# Mathematics

## Browse

### Recent Submissions

Now showing 1 - 5 of 73
• Item
CUBIC B-SPLINE FOR SOLUTIONS OF BOUNDARY VALUE PROBLEMS
(2023-03-15) Doaa Shtayah
Many of the mathematical models of engineering problems are expressed in terms of Boundary Value Problems (BVP). The Finite Difference Method (FDM) is the most modern method for solving (BVP). This is incredibly helpful in resolving challenging issues involving typical geometrical shapes or boundaries. Another numerical method, the B-spline method, has seen growing application in recent years in engineering research to solve mathematical models. The main objective of this study is to examine the effectiveness of cubic B-spline functions in addressing boundary value problems. The derivation of linear, quadratic, and cubic B-spline functions is covered at the start of the study. Subsequently, I use cubic Bspline functions to solve second-order linear boundary value problems with nonhomogeneous boundary conditions for ordinary differential equations, both in cases where coefficients are constant and where they are variable. Results from the examples show that the B-spline method leads to lower error rates compared to the Finite Difference Method. Keywords: Cubic spline, B-spline, differential equations, Boundary value problems, Finite difference methods
• Item
THE FARTHEST POINT PROBLEM IN NORMED SPACES
(2023-03-13) Angham Khabisa
In this study, the researcher discusses the longstanding problem in Approximation Theory, which is called the Farthest Point Problem (FPP). The FPP is partially an unsolved problem asking whether every uniquely remotal set in a Banach/Metric space is a singleton. The researcher considers the convex metric space and demonstrates that every bounded subset is singleton if and only if SF condition is satisfied. Also, the researcher focuses on the Banach spaces. Firstly, in normed space the researcher proved that the singletoness occurs if partially continuous condition of farthest point map P satisfies. Then, the researcher takes a specific space in Banach space, the sequence space ℓ1(R) and shows the positive answer that every uniquely remotal subset of ℓ1(R) is singleton. Finally, the researcher presents partially ideal statistically continuous notion of far- thest point map P and presents the main result, provided that E is a bounded, uniquely remotal set in a Banach space X over R with a Chebyshev center c and the farthest point map P defined on [c, P (c)] is partially ideal statistically continuous at c, then E consists of one element only. Keyword: A Banach/Metric Space; Approximation Theory; Convex Metric Space; Partially Ideal Statistically Continuous
• Item
ELECTROCHEMICAL REDUCTION OF NITRATE ION BY MODIFIED ALUMINUM SHEETS AS ELECTROCATALYSTS: A NOVEL WATER TREATMENT METHOD
(جامعة النجاح الوطنية, 2022-04-27) Eid, Shorooq
Background: Nitrate contamination of surface and ground water has been an issue in many places of the world, which has harmful effects on human health and the environment, were wrong human practices, whether it is industrial or agricultural, have contributed in raising the percentage of pollution allowed according to the World Health Organization (WHO) in water, which we have to find a solution to this problem. Aims: Our main goal of this study was to develop a simple, practical, and cost-effective method for reducing nitrate concentrations in aqueous solutions. Methods: In this study we tested Al electrode and different Al modification electrodes: Al-graphite, Al-graphene, Al-Cu, Al-Cu-graphite, Al-graphite-Cu to remove nitrate from water, by using nitrate electrochemical reduction experiments. Results: The products in these cases were NO2-, NH4+ and it’s expected to produce N2. The most efficient electrode was Al-Cu that can convert NO3- to N2 and the removal efficiency of nitrate 73.73%. The experiment of all electrodes was conducted on -1.8 volt. Conclusion: By studying the kinetics of reduction for Al-Cu, the results indicate that the nitrate electro-reduction is approximately first order with respect to nitrate. XRD was conducted for Al-Cu, Al-graphite and Al-Cu-graphite. Effects of several parameters on Al-Cu electrode efficiency in nitrate ion reduction, such as time and initial nitrate concentration, have been studied. Stability and the electrode material were also studied under experimental conditions. The possibility of reusing Al-Cu electrode again was investigated as well.
• Item
THE RELATIONSHIP BETWEEN MANAGEMENT BY OBJECTIVES AND PARTICIPATORY LEADERSHIP AMONG MEMBERS OF SPORTS FEDERATIONS IN PALESTINE
(جامعة النجاح الوطنية, 2022-07-18) Abdelmajeed, Tareq