We define a total k-labeling φ of graph G as combination an edge labeling φe:E(G)→{1,2,…,ke} and vertex φv:V(G)→{0,2,…,2kv}, such that φ(x)=φv(x) if x∈V(G) φ(x)=φe(x) x∈E(G), where k= max {ke,2kv}. The is called irregular reflexive every two different edges has distinct weights, the weight defined summation label itself its labels. Thus, smallest value k for which strength G. In this paper, we ...

یهدف البحث إلى الکشف عن المصطلحات النقدیة والبلاغیة المزدوجة عند البغدادی الَّتی ذکرها فی کتابه (قانون البلاغة نقد النثر والشعر), وقد عدت إحدى العربیة التی لقیت العنایة والاهتمام من قِبل وممن تقدمه ومن جاء بعده النقاد والبلاغیین، وعلیه فقد توزعت الدراسة على ثلاث مباحث الأول ألقى الضوء الشعریة وهی:(الاستدراک والرجوع, الکنایة والتعریض), والمبحث الثانی تناول النثریة وهی:(السجع والازدواج, الهذر والتبع...

Let A be a unital complex semisimple Banach algebra, and MA denote its maximal ideal space. For matrix M∈An×n, Mˆ denotes the obtained by taking entry-wise Gelfand transforms. M∈Cn×n, σ(M)⊂C set of eigenvalues M. It is shown that if A∈An×n B∈Am×m are such for all φ∈MA, σ(Aˆ(φ))∩σ(Bˆ(φ))=∅, then C∈An×m, Sylvester equation AX−XB=C has unique solution X∈An×m. As an application, Roth's removal rule...

Let A, B be algebras and a∈A, b∈B a fixed pair of elements. We say that map φ:A→B preserves products equal to b if for all a1,a2∈A the equality a1a2=a implies φ(a1)φ(a2)=b. In this paper we study bijective linear maps φ:I(X,F)→I(X,F) preserving primitive idempotents I(X,F), where I(X,F) is incidence algebra finite connected poset X over field F. fully characterize situation, when such φ exists,...

In order to extend the Schützenberger’s factorization to general perturbations, the combinatorial aspects of the Hopf algebra of the φ-deformed stuffle product is developed systematically in a parallel way with those of the shuffle product. and in emphasizing the Lie elements as studied by Ree. In particular, we will give an effective construction of pair of bases in duality.

Let Φ be an irreducible root system (sometimes we denote Φ by Φ(X) to indicate its type X). Choose a simple root system Π in Φ. Let Φ + (resp. Φ~) be the corresponding positive (resp. negative) root system of Φ. By a subsystem Φ' of Φ (resp. of Φ + ) , we mean that Φ' is a subset of Φ (resp. of Φ) which itself forms a root system (resp. a positive root system). We refer the readers to Bourbaki'...

The renormalizability of a quadratic gravity theory with exponential coupling between dilaton field and curvature terms is verified. The wave function for this model is then deduced to first order in e −Φ g2 4 by solving a perturbed second-order Wheeler-DeWitt equation, assuming that the potential is slowly varying with respect to Φ. It is shown how formal expressions for the average paths in m...

We study principles of the form: if a name σ is forced to have certain property φ, then there ground model filter g such that σg satisfies φ. prove general correspondence connecting these forcing axioms. Special cases main theorem are: Any axiom can be expressed as principle. For instance, PFA equivalent to: A principle for rank 1 names (equivalently, nice names) subsets ω1. 2 sets reals. λ-bou...