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.
This research presents the kinetics of the saponification reaction using mixed fats of olein and stearin [in the ratio (3:1)] with NaOH solution. In this reaction, excess solution of NaOH was used to ensure the reaction being irreversible. Three parameters were varied to show their effects on the reaction rate .They are: percentage excess of NaOH solution (10 % - 100 %) , temperature (100-150)oC , and stirring speed (400-1100) rpm. It was noticed that increasing the percentage excess of NaOH solution enhances the rate of reaction while increasing temperature decreases the reaction rate since it is exothermic reaction. Increasing stirring speed also improves the reaction rate because it is mass transfer controlled .Calcu
... Show Moreدر قرآن کريم آياتي وجود دارد که يک يا چند بار به صورت کاملا مشابه در يک سوره و يا چند سوره، تکرار شده است. يکي از مسائل مهم در ترجمه قرآن کريم، ترجمه اينگونه آيات است، از آنجا که مشابه بودن اين آيات از روي حکمت الهي است، مترجمان نيز بايد در ترجمه خود اين مسأله را رعايت کرده و براي آيات مشابه ترجمهاييکسان ارائه کنند. از طرفي ممکن است تفاوت در ترجمه، مفهوم آيه را نيز تحت تأثير قرار دهد و براييک آيه مشابه دو مفهوم
... 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 MoreRecent reports provided evidence that epithelial to mesenchymal transition (EMT) and some matrix metalloproteinases (MMPs) contribute to the invasion and metastasis of cancer cells. This study investigated the expression pattern of some EMT markers (E-cadherin and Vimentin) and some MMPs (MMP-2 and MMP-9) in transitional cell carcinoma (TCC). Fifty five paraffin embedded biopsies were included in this study. Expression pattern of E-cadherin and Vimentin was evaluated by immunohistochemistry while cytoplasmic mRNA expression of both MMP-2 and MMP-9 were determined by in situ hybridization. The expression of all markers were significantly increased with the increase of patient's age (? 50 years), and furthermore an increase in men expression
... Show MoreUse of lower squares and restricted boxes
In the estimation of the first-order self-regression parameter
AR (1) (simulation study)
This current research deals with the "The role of organizational change in the achievement of strategic success" Who are getting increased attention to being one of the important topics and relatively new, And which have a significant impact on the future of the organization So there is a need for this research, which aims to identify the role of organizational change across dimensions (technology, organizational structure, human resources, organizational culture) in the strategic success through its components (a specific strategy, effective implementation, innovation, customer satisfaction)، And that by two main hypotheses, branched about eight hypothes
... Show MoreIn 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 MoreWhen the guard honey bees, Apis mellifera L., form a clump at the hive entrance or on the flight board, the oriental hornet, Vespa orientails L., either creeps toward the clump or hovers over it in order to take a bee. Once the hornet creeps, only few bees facing the hornet become alert, rock their heads and antennae, open their wings, and take a posture of defense. The rest of the clump stays listless without any signal of concern. However, the clump stays dense and the defending bees do not detach themselves neither from the rest of the clump nor from each other. For this reason, it is very difficult for the hornet to grab a bee unless the latter makes a “mistake” by detaching herself from other adjacent bees. If the hornet grabs s
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