Last time we defined problems EXACT -INDSET = {[G, k] | the largest independent set of G has size = k}, MINDNF = {[φ, k] | φ is a DNF that has an equivalent DNF of size ≤ k}, and the complexity classes Σ2 and its dual Π P 2 . Σ P 2 and Π P 2 were defined in analogy with NP and coNP except that there are two levels of quantifiers with alternation ∃∀ and ∀∃, respectively. We observed that MINDNF ...

The quaking viable (qk(v)) mice represent an animal model of dysmyelination. The absence of expression of the QKI-6 and QKI-7 cytoplasmic isoforms in oligodendrocytes (OLs) during CNS myelination causes the qk(v) mouse phenotype. The QKI RNA-binding proteins are known to regulate RNA metabolism of cell cycle proteins and myelin components in OLs; however, little is known of their role in reorga...

Graphs are used in modeling interconnections networks and measuring their properties. Knowing and understanding the graph theoretical/combinatorial properties of the underlying networks are necessary in developing more efficient parallel algorithms as well as fault-tolerant communication/routing algorithms [1] The hypercube is one of the most versatile and efficient networks yet discovered for ...

in the present paper, we introduces the notion of integral type contractive mapping with respect to ordered s-metric space and prove some coupled common fixed point results of integral type contractive mapping in ordered s-metric space. moreover, we give an example to support our main result.

We study symmetry properties of quaternionic K\"ahler manifolds obtained by the HK/QK correspondence. To any Lie algebra $\mathfrak{g}$ infinitesimal automorphisms initial hyper-K\"ahler data we associate a central extension $\mathfrak{g}$, acting resulting manifold. More specifically, metrics one-loop deformation $c$-map construction, proving that projective special manifold gives rise to Kill...

There are very few known examples of manifolds with positive sectional curvature. Apart from the compact rank one symmetric spaces, they exist only in dimensions 24 and below and are all obtained as quotients of a compact Lie group equipped with a biinvariant metric under an isometric group action. They consist of certain homogeneous spaces in dimensions 6, 7, 12, 13 and 24 due to Berger [Be], ...

For a graph G, the k-colour Ramsey number Rk(G) is least integer N such that every k-colouring of edges complete KN contains monochromatic copy G. Let Cn denote cycle on n vertices. We show for fixed k?2 and odd sufficiently large,Rk(Cn)=2k?1(n?1)+1. This resolves conjecture Bondy Erd?s large n. The proof analytic in nature, first step which to use regularity method relate this problem theory o...

The quantum analogs of the derivatives with respect to coordinates qk and momenta pk are commutators with operators Pk and Qk. We consider quantum analogs of fractional Riemann-Liouville and Liouville derivatives. To obtain the quantum analogs of fractional Riemann-Liouville derivatives, which are defined on a finite interval of the real axis, we use a representation of these derivatives for an...

Generalizations of (∈, ∈∨ q)-fuzzy filter of R0-algebras is discussed in the paper [Y. B. Jun, S. Z. Song and J. Zhan, Generalizations of (∈, ∈ ∨ q)-fuzzy filters in R0-algebras, Int. J. Math. Math. Sci. Volume 2010, Article ID 918656, 19 pages]. In this paper, further properties of an (∈, ∈ ∨ qk)-fuzzy filter are investigated. Using a class of filters, an (∈, ∈ ∨ qk)-fuzzy filter is constructe...