Environmental effects on nuclear decay rates

The possible change of nuclear decay rates in different environments has long been an interesting topic due to its importance not only in nuclear physics but also in astrophysics, geological dating, condensed matter physics, etc. The progress in the investigation of variations in nuclear decay rates are reviewed.     

Uniform limit laws of the logarithm for nonparametric estimators of the regression function in presence of censored data

In this paper, we establish uniform-in-bandwidth limit laws of the logarithm for nonparametric Inverse Probability of Censoring Weighted (I.P.C.W.) estimators of the multivariate regression function under random censorship. A similar result is deduced for estimators of the conditional distribution function. The uniform-in-bandwidth consistency for estimators of the conditional density and the conditional hazard rate functions are also derived from our main result. Moreover, the logarithm laws we establish are shown to yield almost sure simultaneous asymptotic confidence bands for the functions we consider. Examples of confidence bands obtained from simulated data are displayed.      

一个奇摄动微分方程非线性混合边值问题

研究了一个三阶半线性微分方程的奇摄动非线性混合边值问题.利用边界层函数法构造了该问题的形式渐近解,并采用微分不等式理论证明了解的存在性,给出了渐近解的误差估计,最后得出了边界层函数指数型衰减的结论.     

Coherent Vibrational Dynamics and High-resolution Nonlinear Spectroscopy： A Comparison with the Air/DMSO Liquid Interface

We present a comparative study on the C-H stretching vibrations at air/DMSO （dimethyl sulfoxide） interface with both the free-induction decay （FID） coherent vibrational dynamics and the sub-wavenumber high resolution sum-frequency generation vibrational spectroscopy measurements. In principle the frequency-domain and time-domain spectroscopic measurements should generate identical information for a given molecular system. However, when the molecular systems are with several coupled or overlapping vibrational modes, obtain- ing detailed spectroscopic and coherent dynamics information is not as straightforward and rather difficult from either the time-domain or the frequency domain measurements. For the case of air/DMSO interface that is with moderately complex vibrational spectra, we show that the frequency-domain measurement with sub-wavenumber high-resolution sum-frequency generation vibrational spectroscopy is probably more advantageous than the time- domain measurement in obtaining quantitative understanding of the structure and coherent dynamics of the molecular interface.     

Antioxidant Activity Degradation,Formulation Optimization,Characterization, and Stability of Equisetum Arvense Extract Nanoemulsion

Equisetum arvense supercritical CO₂ extracts (EAE) contained an initial antioxidant activity of 10.3 mM TEAC that suffered a sharp first order kinetics decay characterized by half-life time (t_1/2) of 1.05 ± 0.03 and 0.86 ± 0.03 weeks at 25 and 4°C, respectively. The aim of the present work was to develop a nanoemulsion formulation for providing EAE protection against deleterious environmental factors and extending its shelf-life functionality. The nanoemulsion area was identified by constructing pseudoternary phase diagrams and response surface methodology was used to optimize the preparation conditions. The best formulation achieved an EAE encapsulation efficiency of 97.5 ± 0.5% and antioxidant activity half-life time (t_1/2) was extended to 12.32 ± 0.40 and 14.56 ± 0.60 weeks at 25 and 4°C, respectively.      

A new approach to pointwise heat kernel upper bounds on doubling metric measure spaces

On doubling metric measure spaces endowed with a strongly local regular Dirichlet form, we show some characterisations of pointwise upper bounds of the heat kernel in terms of global scale-invariant inequalities that correspond respectively to the Nash inequality and to a Gagliardo–Nirenberg type inequality when the volume growth is polynomial. This yields a new proof and a generalisation of the well-known equivalence between classical heat kernel upper bounds and relative Faber–Krahn inequalities or localised Sobolev or Nash inequalities. We are able to treat more general pointwise estimates, where the heat kernel rate of decay is not necessarily governed by the volume growth. A crucial role is played by the finite propagation speed property for the associated wave equation, and our main result holds for an abstract semigroup of operators satisfying the Davies–Gaffney estimates.     

一类Hermitian鞍点矩阵的特征值估计

本文研究了一类大型稀疏Hermitian鞍点线性系统Az=(B E E* 0)(x y)=(f g)=b系数矩阵的特征值,其中B∈C~(p×p)是Hermitian正定阵矩阵,E∈C~(p×q)是列降秩.本文分别给出了该系数矩阵正特征值与负特征值界的一个估计式,同时通过数值算例验证本文所给出的特征值界的估计是合理且有效的.