We show that the Faddeev-Pyatov SL q (N) differential algebra [1] is a subalgebra of the GL q (N) differential algebra constructed by Schupp, Watts and Zumino [2]. In the paper [1], the bicovariant differential algebra on SL q (N) (see below (10), (11)) with generators {T ij , L ij , ˜ Ω ij } i, j = 1,. .. N has been constructed. The elements T ij are generators of the algebra F un(SL q (N)), w...

We quantize the interaction of gravity with Yang-Mills and spinor fields, hence offering a quantum theory incorporating all four fundamental forces nature. Let us\ann{as} abbreviate spatial Hamilton functions Standard Model by $H_{SM}$ function $H_G$. Working in fiber bundle $E$ base space $\socc=\R[n]$, where elements are Riemannian metrics, we can express form $H_G+H_{SM}=H_G+t^{-\frac23}\til...

We consider a square matrix Aǫ whose entries have asymptotics of the form (Aǫ) ij = a ij ǫ A ij + o(ǫ A ij) when ǫ goes to 0, for some complex coefficients a ij and real exponents A ij. We look for asymptotics of the same type for the eigenvalues of Aǫ. We show that the sequence of exponents of the eigenvalues of Aǫ is weakly (super) majorized by the sequence of corners of the min-plus characte...

Transportation networks play a vital role in modern societies. Structural optimization of a transportation system under a given set of constraints is an issue of great practical importance. For a general transportation system whose total cost C is determined by C = Sigma(i<j)C(ij)(I(ij)), with C(ij) (I(ij)) being the cost of the flow I(ij) between node i and node j, Banavar and co-workers [Phys...

Let R be a non-domain commutative ring with identity and A(R) be theset of non-zero ideals with non-zero annihilators. We call an ideal I of R, anannihilating-ideal if there exists a non-zero ideal J of R such that IJ = (0).The annihilating-ideal graph of R is defined as the graph AG(R) with the vertexset A(R) and two distinct vertices I and J are adjacent if and only if IJ =(0). In this paper,...

Let $G$ be a graph and let $m_{ij}(G)$, $i,jge 1$, be the number of edges $uv$ of $G$ such that ${d_v(G), d_u(G)} = {i,j}$. The {em $M$-polynomial} of $G$ is introduced with $displaystyle{M(G;x,y) = sum_{ile j} m_{ij}(G)x^iy^j}$. It is shown that degree-based topological indices can be routinely computed from the polynomial, thus reducing the problem of their determination in each particular ca...

Consider a N × n random matrix Yn = (Y n ij ) where the entries are given by Y n ij = σ(i/N,j/n) √ n X ij , the X n ij being centered i.i.d. and σ : [0, 1] 2 → (0,∞) being a continuous function called a variance profile. Consider now a deterministic N×n matrix Λn = ( Λij ) whose non diagonal elements are zero. Denote by Σn the non-centered matrix Yn+Λn. Then under the assumption that limn→∞ N n...

The notion of δ−open sets in bitopological spaces was introduced by Banerjee [2]. In this paper we more investigate ij− δ−open sets. We study some sets related to ij− δ−open sets. Also, we study some separation axioms in bitopological spaces based on ij − δ−open sets.

OBJECTIVES To determine the spectrum of mutations in the Mediterranean fever gene (MEFV) of Iranian Jews with familial Mediterranean fever (FMF) and to analyse their clinical manifestations. METHODS FMF patients with both parents of Iranian-Jewish (IJ) extraction or with one IJ parent (IJ-other, 10 of each) were characterized for clinical manifestations, and the B30.2 (PRYSPRY) domain of thei...

The non-linear relation between electric polarization and electric field strength is achieved through introducing the retarded electromagnetic interactions between classical charge particles. The result agrees with the phenomenological theory in current non-linear optics, means that the non-linear phenomena in optics come from the retarded electromagnetic interaction between charged particles. ...