This paper is concerned with finding solutions to free-boundary inverse coefficient problems. Mathematically, we handle a one-dimensional non-homogeneous heat equation subject to initial and boundary conditions as well as non-localized integral observations of zeroth and first-order heat momentum. The direct problem is solved for the temperature distribution and the non-localized integral measurements using the Crank–Nicolson finite difference method. The inverse problem is solved by simultaneously finding the temperature distribution, the time-dependent free-boundary function indicating the location of the moving interface, and the time-wise thermal diffusivity or advection velocities. We reformulate the inverse problem as a non-linear optimization problem and use the lsqnonlin non-linear least-square solver from the MATLAB optimization toolbox. Through examples and discussions, we determine the optimal values of the regulation parameters to ensure accurate, convergent, and stable reconstructions. The direct problem is well-posed, and the Crank–Nicolson method provides accurate solutions with relative errors below 0.006% when the discretization elements are M=N=80. The accuracy of the forward solutions helps to obtain sensible solutions for the inverse problem. Although the inverse problem is ill-posed, we determine the optimal regularization parameter values to obtain satisfactory solutions. We also investigate the existence of inverse solutions to the considered problems and verify their uniqueness based on established definitions and theorems.
In The Name of Allah Most Gracious Most Merciful
The fundamentals of jurisprudence have a great role in facilitating the ways to know the Shari’a rulings for everything that takes place between people in terms of relationships, and the actions that are issued by them, because without it, the sources from which the rulings were taken are not known, and the methods used by the imams of ijtihad in taking these rulings from those sources are not understood. The foundations on which they followed in the interpretation of texts and its rules, and Muslim scholars in different eras celebrated this science and gave it great care: with what they wrote in it from the works of different directions, but of course the complexity printed many
... Show MoreBackground: The mechanical properties of 3D-printed denture base resins are crucial factors for determining the quality and performance of dentures inside a patient’s mouth. Tensile strength and diametral compressive strength are two properties that could play significant roles in assessing the suitability of a material. Although they measure different aspects of material behavior, a conceptual link exists between them in terms of overall material strength and resilience. Aim: This study aims to investigate the correlation between tensile strength and diametral compressive strength after incorporating 2% ZrO2 nanoparticles (NPs) by weight into 3D-printed denture base resin. Methods: A total of 40 specimens (20 dumbbell-shaped and
... Show MoreThis book in our hands is a 'book in the science of rhymes' written by the linguistic and grammatical world 'Othman bin Jenni' 'T 392 AH', and included in it: the concept of rhyme, its characters, movements, and disadvantages, with mention of its ramifications, defining them by definition, clarification and martyrdom poetry, It is concise in size, but it is a book containing a full science in its content.
The study was divided into two parts, the first: the study, and included a study of the author and the author, I talked first about his life, such as his name and origin, and scientific status, and the words of scientists in it, and so on, and secondly: the name of the book, and his percentage, and the time of its composition, etc. I
Background: This study aimed to use the combined mesio-distal crowns widths of maxillary incisors and first molars as predictors to the combined mesio-distal crowns widths of maxillary and mandibular canines and premolars. Materials and methods: The sample included 110 Iraqi Arab subjects with an age ranged between 17-25 years and class I skeletal and dental relations. The crown widths of maxillary teeth and mandibular canines and premolars were measured at the largest mesio-distal dimension on the study casts using digital electronic caliper with 0.01 mm sensitivity. Pearson’s correlation coefficient was used to determine the relation between the combined mesio-distal crowns widths of maxillary incisors and first molars and the combined
... Show MoreIn the midst of political, cultural and economic fast developments accelerated, the world witnessed, with the accompanied big communication revolutions, many shapes of powers. Those developments were followed by changes in relations of international level.
The most prominent among those developments was the international public relations which became equal to official international relations. Moreover, the international public relations became a complementary element dur to the growth of public opinion and its affection on political regime. Such growth of public opinion pushed the politicians to address it; and try to gain its support.
The US was the first realized the importance of international public relations. Th
... Show MoreThe current study aimed to measure the attitudes of female teachers towards the use of digital learning and the degree of possessing their digital education skills. The study sample consisted of (180) workers with disabilities (mental disability، auditory impairment، visual disability، hyperactivity and distraction. To achieve the goals of the study, the transformation measure was used towards digital education for people with disabilities. The study reached the following results: the availability of digital learning skills among workers with disabilities. The study concluded with a series of recommendations including holding Training courses to keep up with the challenges of educational trends and modern technology in this area.
The status of women in any society is one of the basic criteria for measuring the degree of progress that society and follow renaissance march side by sidewith men , and is no doubt that women are now of interest to the state , even if limited , which promotes public ideologies on the need for womens participation in economic infrastructure operations and social and the right to gain information and knowledge, entertainment and exercise its role in development through its president and actor in the family and raising the next generation configuration.
And affect the basic tributaries that draws them women information and ideas have a direct impact on the composition of cultural and cognitive entity woman comes satellite channels
... Show MoreObjective: Detection the presumptive prevalence of
silent celiac disease in patients with type 1 diabetes
mellitus with determination of which gender more
likely to be affected.
Methods: One hundred twenty asymptomatic patients
[75 male , 45 female] with type 1 diabetes mellitus
with mean age ± SD of 11.25 ± 2.85 year where
included in the study . All subjects were serologically
screened for the presence of anti-tissue transglutaminase
IgA antibodies (anti-tTG antibodies) by Enzyme-
Linked Immunosorbent Assay (ELISA) & total IgA
was also measured for all using radial
immunodiffusion plate . Anti-tissue transglutaminase
IgG was selectively done for patients who were
expressing negative anti-