The minimal excludant and Schmidt's partition theorem

In this work, we study Schmidt's partition theorem in a combinatorial manner, and find a strong refinement which connects the minimal excludant of ordinary partitions to the length of Schmidt's partitions. As a byproduct, we obtain a bivariate form of an identity recorded in Ramanujan's lost notebook.     

Effect of diamine treatment on the conversion efficiency of PbSe colloidal quantum dot solar cells

Polymer-free photovoltaic devices were fabricated via a solution process using PbSe colloidal quantum dots (QDs) and an organic semiconductor (tetrabenzoporphyrin, BP) that can be prepared in situ from a soluble precursor. The device structure was ITO/PEDOT/BP:QD/QD/Al, where the BP:QD and QD layers correspond to a bulk heterojunction and a buffer layer, respectively. The buffer layer was treated with ethylenediamine (EDA) to crosslink the QDs. As a result, the energy conversion efficiency of the EDA-treated device was superior to that of an untreated device, mainly due to an increase in the short-circuit current density.     

Short syntheses of (−)-clavaminol A and deacetyl (+)-clavaminol H

Concise stereoselective syntheses of (?)-clavaminol A and deacetyl (+)-clavaminol H have been achieved from simple starting materials. Highlights of the synthesis for (?)-clavaminol A include a highly diastereoselective chelation-controlled hydride reduction of an amino ketone to give the anti amino alcohol directly, and NaBH₄-mediated dehalogenation. The main synthetic approach for deacetyl (+)-clavaminol H features a highly diastereoselective chelation-controlled hydride reduction of the amino ketone to construct the anti amino alcohol and a palladium catalyzed hydrogenation reaction at the final step.     

预烧温度对CaO-Li_2 O-Sm_2O_3-TiO_2微波介质陶瓷介电性能的影响

用固相反应法制备了CaO-Li2O-Sm2O3-TiO2(CLST)微波介质陶瓷。通过改变预烧温度(1 000~1 200℃)研究其对CLST微波介质陶瓷介电性能的影响。研究过程中,对预烧粉体与烧结陶瓷进行XRD与SEM分析,对陶瓷的介电性能εr、Q、τf进行了测试。结果表明,预烧温度对CLST微波介质陶瓷介电性能有较大影响,在预烧温度1 150℃,烧结温度1 340℃时可获得较好的介电性能:εr=112,Q=845,τf=52×10-6/℃。     

Immediate regularization of measure-type population densities in a two-dimensional chemotaxis system with signal consumption

This paper deals with the Neumann initial-boundary value problem for a classical chemotaxis system with signal consumption in a disk.In contrast to previous studies which have established a comprehensive theory of global classical solutions for suitably regular nonnegative initial data,the focus in the present work is on the question to which extent initially prescribed singularities can be regularized despite the presence of the nonlinear cross-diffusive interaction.The main result in this paper asserts that at least in the framework of radial solutions immediate regularization occurs under an essentially optimal condition on the initial distribution of the population density.More precisely,it will turn out that for any radially symmetric initial data belonging to the space of regular signed Borel measures for the population density and to L² for the signal density,there exists a classical solution to the Neumann initial-boundary value problem,which is smooth and approaches the given initial data in an appropriate trace sense.     

实轮换对称型及其半正定性判定的可读证明

可读证明是不等式机器证明领域中的热点问题.针对具有对称零点的实轮换对称型,文章提出了其线性空间的一组基以及分拆算法和两种分拆形式用于对不等式进行可读证明研究.讨论了该线性空间的维数,以及轮换对称型半正定性的判别方法.给出了一类具有对称零点的轮换对称型的半正定性判定条件.大量实例表明此分拆方式在轮换对称型半正定性的判定及可读证明上具有很好的实用性.