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 aim of the research is to determine the impact of evaluating the investment projects in the development and preparation of investment budgets prepared by the economic units, since the investment projects are of an important and vital nature of the economic units, because these projects include the length of time for preparation and implementation and the accompanying period of this risk and uncertainties as well as need To the many funds to complete the project , The process of evaluating the implemented projects, which have been prepared an investment budget previously will contribute to the extent of matching the estimated data with the actual results or deviations, which is a step to avoid these errors in future p
... Show MoreThe last decade of this 20th century provides a wide spread of applications of one of the computer techniques, which is called Fuzzy Logic. This technique depends mainly on the fuzzy set theory, which is considered as a general domain with respect to the conventional set theory. This paper presents in initiative the fuzzy sets theory and fuzzy logic as a complete mathematics system. Here it was explained the concept of fuzzy set and defined the operations of fuzzy logic. It contains eleven operations beside the other operations which related to fuzzy algebra. Such search is considered as an enhancement for supporting the others waiting search activities in this field.
The Almighty Allah has addressed His followers by advising them to follow the example of the prophet (PBUH). Allah says: (INDEED IN THE MESSENGER OF ALLAH YOU HAVE A GOOD EXAMPLE TO FOLLOW). So, He was a true and everlasting example for the people to follow and imitate in all aspects of life. Knowledge and learning, especially Qura'nic knowledge, are among the priorities.
The present study is concerned with how to follow the Prophet example (PBUH) in the field of Qur'an reciting. It aims at showing His instructions on Qur'an reciting, and how He was followed by His Companions. The present study falls into an introduction and four sections. Section One deals with the commands given by Allah to follow His prophet. Second Two
... Show MoreThe purpose of this research its study of Natural Consideration that contributed in turning of Dairy products in Baghdad Governorate , this subject deal with centered geographical location in the midlle of Iraq ,it’s also main market in discharge and marketing to rest of Iraqi’s governorate pointed to it’s an active role in localized of it’s factory(milk ,cheese,cream ,butter, yoghurte)and it’s constant ,thus distributedin all district of Baghdad ,flat governorate surface encourage this industry ,also climate (temperature, wind, (it’s speed and it’s direction) ,rainfull and relative wet) also water resources and it’s influenced that nessacity of production process with important inculclusion that researcher came out throu
... Show MoreIt was Aristotle who first drew attention to the superior quality of literature to the other factual fields of knowledge. Contradicting his predecessor Plato on the issue of „truth,‟ Aristotle believed that „poetry is more philosophical and deserves more serious attention than history: for while poetry concerns itself with universal truths, history considers only particular facts.‟ (1) The critical attention to the disparity between the literary truth and the historical truth grew up throughout ages to flourish in the Renaissance and after with a bunch of distinctive views on this subject. Sir Philip Sidney (1554-1586), for example, found that literature does not offer a literal description of reality but rather a heightened vers
... Show MoreEvaluating the part of historical center in Baghdad City
MORALS ARE THE MAIN PILLARS IN HUMAN'S LIFE
This paper discusses reliability R of the (2+1) Cascade model of inverse Weibull distribution. Reliability is to be found when strength-stress distributed is inverse Weibull random variables with unknown scale parameter and known shape parameter. Six estimation methods (Maximum likelihood, Moment, Least Square, Weighted Least Square, Regression and Percentile) are used to estimate reliability. There is a comparison between six different estimation methods by the simulation study by MATLAB 2016, using two statistical criteria Mean square error and Mean Absolute Percentage Error, where it is found that best estimator between the six estimators is Maximum likelihood estimation method.