Notions of strongly regular, regular and left(right) regular $Gamma$−semigroupsare introduced. Equivalent conditions are obtained through fuzzy notion for a$Gamma$−semigroup to be either strongly regular or regular or left regular.

Let I be the ideal generated by alternating polynomials in two sets of n variables. Haiman proved that the q, t-Catalan number is the Hilbert series of the graded vector space M(= ⊕ d1,d2 Md1,d2) spanned by a minimal set of generators for I. In this paper we give simple upper bounds on dim Md1,d2 in terms of partition numbers, and find all bi-degrees (d1, d2) such that dimMd1,d2 achieve the upp...

In this work, a version of the technique for order preference by similarity ideal solution (TOPSIS) with entropic regularization approach is developed for solving the fuzzy multi-objective nonlinear programming (MONLP) problems. Applying the basic principle of compromise of TOPSIS, the fuzzy MONLP problem can be reduced into a fuzzy bi-objective nonlinear programming problem. Moreover, followin...

Abstract: In this study we introduce a new class of a non-associative algebraic structure namely intra-regular Abel Grassmann's groupoid (AG-groupoid in short). We apply generalized fuzzy ideal theory to this class and discuss its related properties. We introduce ) , ( k q ∨ ∈ ∈ -fuzzy semiprime ideals in AG-groupoids and characterize it. Specifically we have characterized intra-regular AG-grou...

The synthesis of nanoscaled β-Bi(2)O(3) starting from the bismuth oxido clusters [Bi(6)O(4)(OH)(4)](NO(3))(6)·H(2)O, [Bi(22)O(26)(OSiMe(2)(t)Bu)(14)], [Bi(38)O(45)(NO(3))(20)(DMSO)(28)](NO(3))(4)·4DMSO and [Bi(38)O(45)(OMc)(24)(DMSO)(9)]·2DMSO·7H(2)O (OMc = O(2)CC(3)H(5)) under ambient conditions is reported. The metal oxido clusters are regarded as ideal precursors for β-Bi(2)O(3) due to their...

Let (f1, . . . , fs) be a polynomial family in Q[X1, . . . , Xn] (with s ≤ n − 1) of degree bounded by D, generating a radical ideal, and defining a smooth algebraic variety V ⊂ C. Consider a generic projection π : C → C, its restriction to V and its critical locus which is supposed to be zero-dimensional. We state that the number of critical points of π restricted to V is bounded by Ds(D−1)n−s...

We study the linear syzygies of a homogeneous ideal I ⊆ S = Symk(V ), focussing on the graded betti numbers bi,i+1 = dimk Tori(S/I, k)i+1. For a variety X and divisor D with V = H(D), what conditions on D ensure that bi,i+1 6= 0? In [2], Eisenbud shows that a decomposition D∼A+B such that A and B have at least two sections gives rise to determinantal equations (and corresponding syzygies) in IX...

We have performed spin- and angle-resolved photoemission spectroscopy of Bi(2)Te(3) and present the first direct evidence for the existence of the out-of-plane spin component on the surface state of a topological insulator. We found that the magnitude of the out-of-plane spin polarization on a hexagonally deformed Fermi surface of Bi(2)Te(3) reaches maximally 25% of the in-plane counterpart, wh...

The aim of this paper is to investigate the ideal theory of Γ-semirings based on intersectional soft sets. Some basic operations are investigated and some related properties are also studied. Finally, some characterizations of regular and intra-regular Γ-semirings are obtained by means of soft intersectional ideals (bi-ideals, quasi-ideals).

We have theoretically proposed and experimentally demonstrated that two EPR photon pairs can be transformed into a threephoton W state by local operation and classical communication (LOCC). The fidelity of the final state to the ideal W state was 0.778±0.043. The obtained expectation value of the witness operator for distinguishing between the three-photon W state and bi-separable states was −0...