Birkhoff's theorem in the f(T) gravity

Generalized from the so-called teleparallel gravity which is exactly equivalent to general relativity, the $f(T)$ gravity has been proposed as an alternative gravity model to account for the dark energy phenomena. In this letter we prove that the external vacuum gravitational field for a spherically symmetric distribution of source matter in the $f(T)$ gravity framework must be static and the conclusion is independent of the radial distribution and spherically symmetric motion of the source matter that is, whether it is in motion or static. As a consequence, the Birkhoff's theorem is valid in the general $f(T)$ theory. We also discuss its application in the de Sitter space-time evolution phase as preferred to by the nowadays dark energy observations.Comment: 5p

Birkhoff's Theorem in f(T) Gravity up to the Perturbative Order

f(T) gravity, a generally modified teleparallel gravity, has become very popular in recent times as it is able to reproduce the unification of inflation and late-time acceleration without the need of a dark energy component or an inflation field. In this present work, we investigate specifically the range of validity of Birkhoff's theorem with the general tetrad field via perturbative approach. At zero order, Birkhoff's theorem is valid and the solution is the well known Schwarzschild-(A)dS metric. Then considering the special case of the diagonal tetrad field, we present a new spherically symmetric solution in the frame of f(T) gravity up to the perturbative order. The results with the diagonal tetrad field satisfy the physical equivalence between the Jordan and the so-called Einstein frames, which are realized via conformal transformation, at least up to the first perturbative order.Comment: 8 pages, no figure. Final version, accepted for publication in EPJ

Extended Birkhoff's Theorem in the f(T) Gravity

The f(T) theory, a generally modified teleparallel gravity, has been proposed as an alternative gravity model to account for the dark energy phenomena. Following our previous work [Xin-he Meng and Ying-bin Wang, EPJC(2011), arXiv:1107.0629v1], we prove that the Birkhoff's theorem holds in a more general context, specifically with the off diagonal tetrad case, in this communication letter. Then, we discuss respectively the results of the external vacuum and internal gravitational field in the f(T) gravity framework, as well as the extended meaning of this theorem. We also investigate the validity of the Birkhoff's theorem in the frame of f(T) gravity via conformal transformation by regarding the Brans-Dicke-like scalar as effective matter, and study the equivalence between both Einstein frame and Jordan frame.Comment: 7 pages, 1 figure, submitted to EPJ-C. arXiv admin note: substantial text overlap with arXiv:1107.062

Polaron features of the one-dimensional Holstein Molecular Crystal Model

The polaron features of the one-dimensional Holstein Molecular Crystal Model are investigated by improving a variational method introduced recently and based on a linear superposition of Bloch states that describe large and small polaron wave functions. The mean number of phonons, the polaron kinetic energy, the electron-phonon local correlation function, and the ground state spectral weight are calculated and discussed. A crossover regime between large and small polaron for any value of the adiabatic parameter $\omega_0/t$ is found and a polaron phase diagram is proposed.Comment: 12 pages, 2 figure

On the effects of the magnetic field and the isotopic substitution upon the infrared absorption of manganites

Employing a variational approach that takes into account electron-phonon and magnetic interactions in $La_{1-x}A_xMnO_3$ perovskites with $0<x<0.5$, the effects of the magnetic field and the oxygen isotope substitution on the phase diagram, the electron-phonon correlation function and the infrared absorption at $x=0.3$ are studied. The lattice displacements show a strong correlation with the conductivity and the magnetic properties of the system. Then the conductivity spectra are characterized by a marked sensitivity to the external parameters near the phase boundary.Comment: 10 figure

