Five-dimensional metric f(R)f(R) gravity and the accelerated universe

The metric $f(R)$ theories of gravity are generalized to five-dimensional spacetimes. By assuming a hypersurface-orthogonal Killing vector field representing the compact fifth dimension, the five-dimensional theories are reduced to their four-dimensional formalism. Then we study the cosmology of a special class of $f(R)=\alpha R^m$ models in a spatially flat FRW spacetime. It is shown that the parameter $m$ can be constrained to a certain range by the current observed deceleration parameter, and its lower bound corresponds to the Kaluza-Klein theory. It turns out that both expansion and contraction of the extra dimension may prescribe the smooth transition from the deceleration era to the acceleration era in the recent past as well as an accelerated scenario for the present universe. Hence five-dimensional $f(R)$ gravity can naturally account for the present accelerated expansion of the universe. Moreover, the models predict a transition from acceleration to deceleration in the future, followed by a cosmic recollapse within finite time. This differs from the prediction of the five-dimensional Brans-Dicke theory but is in consistent with a recent prediction based on loop quantum cosmology.Comment: 14 pages, 9 figures; Version published in PR

Bose and Fermi gases in the early universe with self-gravitational effect

We study the self-gravitational effect on the equation of state (EoS) of Bose and Fermi gases in thermal equilibrium at the end of reheating, the period after quark-hadron transition and before Big Bang Nucleosynthesis (BBN). After introducing new grand canonical partition functions based on the work of Uhlenbeck and Gropper, we notice some interesting features of the newly developed EoSs with distinct behaviors of relativistic and non-relativistic gases under self-gravity. The usual negligence of the self-gravitational effect when solving the background expansion of the early universe is justified with numerical results, showing the magnitude of the self-gravitational modification of the state constant to be less than $O(10^{-78})$. This helps us to clarify the background thermal evolution of the primordial patch. Such clarification is crucial in testing gravity theories, evaluating inflation models and determining element abundances in BBN.Comment: 10 pages, 2 figures, to appear in PR

Effect of ambient temperature on the puffing characteristics of single butanol-hexadecane droplet

© 2018 Elsevier Ltd Puffing characteristics of BUT50 (50% n-butanol and 50% n-hexadecane by mass) were investigated using the droplet suspension technology under 638, 688 and 738 K. Experimental results showed that BUT50 underwent transient heating, fluctuation evaporation and equilibrium evaporation phases under all ambient temperatures. In the fluctuation evaporation phase, the fluctuation frequency of 738 K was higher than that of 638 K. (Dmax/D0)2 of 738 K was lower than that of 638 K. Easy bubble rupture led to high fluctuation frequency and low (Dmax/D0)2 at 738 K. Three turning points were found in transient temperature growth rate at 638 and 738 K. Four characteristic droplet temperatures were analyzed, including droplet temperatures at the start (T1) and end (T2) of transient heating phase, at (Dmax/D0)2 (T3) and at the end of total lifetime (T4). T2 was slightly lower and T3 was slightly higher than the boiling point of n-butanol. T4 was lower than the boiling point of n-hexadecane. Furthermore, the transient heating duration (tTH), fluctuation evaporation duration (tFE) and total lifetime (tTL) decreased with increasing ambient temperature. The reduction of tFE played an important role in the decrease of tTL. The percentages of tTH/tTL and tFE/tTL were stable with increasing ambient temperature

A multiple exp-function method for nonlinear differential equations and its application

A multiple exp-function method to exact multiple wave solutions of nonlinear partial differential equations is proposed. The method is oriented towards ease of use and capability of computer algebra systems, and provides a direct and systematical solution procedure which generalizes Hirota's perturbation scheme. With help of Maple, an application of the approach to the $3+1$ dimensional potential-Yu-Toda-Sasa-Fukuyama equation yields exact explicit 1-wave and 2-wave and 3-wave solutions, which include 1-soliton, 2-soliton and 3-soliton type solutions. Two cases with specific values of the involved parameters are plotted for each of 2-wave and 3-wave solutions.Comment: 12 pages, 16 figure

Identification of genes associated with multiple cancers via integrative analysis

<p>Abstract</p> <p>Background</p> <p>Advancement in gene profiling techniques makes it possible to measure expressions of thousands of genes and identify genes associated with development and progression of cancer. The identified cancer-associated genes can be used for diagnosis, prognosis prediction, and treatment selection. Most existing cancer microarray studies have been focusing on the identification of genes associated with a specific type of cancer. Recent biomedical studies suggest that different cancers may share common susceptibility genes. A comprehensive description of the associations between genes and cancers requires identification of not only multiple genes associated with a specific type of cancer but also genes associated with multiple cancers.</p> <p>Results</p> <p>In this article, we propose the Mc.TGD (Multi-cancer Threshold Gradient Descent), an integrative analysis approach capable of analyzing multiple microarray studies on different cancers. The Mc.TGD is the first regularized approach to conduct "two-dimensional" selection of genes with joint effects on cancer development. Simulation studies show that the Mc.TGD can more accurately identify genes associated with multiple cancers than meta analysis based on "one-dimensional" methods. As a byproduct, identification accuracy of genes associated with only one type of cancer may also be improved. We use the Mc.TGD to analyze seven microarray studies investigating development of seven different types of cancers. We identify one gene associated with six types of cancers and four genes associated with five types of cancers. In addition, we also identify 11, 9, 18, and 17 genes associated with 4 to 1 types of cancers, respectively. We evaluate prediction performance using a Leave-One-Out cross validation approach and find that only 4 (out of 570) subjects cannot be properly predicted.</p> <p>Conclusion</p> <p>The Mc.TGD can identify a short list of genes associated with one or multiple types of cancers. The identified genes are considerably different from those identified using meta analysis or analysis of marginal effects.</p