in this study. A standard root canal access cavity was prepared in each tooth and furcal perforation was made and was standardized by using k file size 100 instrument to get a perforation of (1.32mm) in diameter .The teeth were randomly divided in to three groups of 40 teeth according to the type of material used to repair the perforations (Group A: The furcal

In this study, the researcher aims to analyze the content of the physics textbook for the 3rd intermediate grade according to the criteria for designing and producing infographics, and the research community consists of the content of the physics textbook for the 3rd intermediate grade intermediate grade for the academic year 2021-2022. The researcher adopted the analysis instruments with a number of the criteria for designing and producing infographics. The results revealed randomness in the percentage of the criteria included in the content of the physics textbook for the 3rd intermediate grade, and they are not compatible with the proposed criteria by the experts also.

One of the most important methodologies in operations research (OR) is the linear programming problem (LPP). Many real-world problems can be turned into linear programming models (LPM), making this model an essential tool for today's financial, hotel, and industrial applications, among others. Fuzzy linear programming (FLP) issues are important in fuzzy modeling because they can express uncertainty in the real world. There are several ways to tackle fuzzy linear programming problems now available. An efficient method for FLP has been proposed in this research to find the best answer. This method is simple in structure and is based on crisp linear programming. To solve the fuzzy linear programming problem (FLPP), a new ranking function (R