Parity results for 13-regular partitions and broken 6-diamond partitions

Let \(b_{13}(n)\) denote the number of partitions of n such that no parts are divisible by 13. In this paper, we shall prove several infinite families of congruence relations modulo 2 for \(b_{13}(n)\). In addition, we will give an elementary proof of the parity result on broken 6-diamond partitions, which was established by Radu and Sellers. We also find a new congruence relation modulo 2 for the number of broken 6-diamond partitions of n.     

Divergent Synthesis of Disulfanes and Benzenesulfonothioates Bearing 2-Aminofurans From N-Tosylhydrazone-Bearing Thiocarbamates

An efficient and convenient synthesis of valuable disulfanes and benzenesulfonothioates, having a 2-aminofuran framework, has been developed by employing a copper-catalyzed transformation of readily available N-tosylhydrazone-bearing thiocarbamates. This method features an inexpensive metal catalyst, mild reaction conditions, good functional-group tolerance, short reaction times, and delivers valuable and complex products. A copper carbene generated from an N-tosylhydrazone-bearing thiocarbamate is proposed as the key intermediate for the transformation and it triggers the subsequent cascade. Remarkably, the Ts anion released from N-tosylhydrazone further serves as a nucleophile, thus rendering the formation of benzenesulfonothioates under controlled conditions.     

Cu/Fe‐Cocatalyzed Formation of β‐Ketophosphonates by a Domino Knoevenagel–Decarboxylation–Oxyphosphorylation Sequence from Aromatic Aldehydes and H‐Phosphonates

A domino Knoevenagel–decarboxylation–alkene difunctionalization sequence has been developed for the conversion of benzaldehydes into β‐ketophosphonates, catalyzed by a cooperative Cu/Fe system, whereby C?P and C?O bonds are formed simultaneously in a one‐pot reaction. The reaction proceeds in good yields and with a broad substrate scope and environmentally benign conditions.     

毛细管电泳-电致化学发光联用技术检测烟草中尼古丁含量

建立了毛细管电泳-电致化学发光联用技术(CE-ECL)检测烟草浸出液中尼古丁含量的方法。考察了检测电位、检测池中Ru(bpy)32+浓度和缓冲液pH值、CE运行缓冲液浓度和pH值、进样时间和电压,以及CE分离电压等实验条件对尼古丁测定的影响。在优化的条件下,尼古丁检测的线性范围为低浓度段:1～100μg/L(r>0.999)、高浓度段:100～1500μg/L(r>0.996),检出限为0.5μg/L(S/N=3)。将本方法用于3种品牌的烟草浸出液中尼古丁含量的测量,测定值均与烟盒上尼古丁的标注值相吻合,样品的加标回收率为95%～106%。     

Fast inspection of fruits using nuclear magnetic resonance spectroscopy

High-resolution nuclear magnetic resonance (NMR) spectroscopy is an indispensable technique for obtaining chemical structure information. Its quantitative and noninvasive properties have led to its growing popularity as an analytical tool in many fields, including biology, chemistry, medicine, and food science. During transportation and storage, chemical reactions among the many nutrients lead to a loss of food quality. In these circumstances, portable NMR spectrometers can readily be used for food inspection and quality control. Because of the heterogeneous tissue distribution in food, a high-resolution NMR method is required for detailed food inspection. Therefore, in this study, we demonstrated the feasibility of using an intermolecular double-quantum coherence signal to obtain high-resolution metabolic profiles of several fruits, including grape, cantaloupe, tomato, and watermelon. The resulting high-resolution NMR spectra facilitate the identification of important metabolites, which can be used as biomarkers for food quality control. The method established here may be adapted for food inspection using portable NMR equipment.     

Dimers Belonging to Three Orientations on Plane Honeycomb Lattices

It is well known that there are three types of dimers belonging to the three different orientations in a honeycomb lattice, and in each type all dimers are mutually parallel. Based on a previous result, we can compute the partition function of the dimer problem of the plane (free boundary) honeycomb lattices with three different activities by using the number of its pure dimer coverings (perfect matchings). The explicit expression of the partition function and free energy per dimer for many types of plane honeycomb lattices with fixed shape of boundaries is obtained in this way (for a shape of plane honeycomb lattices, the procedure that the size goes to infinite, corresponds to a way that the honeycomb lattice goes to infinite). From these results, an interesting phenomena is observed. In the case of the regions of the plane honeycomb lattice has zero entropy per dimer—when its size goes to infinite—though in the thermodynamic limit, there is no freedom in placing a dimer at all, but if we distinguish three types of dimers with nonzero activities, then its free energy per dimer is nonzero. Furthermore, a sufficient condition for the plane honeycomb lattice with zero entropy per dimer (when the three activities are equal to 1) is obtained. Finally, the difference between the plane honeycomb lattices and the plane quadratic lattices is discussed and a related problem is proposed.     

凸体诱导的对称函数（英文）

This paper shows some properties of symmetry function induced by a convex body in a normal linear space. Some relationships between symmetry function induced by a convex body and Minkowski functional of the convex body are presented.     

一类具对流项的奇异扩散方程解的逼近性质

讨论了一类带对流项的奇异扩散方.程的Neumann边值问题,证明了整体解的存在唯一性;讨论了带对流项非线性间题解的线性逼近,得到了逼近的显式表示式;同时还对││u-(u)││L2(0,1)进行了估计,得到了解关于时间t充分大时的渐近性态,其中(u)＝∫o/1udx.     

Cone metric spaces and fixed point theorems of contractive mappings

In this paper we introduce cone metric spaces, prove some fixed point theorems of contractive mappings on cone metric spaces.     

螺旋四角系统的Wiener数

推导了螺旋四角系统Wiener数的计算公式