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.
The language of theatre is made by a number of physical tools and moral elements. So as the actors, costumes, lightings and accessories represent the physical aspects of the show, they also represent its moral aspect too. When they transform from plastic words in the space of the visual show to become signs carrying its indications that give the meaning through the link, overlap and arrangement of its movements so as to finally look like as wording in a sentence carries the meaning and represent the language of theatre speech.
The show usually sends the recipient continuous signs that go beyond the limits of expressions that are conveyed by these tools, and that cover the largest part of the meaning. So what is kept hidden or unannoun
Mass customization under the internet of things
It has mixed views on the concept or the role (Portrait) carving human faces across historical periods. The counting and historical document recording profiles for individual, promised impression represents promised impression represents the importance and greatness of personal without attention logs features and individual features, and in all cases the (portrait) was working for celebrated personality, glorifying and out of respect for his role heroic or reputation or social status.
But if we intend carving human faces one varieties of art in sculpture became necessary for us to proceed from the statement which affirms "The requirement of art to be liberated from their recovery forms as they are in the outside world" and here we beg
This research is based on the study of a group of Quranic verses that share a certain part, and these verses are verses of righteousness, and the word righteousness has been mentioned in the Holy Qur’an eight times, and the number of verses in this word was six verses, in four walls, all of which are from the civil fence which is the cow and was There are five words of righteousness contained in them, and the family of Imran is one word, and the table is one word, and the argument is one word. This study adopts the method of analytical interpretation of the Quranic text is a term that means statement and clarification in a way that the researcher produces to divide a Quranic text into its elements that are involved in its formation and
... Show MoreThis research aims to study the performance of comedian in the plays of writer Moliere . The problem of research is to answer the following question: How does comedian Moliere's techniques in a number of his plays and funny acts? The research aims at revealing the means used by the comedian in his performance of a comedic character in the number of Moliere plays.
&
... Show MoreIn this research for each positive integer integer and is accompanied by connecting that number with the number of Bashz Attabq result any two functions midwives to derive a positive integer so that there is a point
In the last few years, following the relative stability of the political, economic, and security environments, Iraq has embarked on a transformation towards an ambitious program of automation across various sectors. However, this automation program faces numerous challenges, including significant investments in technology and training, addressing social impacts, and combating widespread illiteracy
Jurists were unable to comprehend modern terminology and concepts to provide mature answers
On the questions and issues of the age, and what I want to research and raise it; an important and urgent subject, to crystallize the opinion jurisprudence
Islamic, which is the subject of citizenship. The globalization of the concept of citizenship, and the spread of special cultural differences,
The blurring of the identities and specificities of nations due to conflict, or political differences, often results in responses
This trend is inversely rooted and rooted, and as a result, the threat to one's religion or predecessors becomes threatened by one's culture,
Thus destroying the essence of his identity. Man has the highest rank
