Totally geodesic immersions of Kähler manifolds and Kähler Frenet curves

In a given Kähler manifold (M,J) we introduce the notion of Kähler Frenet curves, which is closely related to the complex structure J of M. Using the notion of such curves, we characterize totally geodesic Kähler immersions of M into an ambient Kähler manifold and totally geodesic immersions of M into an ambient real space form of constant sectional curvature .     

Synthesis of bis(azafulvene)s by dehydration of hydroxymethylpyrrole derivatives

Bis(azafulvene) was isolated in 55% yield by the reaction of 4 equivalents of phenyllithium with 5,5'-diformyl-3,3',4,4'-tetraethyl-2,2'-bipyrrole followed by quenching with acetic anhydride. Unstable bis(azafulvene)s were obtained in much higher yields by dehydrating 5,5'-bis(hydroxymethyl) derivatives of 2,2'-bipyrrole and gem-dimethyl-2,2'-dipyrrylmethane with (Boc)2O-DMAP at room temperature. X-Ray crystallography of two bis(azafulvene)s is reported.     

铈掺杂钆镓铝石榴石相玻璃陶瓷的光学及光谱参数

根据X射线衍射图谱对铈掺杂的钆镓铝石榴石相玻璃陶瓷的晶体结构进行分析,采用直径10英寸积分球结合CCD(charge coupled device)探测器系统,对蓝色半导体发光二极管激发下铈掺杂钆镓铝石榴石相玻璃陶瓷的荧光光谱进行测试,解析出样品发光的绝对光谱功率分布,推导出光量子数分布,求得荧光量子产率和组合白光的色坐标及其相关色温。结果表明,所调查的铈掺杂钆镓铝石榴石相玻璃陶瓷在蓝光LED激发下的荧光量子产率为29.2%,所获得组合白光的色坐标x=0.319,y=0.349,相关色温为6 086K。尽管该混晶陶瓷的荧光量子产率稍小于铈掺杂YAG玻璃陶瓷,但其与蓝光LED组合后发光的色温也明显低于后者,从而为舒适型LED照明玻璃陶瓷的进一步优化提供了新思路。     

Search for f(J)(2220) in radiative J/ψ decays

We present a search for f(J)(2220) production in radiative J/ψ→γf(J)(2220) decays using 460 fb?1 of data collected with the BABAR detector at the SLAC PEP-II e(+)e? collider. The f(J)(2220) is searched for in the decays to K(+)K? and K(S)?K(S)?. No evidence of this resonance is observed, and 90% confidence level upper limits on the product of the branching fractions for J/ψ→γf(J)(2220) and f(J)(2220)→K(+)K?(K(S)?K(S)?) as a function of spin and helicity are set at the level of 10??, below the central values reported by the Mark III experiment.     

Direct and inverse problems for degenerate differential equations

We are concerned with a general abstract equation that allows to handle various degenerate first and second order differential equations in Banach spaces. We indicate sufficient conditions for existence and uniqueness of a solution. Periodic conditions are assumed to improve previous approaches on the abstract problem to work on \((-\infty ,\infty )\). Related inverse problems are discussed, too. All general results are applied to some systems of partial differential equations. Inverse problems for degenerate evolution integro-differential equations might be described, too.     

Determining Hilbert modular forms by central values of Rankin–Selberg convolutions: the weight aspect

The purpose of this paper is to prove that a primitive Hilbert cusp form \(\mathbf{g}\) is uniquely determined by the central values of the Rankin–Selberg L-functions \(L(\mathbf{f}\otimes \mathbf{g}, \frac{1}{2})\), where \(\mathbf{f}\) runs through all primitive Hilbert cusp forms of weight \(k\) for infinitely many weight vectors \(k\). This result is a generalization of the work of Ganguly et al. (Math Ann 345:843–857, 2009) to the setting of totally real number fields, and it is a weight aspect analogue of our previous work (Hamieh and Tanabe in Trans Am Math Soc, arXiv:1609.07209, 2016).