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 applying this method
to solve these problems, a comparison is made in this paper between the Newton-Kantorovich method and the
Adomian decomposition method applied to the same non-linear Sturm-Liouville problems under consideration
in this work. As a result of this comparison, the results of the Newton-Kantorovich method agreed with the
results obtained by applying Adomian’s decomposition method.
Abstract: Colloidal gold nanoparticles (ringworm Palm or in the form of paper willow) have been prepared from HAuCl4 containing aqueous solution by hot chemical reduction method. The colloidal gold nanoparticles were characterized by SEM, EDX, and UV-VIS absorption spectroscopy. It was found that the variation of reduction time from boiling point affects the size of the nanoparticles and also in chemical reduction approach the size of nanoparticles can be controlled by varying the amount of variation the volume of reductant material with respect to the volume of HAuCL4.
Scheduling considered being one of the most fundamental and essential bases of the project management. Several methods are used for project scheduling such as CPM, PERT and GERT. Since too many uncertainties are involved in methods for estimating the duration and cost of activities, these methods lack the capability of modeling practical projects. Although schedules can be developed for construction projects at early stage, there is always a possibility for unexpected material or technical shortages during construction stage. The objective of this research is to build a fuzzy mathematical model including time cost tradeoff and resource constraints analysis to be applied concurrently. The proposed model has been formulated using fuzzy the
... Show MoreThe present study aims to develop and apply the unrealistic optimism scale among high school students. The researcher has designed a scale of (38) paragraphs to measure the unrealistic optimism. A sample of (200) male and female students were chosen randomly to collect the needed data. The study found that the unrealistic scale of optimism has good psychometric characteristics. The research sample has a high level of التفاؤل غير الواقعي لدى عينة البحث unrealistic optimism. There is a statistically significant difference between male and female in the unrealistic optimism in favor of the male students. Finally, there is a statistically significant difference between students in the fourth and sixth gra
... Show MoreIn this research, we dealt with the study of the Non-Homogeneous Poisson process, which is one of the most important statistical issues that have a role in scientific development as it is related to accidents that occur in reality, which are modeled according to Poisson’s operations, because the occurrence of this accident is related to time, whether with the change of time or its stability. In our research, this clarifies the Non-Homogeneous hemispheric process and the use of one of these models of processes, which is an exponentiated - Weibull model that contains three parameters (α, β, σ) as a function to estimate the time rate of occurrence of earthquakes in Erbil Governorate, as the governorate is adjacent to two countr
... Show MoreLinear programming currently occupies a prominent position in various fields and has wide applications, as its importance lies in being a means of studying the behavior of a large number of systems as well. It is also the simplest and easiest type of models that can be created to address industrial, commercial, military and other dilemmas. Through which to obtain the optimal quantitative value. In this research, we dealt with the post optimality solution, or what is known as sensitivity analysis, using the principle of shadow prices. The scientific solution to any problem is not a complete solution once the optimal solution is reached. Any change in the values of the model constants or what is known as the inputs of the model that will chan
... Show MoreRutting in asphalt mixtures is a very common type of distress. It occurs due to the heavy load applied and slow movement of traffic. Rutting needs to be predicted to avoid major deformation to the pavement. A simple linear viscous method is used in this paper to predict the rutting in asphalt mixtures by using a multi-layer linear computer programme (BISAR). The material properties were derived from the Repeated Load Axial Test (RLAT) and represented by a strain-dependent axial viscosity. The axial viscosity was used in an incremental multi-layer linear viscous analysis to calculate the deformation rate during each increment, and therefore the overall development of rutting. The method has been applied for six mixtures and at different tem
... Show MoreThis paper deals with load-deflection behavior the jointed plain concrete pavement system using steel dowel bars as a mechanism to transmit load across the expansion joints. Experimentally, four models of the jointed plain concrete pavement system were made, each model consists of two slabs of plain concrete that connected together across expansion by two dowel bars and the concrete slab were supported by the subgrade soil. Two variables were dealt with, the first is diameter of dowel bar (12, 16 and 20 mm) and the second is type of the subgrade soil, two types of soil were used which classified according to the (AASHTO): Type I (A-6) and type II (A-7-6). Experimental results showed that increasing dowel bar diameter from 12 mm to 20 mm
... Show MoreThe evaluation process of transportation problem required finding basic feasible solution (bfs). Represent the base of decision making process. To purpose start anther batter solution to able from decisions taking process, consider the decision making process, find (bfs) represent the standard form in linear programming (LP). Most important stage of update (bsf) stages that achieved minimum cost (the optimal solution). the goal of paper to improving & evaluation (bfs) by new procedure (proposed method) comparison with Vogel method.