On the mean value of some new sequences

The main purpose of this paper is using the elementary and analytic methods to study the mean value properties of the Smarandache repetitional sequence, and give two asymptotic formulas for it

Equilibrium Phase Behavior and Maximally Random Jammed State of Truncated Tetrahedra

Systems of hard nonspherical particles exhibit a variety of stable phases with different degrees of translational and orientational order, including isotropic liquid, solid crystal, rotator and a variety of liquid crystal phases. In this paper, we employ a Monte Carlo implementation of the adaptive-shrinking-cell (ASC) numerical scheme and free-energy calculations to ascertain with high precision the equilibrium phase behavior of systems of congruent Archimedean truncated tetrahedra over the entire range of possible densities up to the maximal nearly space-filling density. In particular, we find that the system undergoes two first-order phase transitions as the density increases: first a liquid-solid transition and then a solid-solid transition. The isotropic liquid phase coexists with the Conway-Torquato (CT) crystal phase at intermediate densities. At higher densities, we find that the CT phase undergoes another first-order phase transition to one associated with the densest-known crystal. We find no evidence for stable rotator (or plastic) or nematic phases. We also generate the maximally random jammed (MRJ) packings of truncated tetrahedra, which may be regarded to be the glassy end state of a rapid compression of the liquid. We find that such MRJ packings are hyperuniform with an average packing fraction of 0.770, which is considerably larger than the corresponding value for identical spheres (about 0.64). We conclude with some simple observations concerning what types of phase transitions might be expected in general hard-particle systems based on the particle shape and which would be good glass formers

The Possible J^{PC}=0^{--} Exotic State

In order to explore the possible existence of the exotic $0^{--}$ state, we have constructed the tetraquark interpolating operators systematically. As a byproduct, we notice the $0^{+-}$ tetraquark operators without derivatives do not exist. The special Lorentz structure of the $0^{--}$ currents forbids the four-quark correction to the spectral density. Now the gluon condensate is the dominant power correction. Within the framework of the finite energy sum rule, none of the seven interpolating currents supports a resonant signal. Therefore we conclude that the exotic $0^{--}$ state does not exist below 2 GeV, which is consistent with the current experimental observations.Comment: 12 pages, 27 figure