and Kk(BA,Br) = span{Br, (BA)Br, . . . , (BA)k−1Br}, (3) where B ∈ Rn×m is the mapping and preconditioning matrix, and apply Krylov subspace iteration methods on these subspaces. For overdetermined problems, applying the standard CG method to Kk(BA,Br) leads to the preconditioned CGLS [3] or CGNR [9] method while for underdetermined problems it leads to preconditioned CGNE [9] method. The GMRES...

A graph G is r-Ramsey for a graph H, denoted by G→ (H)r, if every r-colouring of the edges of G contains a monochromatic copy of H. The graph G is called r-Ramseyminimal for H if it is r-Ramsey for H but no proper subgraph of G possesses this property. Let sr(H) denote the smallest minimum degree of G over all graphs G that are r-Ramseyminimal for H. The study of the parameter s2 was initiated ...

The Kaluza-Klein (KK) modes of graviton are studied in the IIB superstring compactification where the warped geometry is realized at the Klebanov-Strassler (KS) throat. Knowledge of the metric of the KS throat enables us to determine their wave functions with good accuracy, without any further specification of the rest of CalabiYau space, owing to the localization of the KK modes. Mass spectrum...

We find supergravity solutions corresponding to all U(1)× U(1) invariant chiral primaries of the D1-D5-KK system. These solutions are 1/8 BPS, carry angular momentum, and are asymptotically flat in the 3 + 1 dimensional sense. They can be thought of as representing the ground states of the four dimensional black hole constructed from the D1-D5-KK-P system. Demanding the absence of unphysical si...

Universal extra dimension (UED) models with right-handed neutrinos are studied. The introduction of the neutrinos makes us possible not only to describe Dirac neutrino masses but also to solve the cosmological problem called the KK graviton problem. This problem is essentially caused by the late time decay of a KK photon into a KK graviton and a photon, and it distorts the spectrum of the cosmi...

We give a short proof that for any fixed integer k, the maximum number size of a Kk,k-cross free family is linear in the size of the groundset. We also give tight bounds on the maximum size of a Kk-cross free family in the case when F is intersecting or an antichain. Introduction Let F ⊂ 2. Two sets A, B ∈ F cross if 1. A ∩ B 6= ∅. 2. B 6⊂ A and A 6⊂ B. F ⊂ 2 is said to be Kk-cross free if it d...

In the current work we thread the problems of smoothness in non-commutative C∗algebras arising form the Baaj-Julg picture of the KK-theory. We introduce the notion of smoothness based on the pre-C∗-subalgebras of C∗-algebras endowed with the structure of an operator algebra. We prove that the notion of smoothness introduced in the paper may then be used for simplification of calculations in cla...

We study the confinement/deconfinement phase transition of radion field in a warped model with polynomial bulk potential. The backreaction on metric is taken into account by using superpotential formalism, while effective potential obtained from novel formulation which can incorporate backreaction. leads to stochastic gravitational wave background that depends energy scale first Kaluza-Klein re...

AKT and its substrate BAD have been shown to promote prostate cancer cell survival. Agonists, such as carbachol, and hormones that increase intracellular calcium concentration can activate AKT leading to cancer cell survival. The LNCaP prostate cancer cells express the carbachol-sensitive M(3) -subtype of G protein-coupled receptors that cause increases in intracellular calcium and activate the...

Huntington disease (HD) is caused by an expanded polyglutamine (poly(Q)) repeat near the N terminus of the huntingtin (htt) protein. Expanded poly(Q) facilitates formation of htt aggregates, eventually leading to deposition of cytoplasmic and intranuclear inclusion bodies containing htt. Flanking sequences directly adjacent to the poly(Q) domain, such as the first 17 amino acids on the N termin...