Revisiting radiative leptonic B decay

In this paper, we summarize the existing methods of solving the evolution equation of the leading-twist \begin{document}$B$\end{document}-meson LCDA. Then, in the Mellin space, we derive a factorization formula with next-to-leading-logarithmic (NLL) resummation for the form factors \begin{document}$F_{A,V}$\end{document} in the \begin{document}$B \to \gamma \ell\nu$\end{document} decay at leading power in \begin{document}$\Lambda/m_b$\end{document}. Furthermore, we investigate the power suppressed local contributions, factorizable non-local contributions (which are suppressed by \begin{document}$1/E_\gamma$\end{document} and \begin{document}$1/m_b$\end{document}), and soft contributions to the form factors. In the numerical analysis, which employs the two-loop-level hard function and the jet function, we find that both the resummation effect and the power corrections can sizably decrease the form factors. Finally, the integrated branching ratios are also calculated for comparison with future experimental data.     

An α/β-HSQC-α/β Experiment for Spin-State Selective Editing of IS Cross Peaks

A generalized version of the TROSY experiment allows the spin-state selective editing of the four multiplet components of¹⁵N–¹H cross peaks of amide groups in proteins into four different subspectra, with no penalty in sensitivity. An improvement by in sensitivity results, if only two of the four multiplet components are selected. Use of the experiment for the measurement of¹J_HNcoupling constants is discussed. A water flip-back version of the experiment is demonstrated with a 45 kDa fragment of¹⁵N/²H labeledStaphylococcus aureusgyrase B.     

The number oft-wise balanced designs

We prove that the number oft-wise balanced designs of ordern is asymptotically , provided that blocks of sizet are permitted. In the process, we prove that the number oft-profiles (multisets of block sizes) is bounded below by and above by for constants c₂>c₁>0.     

Contingent derivatives of set-valued maps and applications to vector optimization

In this paper we investigate contingent derivatives of set-valued maps and their lower and upper semidifferentiability properties. We provide also some calculus rules for these derivatives in infinite dimensional spaces. The concept of contingent derivatives is then applied to produce several necessary and sufficient conditions for vector optimization problems with set-valued objectives.This paper was written when the author was at the University of Erlangen-Nurnberg under a grant of the Alexander von Humboldt Foundation.On leave from the Institute of Mathematics, Hanoi, Vietnam.     

平面上的近似连续积分

近似连续Ｐｅｒｒｏｎ 积分首先由Ｂｕｒｋｉｌｌ提出,称之为ＡＰ积分,由于近似复盖具有划分性质,因而可以给出ＡＰ积分的Ｒｉｅｍ ａｎｎ型定义． 但是,在平面上近似复盖是否具有划分性质还不知道． 本文给出了一种方法,用这种方法可以在平面上给出ＡＰ积分的Ｒｉｅｍ ａｎｎ型定义而不需要证明划分的存在性．     

Synergistic influences of titanium,boron, and oxygen on large-size single-crystal diamond growth at high pressure and high temperature

The synergistic influences of boron, oxygen, and titanium on growing large single-crystal diamonds are studied using different concentrations of B₂O₃ in a solvent-carbon system under 5.5 GPa-5.7 GPa and 1300 ℃-1500 ℃. It is found that the boron atoms are difficult to enter into the crystal when boron and oxygen impurities are doped using B₂O₃ without the addition of Ti atoms. However, high boron content is achieved in the doped diamonds that were synthesized with the addition of Ti. Additionally, boron-oxygen complexes are found on the surface of the crystal, and oxygen-related impurities appear in the crystal interior when Ti atoms are added into the FeNi-C system. The results show that the introduction of Ti atoms into the synthesis cavity can effectively control the number of boron atoms and the number of oxygen atoms in the crystal. This has important scientific significance not only for understanding the synergistic influence of boron, oxygen, and titanium atoms on the growth of diamond in the earth, but also for preparing the high-concentration boron or oxygen containing semiconductor diamond technologies.     

Effects of gas sparging and mechanical mixing on sonochemical oxidation activity

The effects of air sparging (0–16 L min⁻¹) and mechanical mixing (0–400 rpm) on enhancing the sonochemical degradation of rhodamine B (RhB) was investigated using a 28 kHz sonoreactor. The degradation of RhB followed pseudo first-order kinetics, where sparging or mixing induced a large sonochemical enhancement. The kinetic constant varied in three stages (gradually increased → increased exponentially → decreased slightly) as the rate of sparging or mixing increased, where the stages were similar for both processes. The highest sonochemical activity was obtained with sparging at 8 L min⁻¹ or mixing at 200 rpm, where the standing wave field was significantly deformed by sparging and mixing, respectively. The cavitational oxidation activity was concentrated at the bottom of the sonicator when higher sparging or mixing rates were employed. Therefore, the large enhancement in the sonochemical oxidation was attributed mainly to the direct disturbance of the ultrasound transmission and the resulting change in the cavitation-active zone in this study. The effect of the position of air sparging and mixing was investigated. The indirect inhibition of the ultrasound transmission resulted in less enhancement of the sonochemical activity. Moreover, the effect of various sparging gases including air, N₂, O₂, Ar, CO₂, and an Ar/O₂ (8:2) mixture was compared, where all gases except CO₂ induced an enhancement in the sonochemical activity, irrespective of the concentration of dissolved oxygen. The highest activity was obtained with the Ar/O₂ (8:2) mixture. Therefore, it was revealed that the sonochemical oxidation activity could be further enhanced by applying gas sparging using the optimal gas.     

The left-definite Legendre type boundary problem

The left-definite Legendre type boundary problem concerns the study of a fourth-order singular differential expressionM _k [–] in a weighted Sobolev spaceH generated by a Dirichlet inner product. The fourth-order differential equation

平面三次Pythagorean-Hodograph Hyperbolic曲线

本文基于Pythagorean-hodograph (PH)曲线和代数双曲线的良好几何特性,构造了Pythagorean-Hodograph Hyperbolic (PH-H)曲线,并给出了PH-H曲线的定义以及相应性质.同时,分别利用Hyperbolic基函数和Algebraic Hyperbolic (AH) B\''ezier基函数,得到了平面三次AH B\''ezier曲线为PH曲线的两个不同的充要条件.此外,三次PH-H曲线也被用于求解具有确定解的$G^1$ Hermite插值问题.文中给出了具体实例来说明我们的方法.     

Hardy–Littlewood–Sobolev and Stein–Weiss inequalities and integral systems on the Heisenberg group

In this paper, we study two types of weighted Hardy–Littlewood–Sobolev (HLS) inequalities, also known as Stein–Weiss inequalities, on the Heisenberg group. More precisely, we prove the |u|$\left|u\right|$ weighted HLS inequality in Theorem 1.1 and the |z|$\left|z\right|$ weighted HLS inequality in Theorem 1.5 (where we have denoted u=(z,t)$u=(z,t)$ as points on the Heisenberg group). Then we provide regularity estimates of positive solutions to integral systems which are Euler–Lagrange equations of the possible extremals to the Stein–Weiss inequalities. Asymptotic behavior is also established for integral systems associated to the |u|$\left|u\right|$ weighted HLS inequalities around the origin. By these a priori estimates, we describe asymptotically the possible optimizers for sharp versions of these inequalities.