Hamiltonian properties of graphs with large neighborhood unions

AbstractLet G be a graph of order n, σk = min{ϵi=1kd(νi): {ν1,…, νk} is an independent set of vertices in G}, NC = min{|N(u)∪ N(ν)|: uν∉E(G)} and NC2 = min{|N(u)∪N(ν)|: d(u,ν)=2}. Ore proved that G is hamiltonian if σ2⩾n⩾3, while Faudree et al. proved that G is hamiltonian if G is 2-connected and NC⩾13(2n−1). It is shown that both results are generalized by a recent result of Bauer et al. Various other existing results in hamiltonian graph theory involving degree-sums or cardinalities of neighborhood unions are also compared in terms of generality. Furthermore, some new results are proved. In particular, it is shown that the bound 13(2n−1) on NC in the result of Faudree et al. can be lowered to 13(2n−1), which is best possible. Also, G is shown to have a cycle of length at least min{n, 2(NC2)} if G is 2-connected and σ3⩾n+2. A Dλ-cycle (Dλ-path) of G is a cycle (path) C such that every component of G−V(C) has order smaller than λ. Sufficient conditions of Lindquester for the existence of Hamilton cycles and paths involving NC2 are extended to Dλ-cycles and Dλ-paths

A note on autodense related languages

In this paper, some algebraic properties of autodense languages and pure autodense languages are studied. We also investigate the algebraic properties concerning anti-autodense languages. The family of anti-autodense languages contains infix codes, comma-free codes, and some subfamilies of new codes which are anti-autodense prefix codes, anti-autodense suffix codes and anti-autodense codes. The relationships among these subfamilies of new codes are investigated. The characterization of L (n) , n a parts per thousand yen 2, which are anti-autodense is studied

Blowup Criterion for the Compressible Flows with Vacuum States

We prove that the maximum norm of the deformation tensor of velocity gradients controls the possible breakdown of smooth(strong) solutions for the 3-dimensional compressible Navier-Stokes equations, which will happen, for example, if the initial density is compactly supported \cite{X1}. More precisely, if a solution of the compressible Navier-Stokes equations is initially regular and loses its regularity at some later time, then the loss of regularity implies the growth without bound of the deformation tensor as the critical time approaches. Our result is the same as Ponce's criterion for 3-dimensional incompressible Euler equations (\cite{po}). Moreover, our method can be generalized to the full Compressible Navier-Stokes system which improve the previous results. In addition, initial vacuum states are allowed in our cases.Comment: 17 page

Exact diagonalization of the generalized supersymmetric t-J model with boundaries

We study the generalized supersymmetric $t-J$ model with boundaries in three different gradings: FFB, BFF and FBF. Starting from the trigonometric R-matrix, and in the framework of the graded quantum inverse scattering method (QISM), we solve the eigenvalue problems for the supersymmetric $t-J$ model. A detailed calculations are presented to obtain the eigenvalues and Bethe ansatz equations of the supersymmetric $t-J$ model with boundaries in three different backgrounds.Comment: Latex file, 32 page

Optimal Sizes of Dielectric Microspheres for Cavity QED with Strong Coupling

The whispering gallery modes (WGMs) of quartz microspheres are investigated for the purpose of strong coupling between single photons and atoms in cavity quantum electrodynamics (cavity QED). Within our current understanding of the loss mechanisms of the WGMs, the saturation photon number, n, and critical atom number, N, cannot be minimized simultaneously, so that an "optimal" sphere size is taken to be the radius for which the geometric mean, (n x N)^(1/2), is minimized. While a general treatment is given for the dimensionless parameters used to characterize the atom-cavity system, detailed consideration is given to the D2 transition in atomic Cesium (852nm) using fused-silica microspheres, for which the maximum coupling coefficient g/(2*pi)=750MHz occurs for a sphere radius a=3.63microns corresponding to the minimum for n=6.06x10^(-6). By contrast, the minimum for N=9.00x10^(-6) occurs for a sphere radius of a=8.12microns, while the optimal sphere size for which (n x N)^(1/2) is minimized occurs at a=7.83microns. On an experimental front, we have fabricated fused-silica microspheres with radii a=10microns and consistently observed quality factors Q=0.8x10^(7). These results for the WGMs are compared with corresponding parameters achieved in Fabry-Perot cavities to demonstrate the significant potential of microspheres as a tool for cavity QED with strong coupling.Comment: 12 pages, 14 figure

Thermopower and thermal conductivity of superconducting perovskite MgCNi3MgCNi_3

The thermopower and thermal conductivity of superconducting perovskite $MgCNi_3$ ($T_c \approx$ 8 K) have been studied. The thermopower is negative from room temperature to 10 K. Combining with the negative Hall coefficient reported previously, the negative thermopower definetly indicates that the carrier in $MgCNi_3$ is electron-type. The nonlinear temperature dependence of thermopower below 150 K is explained by the electron-phonon interaction renormalization effects. The thermal conductivity is of the order for intermetallics, larger than that of borocarbides and smaller than $MgB_2$. In the normal state, the electronic contribution to the total thermal conductivity is slightly larger than the lattice contribution. The transverse magnetoresistance of $MgCNi_3$ is also measured. It is found that the classical Kohler's rule is valid above 50 K. An electronic crossover occures at $T^* \sim 50 K$, resulting in the abnormal behavior of resistivity, thermopower, and magnetoresistance below 50 K.Comment: Revised on 12 September 2001, Phys. Rev. B in pres

