This paper investigates the recovery for time-dependent coefficient and free boundary for heat equation. They are considered under mass/energy specification and Stefan conditions. The main issue with this problem is that the solution is unstable and sensitive to small contamination of noise in the input data. The Crank-Nicolson finite difference method (FDM) is utilized to solve the direct problem, whilst the inverse problem is viewed as a nonlinear optimization problem. The latter problem is solved numerically using the routine optimization toolbox lsqnonlin from MATLAB. Consequently, the Tikhonov regularization method is used in order to gain stable solutions. The results were compared with their exact solution and tested via

Increased diseases and obesity currently due to increased production and excessive consumption of foods manufactured from non-food sweeteners without attention to the risk of consuming those additional high calories due to consuming these refreshing products such as juices and other various drinks, especially in the summer season by most segments of Iraqi society, especially workers, children and school students the aim of this study. Therefore, the study designed to replace sucrose with 0.03, 0.04 and 0.05% of each of the white stevia crystals and milled dry stevia leaves in the laboratory manufacture of juices and its effect on the general and sensory characteristics and the extent of their acceptability among the specialized r

The analysis of detective novels has taken different aspects. The linguistic analysis of them, for example, has tackled the linguistic systems of morphology, phonology, syntax, semantics, and pragmatics. In line with the linguistic analysis, this study explores the various pragmatic and stylistic devices realized through detective novels for the purpose of misdirecting and deceiving the reader. The problem is that when readers try to reach to the truth, they face difficulties. They might not reach to the right solution or infer wrong conclusions because writers use some techniques to hide the truth and mislead them. This study aims at examining these techniques and devices; namely, Grice's Maxims and ambiguity as pragmatic devices on the

This study was performed on the Tigris River (Baghdad city section) during the period between December 2016 and December 2018 to assess seasonal variation in water quality using the Overall Index of Pollution (OIP). The OIP is one of the reliable tools for the assessment of surface water quality. To calculate OIP-values, eight parameters were measured ( pH, Dissolved Oxygen "DO", Biological Oxygen Demand "BOD", Total Dissolved Solid "TDS", Total Hardness "TH", calcium "Ca", Sulphate "SO4" and Alkalinity). The results showed the anthropogenic activities impact of Baghdad population that directly discharge of "inadequate treated" waste water to the river.  OIP values were acceptable (1˃OIP˃ 1.7) in 2011, 2012, 2013 and 2018. However, in

       In this paper, a fixed point theorem of nonexpansive mapping is established to study the existence and sufficient conditions for the controllability of nonlinear fractional control systems in reflexive Banach spaces. The result so obtained have been modified and developed in arbitrary space having Opial’s condition by using fixed point theorem deals with nonexpansive mapping defined on a set has normal structure. An application is provided to show the effectiveness of the obtained result.

Thank God also taught us that thanks . thank meets the blessings and rewards mazidk glory we have no knowledge except what you have taught you Alim hakim , not counted praise you as yourself praised and pray and to recognize the envoy mercy to the worlds , prophet Mohammed and his family and companions and guided to the day of judgment .
But after :
Aware of the interpretation of the most important science needed by Muslims because God Almighty sent down the Quraan to be a way of the life for Muslims is subject to a healing for what is in the breasts and it slaham and flaham and has spared the nation from crisisThe stats of the monks , like other verses talking about Christians and Jews and what they have invented in the religion o

The subject of fear is one of the most important tasks that one should seek to find out the reasons behind it, and push it up with all its sound mental concepts.
     The main reason for the lack of security and fear and disturbance in the world is to commit the legitimate violations that God warned us in his Holy Book as well as in the Sunnah of His Prophet (peace be upon him).
    The talk about the causes of fear in the Koran is not limited to the word (fear) Fakk but came in different and varied methods such as (horror) and (awe) and (shares) and (narrow).

The research is a vision of the future of industry in Iraq, so it is may be outside the ceiling of the capabilities of the Iraqi economy, and therefore it is exaggerated. Therefore, future plans must be applicable through the availability of capabilities. Everyone knows that the financial and administrative corruption and mismanagement of resources are the main cause of the inefficiency of the industrial sector, and the failure to exercise its real role in achieving economic development.; as well as the political situation and the dominance of parties and their insistence on addressing positions that have a strong relationship in managing the economic sector that has a significant impact on drawing the economic map in its current

      Data security is an important component of data communication and transmission systems. Its main role is to keep sensitive information safe and integrated from the sender to the receiver. The proposed system aims to secure text messages through two security principles encryption and steganography. The system produced a novel method for encryption using graph theory properties; it formed a graph from a password to generate an encryption key as a weight matrix of that graph and invested the Least Significant Bit (LSB) method for hiding the encrypted message in a colored image within a green component. Practical experiments of (perceptibility, capacity, and robustness) were calculated using similarity measures like PSNR, MSE, and

The technological development in the field of information and communication has been accompanied by the emergence of security challenges related to the transmission of information. Encryption is a good solution. An encryption process is one of the traditional methods to protect the plain text, by converting it into inarticulate form. Encryption implemented can be occurred by using some substitute techniques, shifting techniques, or mathematical operations. This paper proposed a method with two branches to encrypt text. The first branch is a new mathematical model to create and exchange keys, the proposed key exchange method is the development of Diffie-Hellman. It is a new mathematical operations model to exchange keys based on prime num