We investigate mathematical models of the Hepatitis B and C viruses in the study, considering vaccination effects into account. By utilising fractional and ordinary differential equations, we prove the existence of equilibrium and the well-posedness of the solution. We prove worldwide stability with respect to the fundamental reproduction number. Our numerical techniques highlight the biological relevance and highlight the effect of fractional derivatives on temporal behaviour. We illustrate the relationships among susceptible, immunised, and infected populations in our epidemiological model. Using comprehensive numerical simulations, we analyse the effects of fractional derivatives and highlight solution behaviours. Subsequent investigatio

The numerical investigation has been performed to study the radiation affected steady state laminar mixed convection induced by a hot inner varied positions circular core in a horizontal rectangular channel for a fully developed flow. To examine the effects of thermal radiation on thermo fluid dynamics behavior in the eccentric geometry channel, the generalized body fitted co-ordinate system is introduced while the finite difference method is used for solving the radiative transport equation. The governing equations which used are continuity, momentum and energy equations. These equations are normalized and solved using the Vorticity-Stream function. After validating numerical results for the case without radiation, the detailed rad

We study in this paper the composition operator that is induced by ?(z) = sz + t. We give a characterization of the adjoint of composiotion operators generated by self-maps of the unit ball of form ?(z) = sz + t for which |s|?1, |t|<1 and |s|+|t|?1. In fact we prove that the adjoint is a product of toeplitz operators and composition operator. Also, we have studied the compactness of C? and give some other partial results.

  Amidst the changes resulting from the subject matter of expression in art. The necessity of searching for the expressive features of thought that leaves different imprints with aesthetic features and values which called for re-modifying the expressive vision of contemporary drawings. Therefore, this research has been concerned with the study of (abstract expressive features in the drawings of (Serwan Baran) and (Eric Barto) - a comparative study), and the research includes four chapters. The first chapter is devoted to explaining the research problem, its importance, need, purpose, and limits, then determining the most important terms mentioned in it. Where the research problem dealt with the subject of abstract expressive feature

This study was conducted to determine the ability of water treatment system (Vortisand) to reduce some chemical and physical properties for tigris river raw water, It consisted of turbidity, electrical conductivity, pH, total hardness, calcium Hardness as well as temperature in order to determine the unit`s efficiency for reducing their concentration as compared to those in the water produced by some classical potable water projects (Dora and Wathba) in Baghdad. Samples were collected during the cold months (December 2016 and January 2017) and during the hot months (May and June 2017). The results showed that this system has the ability to reduce some properties such as turbidity, the values were 215NTU in raw water and decreased to NTU

The banking industry, as a result of the great challenges it faced, required continuous development of the principles of management, control and mechanisms used. The Basel Committee on Banking Supervision has played a leading role in legalizing many of these developments and has been able to contribute significantly to establishing a common framework for banking supervision, The central role in the various countries of the world is based on coordination between the various regulatory authorities and thinking about finding mechanisms to confront the risks faced by banks, recognizing the importance of the banking sector in the stability of domestic and international banking systems or the danger of this sector in the emergence of F

We found that 4,5- diphenyl- 3(2- propynyl) thio- 1??-triazole [1? forms a complex with Pd (11) ion of ratio 1:1 which absorbs light in CH2CI2 at 400 nm, and 4,5- diphenyl- 3(2- propenyl) thio- 1,2,4- triazole [II] forms complexes with Pd (II) ion of ratio 1:1 which absorbs light at 390 nm, and of ratio 2:1 which absorbs light at 435 nm. On the other hand, we found that the new derivative 4- phenyl- 5( p- amino phenyl) -3- mercapto- 1,2,4- triazole ?111? forms complexes with Cu (II) ion of the ratio 1:1 which absorbs light at 380 nm, with Ni (II) ion of the ratio 3:1 which absorbs light at 358 nm; and with Co (11) ion of the ratio 3.2:1 which absorbs light at 588 nm. The ratio of the complexes were determined by measuring the electronic spe

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The research deals with the statement of the importance of unanimous in Islamic Sharia in terms of being the third source of Islamic legislation after the Holy Qur’an and the Sunnah of the Prophet, and the extent of interest of the scholars of interpretation in it, and those who took great interest in mentioning what was agreed upon in every site that necessitated mentioning its issues within, or mentioning an event that has encountered an unanimous, and in various sciences, to extract and extrapolate Sharia rules when these rules are lost in the texts, because it is based on them and derived from them. Among these distinguished scholars is Muhammad bin Jarir al-Tabari. Besides, the research discusses in