In this paper the chain length of a space of fuzzy orderings is defined, and various properties of this invariant are proved. The structure theorem for spaces of finite chain length is proved. Spaces of Fuzzy Orderings Throughout X = (X,A) denoted a space of fuzzy orderings. That is, A is a fuzzy subgroup of abelian group G of exponent 2. (see [1] (i.e. x 2 = 1,  x  G), and X is a (non empty) fuzzy subset of the character group ï£ (A) = Hom(A,{1,–1}) satisfying: 1. X is a fuzzy closed subset of ï£ (A). 2.  an element e  A such that ï³(e) = – 1  ï³ ïƒŽ X. 3. Xïž :={a  A\ ï³(a) = 1  ï³ ïƒŽ X} = 1. 4. If f and g are forms over A and if x  D( f  g) then  y  D( f ) and z  D(g) such that x  D<y, z >. Observe, by 3, that the element e  A whose existence is asserted by 2 is unique. Also, e  1 (since ï³(1) = 1  ï³ ïƒŽ X). Notice that for a  A, the set X(a):= {ï³ ïƒŽ Xï³(a) = 1} is clopen (i.e. both closed and open) in X. Moreover, ï³(a) = – 1  ï³(– a) = 1 holds for any ï³ ïƒŽ X (by 2).
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Recent reports of new pollution issues brought on by the presence of medications in the aquatic environment have sparked a great deal of interest in studies aiming at analyzing and mitigating the associated environmental risks, as well as the extent of this contamination. The main sources of pharmaceutical contaminants in natural lakes and rivers include clinic sewage, pharmaceutical production wastewater, and sewage from residences that have been contaminated by drug users' excretions. In evaluating the health of rivers, pharmaceutical pollutants have been identified as one of the emerging pollutants. The previous studies showed that the contaminants in pharmaceuticals that are widely used are non-steroidal anti-inflammatory drugs, ant
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Nystatin is the drug of choice for treatment of cutaneous fungal infections with main disadvantage that is the need for multiple applications to achieve complete eradication which may reduce patient compliance. Microparticles offer a solution for such issue as they are one of sustained release preparations that achieve slow release of drug over an extended period of time. The objectives of this study were to fabricate nystatin-loaded chitosan microparticles with the ultimate goal of prolonging drug release and to analyze the influence of polymer concentration on various properties of microparticles. Microparticles were prepared by chemical cross-linking method using glutaraldehyde as cross-linking agent. Five formulas, namely N1C1, N1C2,
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In this paper, the dynamical behavior of a three-dimensional fractional-order prey-predator model is investigated with Holling type III functional response and constant rate harvesting. It is assumed that the middle predator species consumes only the prey species, and the top predator species consumes only the middle predator species. We also prove the boundedness, the non-negativity, the uniqueness, and the existence of the solutions of the proposed model. Then, all possible equilibria are determined, and the dynamical behaviors of the proposed model around the equilibrium points are investigated. Finally, numerical simulations results are presented to confirm the theoretical results and to give a better understanding of the dynami
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In this paper, the general framework for calculating the stability of equilibria, Hopf bifurcation of a delayed prey-predator system with an SI type of disease in the prey population, is investigated. The impact of the incubation period delay on disease transmission utilizing a nonlinear incidence rate was taken into account. For the purpose of explaining the predation process, a modified Holling type II functional response was used. First, the existence, uniform boundedness, and positivity of the solutions of the considered model system, along with the behavior of equilibria and the existence of Hopf bifurcation, are studied. The critical values of the delay parameter for which stability switches and the nature of the Hopf bifurcat
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The educational service industry is one of the most negatively affected industries by the spread of the COVID-19 pandemic. Government agencies have taken many measures to slow its spread, and then restrict movement and gatherings and stop recreational activities. Furthermore, the repercussions of the curfew had a significant impact due to the interruption in actual attendance for students and employees, and the severity of the Covid-19 crisis and its (economic, social, security, humanitarian and behavioral) effects on all societies and work sectors is no secret to anyone. Iraq, like other countries, was also affected by the negative impact of Covid-19 pandemic in all fields of institutional work, especially public fields, and specifically t
... Show MoreThe modernity of election practices of the elections in Iraq, according to the democratic approach, has led to a struggle between political rival forces reflecting a deep pressure on the tools involved in the management, marketing or control of these elections across the general social level. Hence the problem of research resides in answering the following question: What is the nature and size of the pressures affecting the media performance of Al-Iraqia News channel before the legislative elections of 2018 in Iraq?
The objectives of the research were the following:
1. to identify the nature of the pressures that limit the Al-Iraqia News channel’s perfo
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