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.
في بداية الستينيات ظهرت شبكة الإنترنت لاستعمالها في أغراض غير تجارية ، ثم تطورت بشكل مذهل خلال السنوات الأخيرة، فبعد أن كانت مجرد شبكة صغيرة أصبحت الآن تضم ملايين المستخدمين حول العالم ، وتحولت من مجرد شبكة بحث أكاديمي إلى بيئة متكاملة للاستثمار والعمل والإنتاج والإعلام والحصول على المعلومات .
وفي بداية تأسيس الشبكة لم يكن ثمة اهتمام بمسائل الأمن بقدر ما كان الاهتمام ببنائها وتوسيع نش
... Show MoreThis article discusses the most beloved and creative dialect of the Arabs - the Iraqi dialect, despite its complexity, but it has a lot of beautiful foreign vocabulary. We followed a descriptive and historical approach, also tracked phonetic changes in this dialect, and then gave phonological explanations for these phenomena, trying to connect most of the phenomena with their historical roots in the standard Arabic "al-Fussha" and in ancient Arabic dialects. Most modern linguists have realized the need to study these dialects, since many of the modern dialect characteristics are only extensions of some ancient Arabic dialects, and do not refer them to the classical language. The study of modern Arabic dialects may be faced with a nu
... Show MoreThis study examined the effect of transformational leadership four main dimensions (ideal influence, inspirational motivation, intellectual stimulation, individual considerations) as the independent variable on the dimensions of empowerment (knowledge and skill, communication, trust, incentives).
The study sought to achieve a set of goals and most important: the study of the reality of the organization surveyed to identify strategies or policies with employees by transformational leadership, moreover see how much support such a leadership strategy for empowerment and describe the dimensions of empowerment of (knowledge and skill, communication, and trust , and incentives) and the extent of its contributio
... Show MoreThe survival of dried spores of A.flavus, Penicillia Spp., and Cladosporia Spp.inoculated into multivitamins and folic acid tablets were examined at different compression pressures.Survival of fungal spores decreased with increasing compression pressure. The level of survival at particular pressures was shown to depend on the size of the contaminating fungal spores.The lethal effect of tabletting was attributed to shearing forces upon the contaminating spores generated by interparticulate movement. This hypothesis was supported by the dependence of survival upon spore size.
Key words: Fungal spores, microbial contamination.
In this research was study the effect of increasing the number of layers of the semiconductor films as PbS on the average grain sizes and illustrate the relationship between the increase in the average grain size and thickness of the membrane, and membrane was prepared using the easy and simple and does not need the complexity of which is that the chemical bath , and from an X-ray diffraction found that the material and the installation of a random cubic and when increasing the number of layers deposited note the emergence of a number of vertices of a substance and PbS at different levels but the level is more severe (200) as well as the value is calculated optical energy gap and found to be not affected by increase thickness and from th
... Show MoreIt is no secret to anyone that the Koran is a speech to people, and how it is not a speech to humans is a home to them and suitable for their understandings, and the people of rhetoric mean great care has never been before in the division of the Koranic discourse, followed by linguists and science of the Koran. After reading the letter, I followed it in the Holy Quran, taking advantage of what was written by former writers in language and interpretation. Thanks to God, I have done what I wanted. Perhaps one of the most important reasons that led me to write my research and optional for this topic; is related to the Koran. So I started to develop the research plan, and divided it as I saw it, I started to pave the way, and then divided it
... Show More An analytical form of the ground state charge density distributions
for the low mass fp shell nuclei ( 40 A 56 ) is derived from a
simple method based on the use of the single particle wave functions
of the harmonic oscillator potential and the occupation numbers of
the states, which are determined from the comparison between theory
and experiment.
For investigating the inelastic longitudinal electron scattering form
factors, an expression for the transition charge density is studied
where the deformation in nuclear collective modes is taken into
consideration besides the shell model space transition density. The
core polarization transition density is evaluated by adopting the
shape of Tass
The aim of this study is to estimate the parameters and reliability function for kumaraswamy distribution of this two positive parameter (a,b > 0), which is a continuous probability that has many characterstics with the beta distribution with extra advantages.
The shape of the function for this distribution and the most important characterstics are explained and estimated the two parameter (a,b) and the reliability function for this distribution by using the maximum likelihood method (MLE) and Bayes methods. simulation experiments are conducts to explain the behaviour of the estimation methods for different sizes depending on the mean squared error criterion the results show that the Bayes is bet
... Show MoreHigh-quality academic publishing is built on rigorous peer review [...]