From the expression of prime numbers to Goldbach conjecture

Operation instead of screening method to solve the congruence equation. Discussion on the expression of prime numbers and its applications; Setting up the residual model to solve the problem of related distribution; The problem of solving the problems about prime pairs of even numbers with the correspondence model of even numbers

Unifying Description of Competing Orders in Two Dimensional Quantum Magnets

Quantum magnets provide the simplest example of strongly interacting quantum matter, yet they continue to resist a comprehensive understanding above one spatial dimension (1D). In 1D, a key ingredient to progress is Luttinger liquid theory which provides a unified description. Here we explore a promising analogous framework in two dimensions, the Dirac spin liquid (DSL), which can be constructed on several different lattices. The DSL is a version of Quantum Electrodynamics ( QED$_3$) with four flavors of Dirac fermions coupled to photons. Importantly, its excitations also include magnetic monopoles that drive confinement. By calculating the complete action of symmetries on monopoles on the square, honeycomb, triangular and kagom\`e lattices, we answer previously open key questions. We find that the stability of the DSL is enhanced on the triangular and kagom\`e lattices as compared to the bipartite (square and honeycomb) lattices. We obtain the universal signatures of the DSL on the triangular and kagom\`e lattices, including those that result from monopole excitations, which serve as a guide to numerics and to experiments on existing materials. Interestingly, the familiar 120 degree magnetic orders on these lattices can be obtained from monopole proliferation. Even when unstable, the Dirac spin liquid unifies multiple ordered states which could help organize the plethora of phases observed in strongly correlated two-dimensional materials.Comment: 13+9 pages, 7 figure

Elaboration and characterization of nanoplate structured alpha-Fe2O3 films by Ag3PO4

A new strategy for surface treatment of hematite nanoplates for efficient photoelectrochemical (PEC) performances is proposed. Silver orthophosphate (Ag₃PO₄) has been adopted to mediate the formation of α-Fe₂O₃ films. Phosphate ions in Ag₃PO₄ is found to cause a significant morphology change during annealing process, from β-FeOOH nanorod arrays to hematite nanoplates. Meanwhile, Ag ions is doped into α-Fe₂O₃ film. The obtained nanoplate structured Fe₂O₃ –Ag–P films demonstrate much higher photoelectrochemical performance as photoanodes than the bare Fe₂O₃ nanorod thin films. The effects of phosphate and silver ions on the morphology, surface characteristics and the PEC properties of the photoanodes are investigated

Anomalous pressure behavior of tangential modes in single-wall carbon nanotubes

Using the molecular dynamics simulations and the force constant model we have studied the Raman-active tangential modes (TMs) of a (10, 0) single-wall carbon nanotube (SWNT) under hydrostatic pressure. With increasing pressure, the atomic motions in the three TMs present obvious diversities. The pressure derivative of E1g, A1g, and E2g mode frequency shows an increased value (), a constant value (), and a negative value () above 5.3 GPa, respectively. The intrinsic characteristics of TMs consumedly help to understand the essence of the experimental T band of CNT. The anomalous pressure behavior of the TMs frequencies may be originated from the tube symmetry alteration from D10h to D2h then to C2h.Comment: 15 pages, 3 pages, submitted to Phys. Rev.

Analysis of interspecies adherence of oral bacteria using a membrane binding assay coupled with polymerase chain reaction-denaturing gradient gel electrophoresis profiling.

Information on co-adherence of different oral bacterial species is important for understanding interspecies interactions within oral microbial community. Current knowledge on this topic is heavily based on pariwise coaggregation of known, cultivable species. In this study, we employed a membrane binding assay coupled with polymerase chain reaction-denaturing gradient gel electrophoresis (PCR-DGGE) to systematically analyze the co-adherence profiles of oral bacterial species, and achieved a more profound knowledge beyond pairwise coaggregation. Two oral bacterial species were selected to serve as "bait": Fusobacterium nucleatum (F. nucleatum) whose ability to adhere to a multitude of oral bacterial species has been extensively studied for pairwise interactions and Streptococcus mutans (S. mutans) whose interacting partners are largely unknown. To enable screening of interacting partner species within bacterial mixtures, cells of the "bait" oral bacterium were immobilized on nitrocellulose membranes which were washed and blocked to prevent unspecific binding. The "prey" bacterial mixtures (including known species or natural saliva samples) were added, unbound cells were washed off after the incubation period and the remaining cells were eluted using 0.2 mol x L(-1) glycine. Genomic DNA was extracted, subjected to 16S rRNA PCR amplification and separation of the resulting PCR products by DGGE. Selected bands were recovered from the gel, sequenced and identified via Nucleotide BLAST searches against different databases. While few bacterial species bound to S. mutans, consistent with previous findings F. nucleatum adhered to a variety of bacterial species including uncultivable and uncharacterized ones. This new approach can more effectively analyze the co-adherence profiles of oral bacteria, and could facilitate the systematic study of interbacterial binding of oral microbial species

Hadronic Rapidity Spectra in Heavy Ion Collisions at SPS and AGS energies in a Quark Combination Model

The quark combination mechanism of hadron production is applied to nucleus-nucleus collisions at the CERN Super Proton Synchrotron (SPS) and BNL Alternating Gradient Synchrotron (AGS). The rapidity spectra of identified hadrons and their spectrum widths are studied. The data of $\pi^{-}$, $K^{\pm}$, $\phi$, $\Lambda$, $\bar{\Lambda}$, $\Xi^{-}$, and $\bar{\Xi}^{+}$ at 80 and 40 AGeV, in particular at 30 and 20 AGeV where the onset of deconfinement is suggested to happen, are consistently described by the quark combination model. However at AGS 11.6 AGeV below the onset the spectra of $\pi^{\pm}$, $K^{\pm}$ and $\Lambda$ can not be simultaneously explained, indicating the disappearance of intrinsic correlation of their production in the constituent quark level. The collision-energy dependence of the rapidity spectrum widths of constituent quarks and the strangeness of the hot and dense quark matter produced in heavy ion collisions are obtained and discussed.Comment: 7 pages, 5 figure