This paper is the third and last instalment of our project of computation of the low-degree unramified cohomology of quadrics. As in the previous papers [15] and [16], we denote by η X the map H(F,Q/Z(n− 1))→ H nr(F (X)/F,Q/Z(n− 1)) for a smooth, projective quadric X defined over a field F of characteristic 6= 2. Recall that in these papers we proved that Ker η X is generated by symbols for n ≤...

Lecture Notes taken by Nilufer Koldan In this lecture I will describe one of the most significant achievements of the second half of the XX century – the Atiyah-Singer index theorem. I will also discuss some more recent developments in the area as well as some open problems. 1. The definition of the index 1.1. The finite-dimensional case. Let A : V 1 → V 2 be a linear map between finite dimensi...

Introduction FCC decant oil is the primary feedstock to delayed coker to produce needle coke, a premium carbon precursor to synthetic graphite electrodes. Mesophase development during coking, determines the graphitizability of the needle coke product. Mesophase development, in turn, depends on the molecular composition of the feedstocks [1,2]. In a commercial delayed coking unit, liquid-phase c...

This paper is motivated by two problems recently proposed by Coker on combinatorial identities related to the Narayana polynomials and the Catalan numbers. We find that a bijection of Chen, Deutsch and Elizalde can be used to provide combinatorial interpretations of the identities of Coker when it is applied to weighted plane trees. For the sake of presentation of our combinatorial corresponden...

K. T. Atanassov, ?Intuitionistic fuzzy sets?, Fuzzy Sets and Systems, 20(1986), 87-96. S. S. Benchalli and Jenifer J. Karnel, ?On fuzzy b open sets in fuzzy topological spaces?, J. Comp. & Math. Sci, 1(2010), 127 – 134. C. L. Chang, ?Fuzzy topological spaces?, J. Math. Anal. Appl, 24(1968), 182-190. D. Coker, ?An introduction to intuitionistic fuzzy topological spaces?, Fuzzy Sets and Systems, ...

We investigate to what extent homotopy invariant, excisive and matrix stable homology theories help one distinguish between the Leavitt path algebras $L(E)$ $L(F)$ of graphs $E$ $F$ over a commutative ground ring $\ell$. approach this by studying structure such under bivariant algebraic $K$-theory $kk$, which is universal theory with properties above. show that very mild assumptions on $\ell$, ...