QCD ghost f(T)-gravity model

Within the framework of modified teleparallel gravity, we reconstruct a f(T) model corresponding to the QCD ghost dark energy scenario. For a spatially flat FRW universe containing only the pressureless matter, we obtain the time evolution of the torsion scalar T (or the Hubble parameter). Then, we calculate the effective torsion equation of state parameter of the QCD ghost f(T)-gravity model as well as the deceleration parameter of the universe. Furthermore, we fit the model parameters by using the latest observational data including SNeIa, CMB and BAO data. We also check the viability of our model using a cosmographic analysis approach. Moreover, we investigate the validity of the generalized second law (GSL) of gravitational thermodynamics for our model. Finally, we point out the growth rate of matter density perturbation. We conclude that in QCD ghost f(T)-gravity model, the universe begins a matter dominated phase and approaches a de Sitter regime at late times, as expected. Also this model is consistent with current data, passes the cosmographic test, satisfies the GSL and fits the data of the growth factor well as the LCDM model.Comment: 19 pages, 9 figures, 2 tables. arXiv admin note: substantial text overlap with arXiv:1111.726

Establishing Nash equilibrium of the manufacturer-supplier game in supply chain management

We study a game model of multi-leader and one-follower in supply chain optimization where n suppliers compete to provide a single product for a manufacturer. We regard the selling price of each supplier as a pre-determined parameter and consider the case that suppliers compete on the basis of delivery frequency to the manufacturer. Each supplier’s profit depends not only on its own delivery frequency, but also on other suppliers’ frequencies through their impact on manufacturer’s purchase allocation to the suppliers. We first solve the follower’s (manufacturer’s) purchase allocation problem by deducing an explicit formula of its solution. We then formulate the n leaders’ (suppliers’) game as a generalized Nash game with shared constraints, which is theoretically difficult, but in our case could be solved numerically by converting to a regular variational inequality problem. For the special case that the selling prices of all suppliers are identical, we provide a sufficient and necessary condition for the existence and uniqueness of the Nash equilibrium. An explicit formula of the Nash equilibrium is obtained and its local uniqueness property is proved

Measurements of the Mass and Full-Width of the ηc\eta_c Meson

In a sample of 58 million $J/\psi$ events collected with the BES II detector, the process J/$\psi\to\gamma\eta_c$ is observed in five different decay channels: $\gamma K^+K^-\pi^+\pi^-$, $\gamma\pi^+\pi^-\pi^+\pi^-$, $\gamma K^\pm K^0_S \pi^\mp$ (with $K^0_S\to\pi^+\pi^-$), $\gamma \phi\phi$ (with $\phi\to K^+K^-$) and $\gamma p\bar{p}$. From a combined fit of all five channels, we determine the mass and full-width of $\eta_c$ to be $m_{\eta_c}=2977.5\pm1.0 ({stat.})\pm1.2 ({syst.})$ MeV/$c^2$ and $\Gamma_{\eta_c} = 17.0\pm3.7 ({stat.})\pm7.4 ({syst.})$ MeV/$c^2$.Comment: 9 pages, 2 figures and 4 table. Submitted to Phys. Lett.

An Integrated TCGA Pan-Cancer Clinical Data Resource to Drive High-Quality Survival Outcome Analytics

For a decade, The Cancer Genome Atlas (TCGA) program collected clinicopathologic annotation data along with multi-platform molecular profiles of more than 11,000 human tumors across 33 different cancer types. TCGA clinical data contain key features representing the democratized nature of the data collection process. To ensure proper use of this large clinical dataset associated with genomic features, we developed a standardized dataset named the TCGA Pan-Cancer Clinical Data Resource (TCGA-CDR), which includes four major clinical outcome endpoints. In addition to detailing major challenges and statistical limitations encountered during the effort of integrating the acquired clinical data, we present a summary that includes endpoint usage recommendations for each cancer type. These TCGA-CDR findings appear to be consistent with cancer genomics studies independent of the TCGA effort and provide opportunities for investigating cancer biology using clinical correlates at an unprecedented scale. Analysis of clinicopathologic annotations for over 11,000 cancer patients in the TCGA program leads to the generation of TCGA Clinical Data Resource, which provides recommendations of clinical outcome endpoint usage for 33 cancer types