Some New Inequalities of Dirichlet Eigenvalues for Laplace Operator with any Order

In this paper, we establish several inequalities of Dirichlet eigenvalues for Laplace operator $\Delta$ with any order on \emph{n}-dimensional Euclidean space. These inequalities are more general than known Yang's inequalities and contain new consequences. To obtain them, we borrow the approach of Illias and Makhoul, and use a generalized Chebyshev's inequality

De facto currency baskets of China and East Asian economies: The rising weights

We employ Bayesian method to estimate a time-varying coefficient version of the de facto currency basket model of Frankel and Wei (2007) for the RMB of China, using daily data from February 2005 to July 2011. We estimate jointly the implicit time-varying weights of all 11 currencies in the reference basket announced by the Chinese government. We find the dollar weight has been reduced and sometimes significantly smaller than one, but there is no evidence of systematic operation of a currency basket with discernable pattern of significant weights on other currencies. During specific periods, the reduced dollar weight has not been switched to other major international currencies, but to some East Asian currencies, which is hard to explain by trade importance to or trade competition with China. We examine currency baskets of these East Asian Economies, including major international currencies and the RMB in their baskets. We find an evident tendency of Malaysia and Singapore to increase the weights of RMB in their own currency baskets, and a steadily and significantly positive weight of RMB in the basket of Thailand. These evidences suggest that, the positive weights of some East Asian currencies in RMB currency basket during specific periods largely reflect the fact that these East Asia economies have been systematically placing greater weights on RMB under the new regime of RMB exchange rate.RMB currency basket; time-varying regressions; East Asia; China; US

Classification of solutions for some mixed order elliptic system

In this paper, we classify the solution of the following mixed-order conformally invariant system with coupled nonlinearity in $\mathbb{R}^4$: \begin{equation}\left\{ \begin{aligned} & -\Delta u(x) = u^{p_1}(x) e^{q_1v(x)}, \quad x\in \mathbb{R}^4,\\ & (-\Delta)^2 v(x) = u^{p_2}(x) e^{q_2v(x)}, \quad x\in \mathbb{R}^4, \end{aligned} \right. \end{equation} where $0\leq p_1 0$, $q_1 > 0$, $q_2 \geq 0$, $u>0$ and satisfies $$\int_{\mathbb{R}^4} u^{p_1}(x) e^{q_1v(x)} dx < \infty,\quad \int_{\mathbb{R}^4} u^{p_2}(x) e^{q_2 v(x)} dx < \infty.$$ Under additional assumptions (H1) or (H2), we study the asymptotic behavior of the solutions to the system and we establish the equivalent integral formula for the system. By using the method of moving spheres, we obtain the classification results of the solutions in the system.Comment: 33 page

Evidence against the energetic cost hypothesis for the short introns in highly expressed genes

<p>Abstract</p> <p>Background</p> <p>In animals, the moss <it>Physcomitrella patens </it>and the pollen of <it>Arabidopsis thaliana</it>, highly expressed genes have shorter introns than weakly expressed genes. A popular explanation for this is selection for transcription efficiency, which includes two sub-hypotheses: to minimize the energetic cost or to minimize the time cost.</p> <p>Results</p> <p>In an individual human, different organs may differ up to hundreds of times in cell number (for example, a liver versus a hypothalamus). Considered at the individual level, a gene specifically expressed in a large organ is actually transcribed tens or hundreds of times more than a gene with a similar expression level (a measure of mRNA abundance per cell) specifically expressed in a small organ. According to the energetic cost hypothesis, the former should have shorter introns than the latter. However, in humans and mice we have not found significant differences in intron length between large-tissue/organ-specific genes and small-tissue/organ-specific genes with similar expression levels. Qualitative estimation shows that the deleterious effect (that is, the energetic burden) of long introns in highly expressed genes is too negligible to be efficiently selected against in mammals.</p> <p>Conclusion</p> <p>The short introns in highly expressed genes should not be attributed to energy constraint. We evaluated evidence for the time cost hypothesis and other alternatives.</p

Research on Random Fatigue Load Model of Highway Bridge by Vehicle Traffic Based on GMM

Highway bridges have often suffered accidents due to fatigue damage. This paper studies the influence of vehicle operating state on the fatigue performance of bridges. Based on GMM method and K-S test in information statistics, this paper proposes an improved Gaussian hybrid modelling method, and studies the various parameters of vehicle operating state on beam bridge fatigue, such as the impact of the damage and its fatigue life assessment. On this basis, the fatigue cumulative damage formula of multi-vehicle upper bridge is proposed. The traffic load of Shandong JiNan-QingDao expressway has been GMMly analysed by GMM. The Gaussian mixture model is used to fit the vehicle load probability function by standard fatigue vehicle model. Based on the expressway, the vehicle fatigue has been established to facilitate the fatigue load and evaluate the fatigue life. Gradually this paper helps to improve the accuracy and convenience of the probability model, which is conducive to the establishment of a scientific and efficient load probability model for road vehicles