Array of nanosheets render ultrafast and high-capacity Na-ion storage by tunable pseudocapacitance

Sodium-ion batteries are a potentially low-cost and safe alternative to the prevailing lithium-ion battery technology. However, it is a great challenge to achieve fast charging and high power density for most sodium-ion electrodes because of the sluggish sodiation kinetics. Here we demonstrate a high-capacity and high-rate sodium-ion anode based on ultrathin layered tin(II) sulfide nanostructures, in which a maximized extrinsic pseudocapacitance contribution is identified and verified by kinetics analysis. The graphene foam supported tin(II) sulfide nanoarray anode delivers a high reversible capacity of ∼1,100 mAh g−1 at 30 mA g−1 and ∼420 mAh g−1 at 30 A g−1, which even outperforms its lithium-ion storage performance. The surface-dominated redox reaction rendered by our tailored ultrathin tin(II) sulfide nanostructures may also work in other layered materials for high-performance sodium-ion storage.Dongliang Chao, Changrong Zhu, Peihua Yang, Xinhui Xia, Jilei Liu, Jin Wang, Xiaofeng Fan, Serguei V. Savilov, Jianyi Lin, Hong Jin Fan, Ze Xiang She

The Horizontal Component of Photospheric Plasma Flows During the Emergence of Active Regions on the Sun

The dynamics of horizontal plasma flows during the first hours of the emergence of active region magnetic flux in the solar photosphere have been analyzed using SOHO/MDI data. Four active regions emerging near the solar limb have been considered. It has been found that extended regions of Doppler velocities with different signs are formed in the first hours of the magnetic flux emergence in the horizontal velocity field. The flows observed are directly connected with the emerging magnetic flux; they form at the beginning of the emergence of active regions and are present for a few hours. The Doppler velocities of flows observed increase gradually and reach their peak values 4-12 hours after the start of the magnetic flux emergence. The peak values of the mean (inside the +/-500 m/s isolines) and maximum Doppler velocities are 800-970 m/s and 1410-1700 m/s, respectively. The Doppler velocities observed substantially exceed the separation velocities of the photospheric magnetic flux outer boundaries. The asymmetry was detected between velocity structures of leading and following polarities. Doppler velocity structures located in a region of leading magnetic polarity are more powerful and exist longer than those in regions of following polarity. The Doppler velocity asymmetry between the velocity structures of opposite sign reaches its peak values soon after the emergence begins and then gradually drops within 7-12 hours. The peak values of asymmetry for the mean and maximal Doppler velocities reach 240-460 m/s and 710-940 m/s, respectively. An interpretation of the observable flow of photospheric plasma is given.Comment: 20 pages, 10 figures, 3 tables. The results of article were presented at the ESPM-13 (12-16 September 2011, Rhodes, Greece, Abstract Book p. 102, P.4.12, http://astro.academyofathens.gr/espm13/documents/ESPM13_abstract_programme_book.pdf

4pi Models of CMEs and ICMEs

Coronal mass ejections (CMEs), which dynamically connect the solar surface to the far reaches of interplanetary space, represent a major anifestation of solar activity. They are not only of principal interest but also play a pivotal role in the context of space weather predictions. The steady improvement of both numerical methods and computational resources during recent years has allowed for the creation of increasingly realistic models of interplanetary CMEs (ICMEs), which can now be compared to high-quality observational data from various space-bound missions. This review discusses existing models of CMEs, characterizing them by scientific aim and scope, CME initiation method, and physical effects included, thereby stressing the importance of fully 3-D ('4pi') spatial coverage.Comment: 14 pages plus references. Comments welcome. Accepted for publication in Solar Physics (SUN-360 topical issue

Confirmation of a pi_1^0 Exotic Meson in the \eta \pi^0 System

The exclusive reaction $\pi^- p \to \eta \pi^0 n$, $\eta \to \pi^+ \pi^- \pi^0$ at 18 GeV$/c$ has been studied with a partial wave analysis on a sample of 23~492 $\eta \pi^0 n$ events from BNL experiment E852. A mass-dependent fit is consistent with a resonant hypothesis for the $P_+$ wave, thus providing evidence for a neutral exotic meson with $J^{PC} = 1^{-+}$, a mass of $1257 \pm 20 \pm 25$ MeV$/c^2$, and a width of $354 \pm 64 \pm 60$ MeV$/c^2$. New interpretations of the meson exotics in neutral $\eta \pi^0$ system observed in E852 and Crystal Barrel experiments are discussed.Comment: p3, rewording the paragraph (at the bottom) about the phase variations. p4, rewording paragrath "The second method ..." . p4, at the bottom of paragrath "The third method ..." added consistent with the results of methods 1 and 2