Holographic R\'enyi entropy in AdS3_3/LCFT2_2 correspondence

The recent study in AdS$_3$/CFT$_2$ correspondence shows that the tree level contribution and 1-loop correction of holographic R\'enyi entanglement entropy (HRE) exactly match the direct CFT computation in the large central charge limit. This allows the R\'enyi entanglement entropy to be a new window to study the AdS/CFT correspondence. In this paper we generalize the study of R\'enyi entanglement entropy in pure AdS$_3$ gravity to the massive gravity theories at the critical points. For the cosmological topological massive gravity (CTMG), the dual conformal field theory (CFT) could be a chiral conformal field theory or a logarithmic conformal field theory (LCFT), depending on the asymptotic boundary conditions imposed. In both cases, by studying the short interval expansion of the R\'enyi entanglement entropy of two disjoint intervals with small cross ratio $x$, we find that the classical and 1-loop HRE are in exact match with the CFT results, up to order $x^6$. To this order, the difference between the massless graviton and logarithmic mode can be seen clearly. Moreover, for the cosmological new massive gravity (CNMG) at critical point, which could be dual to a logarithmic CFT as well, we find the similar agreement in the CNMG/LCFT correspondence. Furthermore we read the 2-loop correction of graviton and logarithmic mode to HRE from CFT computation. It has distinct feature from the one in pure AdS$_3$ gravity.Comment: 28 pages. Typos corrected, published versio

Averaged transverse momentum correlations of hadrons in relativistic heavy-ion collisions

We compile experimental data for the averaged transverse momentum ($\left\langle p_{T}\right\rangle$) of proton, $\Lambda$, $\Xi^{-}$, $\Omega^{-}$ and $\phi$ at mid-rapidity in Au+Au collisions at $\sqrt{s_{NN}}=$ 200, 39, 27, 19.6, 11.5, 7.7 GeV and in Pb+Pb collisions at $\sqrt{s_{NN}}=$ 2.76 TeV, and find that experimental data of these hadrons exhibit systematic correlations. We apply a quark combination model with equal-velocity combination approximation to derive analytic formulas of hadronic $\left\langle p_{T}\right\rangle$ in the case of exponential form of quark $p_{T}$ spectra at hadronization. We use them to successfully explain the systematic correlations exhibited in $\left\langle p_{T}\right\rangle$ data of $p\Lambda$, $\Lambda\Xi^{-}$, $\Xi^{-}\Omega^{-}$ and $\Xi^{-}\phi$ pairs. We also use them to successfully explain the regularity observed in $\left\langle p_{T}\right\rangle$ of these hadrons as the function of $(dN_{ch}/dy)/(N_{part}/2)$ at mid-rapidity in central heavy-ion collisions at both RHIC and LHC energies. Our results suggest that the constituent quark degrees of freedom and the equal-velocity combination of these constituent quarks at hadronization play important role in understanding the production of baryons and $\phi$ meson at these RHIC and LHC energies.Comment: 10 pages, 7 figure

Selection of Programming Language in the Development of Computer Application Software

Research showed that the popularization of the Internet among people can be attributed to recent years’ continuous development of science and technology, making it an important part of people’s daily life. Researcher showed that, for the better development of software application, the related staff should throw themselves actively into the appropriate selection and application of programming language. The variety of the programming languages in network system have imposed a restriction on the optimization of programmers’ level, as a result, developers often find it difficult to effectively implement the application of relevant programming languages. The appropriate management of this problem requires active analysis of the various programming languages, and it also has becoming an important issue in the development of China’s Internet industry. Aiming at promote the level of computer software development. This article explored the programming language selection under the process of computer application software development

Size variations in foraminifers from the early Permian to the Late Triassic: Implications for the Guadalupian-Lopingian and the Permian-Triassic mass extinctions

The final 10 Myr of the Paleozoic saw two of the biggest biological crises in Earth history: the middlePermian extinction (often termed the Guadalupian–Lopingian extinction [GLE]) that was followed 7–8 Myr later by Earth's most catastrophic loss of diversity, the Permian–Triassic mass extinction (PTME). These crises are not only manifest as sharp decreases in biodiversity and—particularly for the PTME—total ecosystem collapse, but they also drove major changes in biological morphological characteristics such as the Lilliput effect. The evolution of test size among different clades of foraminifera during these two extinction events has been less studied. We analyzed a global database of foraminiferal test size (volume) including 20,226 specimens in 464 genera, 98 families, and 9 suborders from 632 publications. Our analyses reveal significant reductions in foraminiferal mean test size across the Guadalupian/Lopingian boundary (GLB) and the Permian/Triassic boundary (PTB), from 8.89 to 7.60 log10 μm3 (lg μm3) and from 7.25 to 5.82 lg μm3, respectively. The decline in test size across the GLB is a function of preferential extinction of genera exhibiting gigantism such as fusulinoidean fusulinids. Other clades show little change in size across the GLB. In contrast, all Lopingian suborders in our analysis (Fusulinina, Lagenina, Miliolina, and Textulariina) experienced a significant decrease in test size across the PTB, mainly due to size-biased extinction and within-lineage change. The PTME was clearly a major catastrophe that affected many groups simultaneously, and the GLE was more selective, perhaps hinting at a subtler, less extreme driver than the later PTME

A note on pentavalent s-transitive graphs

AbstractA graph, with a group G of its automorphisms, is said to be (G,s)-transitive if G is transitive on s-arcs but not on (s+1)-arcs of the graph. Let X be a connected (G,s)-transitive graph for some s≥1, and let Gv be the stabilizer of a vertex v∈V(X) in G. In this paper, we determine the structure of Gv when X has valency 5 and Gv is non-solvable. Together with the results of Zhou and Feng [J.-X. Zhou, Y.-Q. Feng, On symmetric graphs of valency five, Discrete Math. 310 (2010) 1725–1732], the structure of Gv is completely determined when X has valency 5. For valency 3 or 4, the structure of Gv is known