A quantum field theory formalism is reviewed that leads to a selfconsistent, finite quantum gravity, Yang-Mills and Higgs theory, which is unitary and gauge invariant to all orders of perturbation theory. The gauge hierarchy problem is solved due to the exponential damping of the Higgs self-energy loop graph for energies greater than a scale ΛH ≤ 1 TeV. The cosmological constant problem is solv...

An L(h, 1, 1)-labeling of a graph is an assignment of labels from the set of integers {0, · · · , λ} to the vertices of the graph such that adjacent vertices are assigned integers of at least distance h ≥ 1 apart and all vertices of distance three or less must be assigned different labels. The aim of the L(h, 1, 1)-labeling problem is to minimize λ, denoted by λh,1,1 and called span of the L(h,...

We investigate nonlinear singular fourth-order eigenvalue problems with nonlocal boundary condition u 4 t − λh t f t, u, u′′ 0, 0 < t < 1, u 0 u 1 ∫0a s u s ds, u′′ 0 u′′ 1 ∫1 0b s u ′′ s ds, where a, b ∈ L1 0, 1 , λ > 0, h may be singular at t 0 and/or 1. Moreover f t, x, y may also have singularity at x 0 and/or y 0. By using fixed point theory in cones, an explicit interval for λ is derived ...

A quantum field theory formalism is reviewed that leads to a selfconsistent, finite quantum gravity, Yang-Mills and Higgs theory, which is unitary and gauge invariant to all orders of perturbation theory. The gauge hierarchy problem is solved due to the exponential damping of the Higgs self-energy loop graph for energies greater than a scale ΛH ≤ 1 TeV. The cosmological constant problem is solv...

For any non negative real values h and k, an L(h, k)-labeling of a graph G = (V,E) is a function L : V → IR such that |L(u)− L(v)| ≥ h if (u, v) ∈ E and |L(u)− L(v)| ≥ k if there exists w ∈ V such that (u,w) ∈ E and (w, v) ∈ E. The span of an L(h, k)-labeling is the difference between the largest and the smallest value of L, so it is not restrictive to assume 0 as the smallest value of L. We de...

The solubility data of sodium theophylline salt in the water and aqueous hydroxide systems with molarities 0.00, 0.01, 0.10, 0.20, 0.49, 0.96 mol kg −1 at temperatures ranging from 283.15 to 368.15 K are determined via equilibrium method. experimental results show that increases on increasing temperature same concentration NaOH solution decreases an increase temperature. These correlate well po...

Massless interacting scalar fields in de Sitter space have long been known to experience large fluctuations over length scales larger than Hubble distances. A similar situation arises in condensed matter physics in the vicinity of a critical point, and in this betterunderstood situation these large fluctuations indicate the failure in this regime of mean-field methods. We argue that for non-Gol...

In this paper first it is proved that if ξ is a nontrivial closed conformal vector field on an n-dimensional compact Riemannian manifold (M, g) with constant scalar curvature S satisfying S ≤ λ1(n − 1), λ1 being first nonzero eigenvalue of the Laplacian operator ∆ on M and Ricci curvature in direction of a certain vector field is non-negative, then M is isometric to the n-sphere S(c), where S =...

A complex valued function f = u+ iv defined in a domain D ⊂ C, is harmonic in D, if u and v are real harmonic. Such functions can be represented as f(z) = h(z) + g(z), where h an g are analytic in D. In this paper we study some convolution properties preserved by the integral operator In H,λf, n ∈ N0 = N ∪ {0}, λ > 0, where the functions f are univalent harmonic and sense-preserving in the open...

We argue that the ratio S 3 = ΛH/( 3He × Λp ) is a good representation of the local correlation between baryon number and strangeness, and therefore is a valuable tool to probe the nature of the dense matter created in high energy heavyion collision: quark gluon plasma or hadron gas. A multiphase transport model (AMPT) plus a dynamical coalescence model is used to elucidate our arguments. We fi...