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).
Futsal and blind football are group games of a competitive nature due to their excitement, excitement, fun, and aesthetic goals with charming artistic touches. This explains the public's passion for these two games, whether healthy people or blind people play them, to expand their vision and knowledge. About these two games, a historical approach is presented about their origins, development, and how they became globally recognized competitive sports with unified rules and world championships at various levels. Studying the origin and global spread of both futsal and blind football and identifying the most prominent developments in the rules and tools for futsal and blind football. The most important findings were that both futsal and footb
... Show MoreThis study is an attempt to investigate the conceptual metaphor of UP and DOWN commonly used in Iraqi community. Some of the metaphorical expressions in Iraqi colloquial Arabicarewidely used by Iraqi speakers in everyday language. Ithas been analyzed by following the cognitive theory of metaphor (Lakoff& Johnson,1980).The study indicates that the Iraqi speakerexperiences more of the metaphorical expressions of UP and DOWN to referto many of the abstract concepts that shape his/her impression of everyday life situations.
A stylistic study in the poetry of Hafiz Ibrahim, praise be to God, Lord of the worlds, and prayers and peace be upon his best messengers, and the seal of his prophets, Muhammad and his good and pure family, and after ...
The poet Hafez Ibrahim is considered one of the well-known poets in the modern era, and his language was distinguished by sobriety, eloquence in expressions, and beautiful meanings And he had my journey in the study of his poetry a stylistic study, and the research came with an introduction in which the concept of stylistics was briefly explained, since it was studied by many researchers, then divided the research into three topics: I studied in the first the construction of the poem, and I stood at the most importan
Background: Maxillary sinusitis can arise after sinus floor elevation surgery and should be treated immediately to prevent further complications which included dental implants failure, graft lost, and oro-antral fistula. This is the first systematic review to assess the incidence, causes, and treatment of sinusitis after sinus lift surgery. Materials and methods: An electronic search included MEDLINE (PUBMED) data base site was carried out for articles involving development of sinusitis after sinus lift surgery from September 1997 up to April, 8, 2017. The search was done and reviewed by two independent authors. Results: The total results of electronic search were (182) abstracts and articles, the extracted articles which involved develo
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The present study is a linguistic study of comment clauses in the American Series „Friends‟ .Comment clauses refer to those clauses which comment on the content of the main clause or the attitude of the speaker towards the way of speaking .The problem of this study is to answer the following questions ; what types of comment clauses can be used in the face- to –face conversations , for what functions these comment clauses could be used , and how these comment clauses are used by the participants of these conversations . This study is a qualitative one . The study aims to investigate the types of comment clauses used in the American Series “Friends‟. The study also aims to investigate the pragmatic functions of these comment clause
... Show MoreThis case series aims to evaluate patients affected with post COVID‐19 mucormycosis from clinical presentation to surgical and pharmacological treatment to improve the disease prognosis.
This case series was conducted at a specialized surgery hospital in Baghdad Medical City for over 10 months. Fifteen cases who had mild to severe COVID‐19 infections followed by symptoms similar to aggressive periodontitis, such as mobility and bone resorption around the multiple maxillary teeth, were included in this case series.
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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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