On the meromorphic solutions of linear differential equations on the complex plane

In this paper we investigate the iterated order, iterated type and iterated convergence exponent of zeros of meromorphic solutions of the equations

     

巴戟天内生真菌Trichoderma spirale A725中两个新的聚酮类化合物(英文)

综合运用硅胶柱色谱、反相硅胶柱色谱、Sephadex LH-20凝胶柱色谱以及制备型高效液相色谱技术对药用植物巴戟天内生真菌Trichoderma spirale A725的次生代谢产物进行分离纯化,得到6个聚酮类化合物,采用多种现代波谱技术确定其结构,分别为:6-羟基-4-异丙基-1,8-二甲基螺环[4.5]癸-1,8-二烯-7-酮(1),2-羟基-2,5-二甲基-7-氧代-5,7-二氢-2H-呋喃[3,4-b]吡喃-4-羧酸(2), 3-乙基-4-羟基-6-甲基-二氢-吡喃-2-酮(3),苯乙内酯A (4), 3-羟基-5-(4-羟基苄基)二氢呋喃-2(3H)-酮(5), 4-乙酰-3-羟基-6-甲基吡喃-2-酮(6).其中化合物1和2为新化合物,化合物3为新天然产物.此外,利用四株肿瘤细胞株(Hep G-2、MCF-7、SF-268及A549)对化合物1~6细胞毒活性进行评估,结果表明化合物1~6对上述肿瘤细胞均无明显的细胞毒活性.     

掺铒光纤环镜中超短光孤子的放大与压缩Ⅱ.环镜及输入脉冲特性对放大结果的影响

最近的研究发现,用掺铒光纤环镜放大并压缩超短光孤子不仅能避免常规掺铒光纤放大器中由于非线性效应引起的孤子畸变,而且可克服绝热放大技术中放大器长度随输入脉宽增大而指数规律增大的困难。进一步研究了环镜及输入脉冲特性对放大结果的影响。数值计算表明,对于确定的输入脉冲,当环镜参量(环镜长度、增益、耦合器功率耦合系数)在较大范围内变化时,环镜放大器的孤子输出性能基本稳定。对于确定的环镜,输入脉冲形状的变化、初始输入功率的起伏以及高阶效应等因素对放大结果的影响较小;相对而言,初始频率啁啾对输出孤子宽度的影响较大,但对输出孤子质量的影响并不严重。     

On soft equality

Molodtsov introduced the concept of soft sets, which can be seen as a new mathematical tool for dealing with uncertainty. In this paper, we deal with the algebraic structure of soft sets. The lattice structures of soft sets are constructed. The concept of soft equality is introduced and some related properties are derived. It is proved that soft equality is a congruence relation with respect to some operations and the soft quotient algebra is established.     

Acid-base Vapor Sensing Enabled by ESIPT-attributed Cd(II) Coordination Polymer with Switchable Luminescence

Fluorescence materials based on excited state intramolecular proton transfer(ESIPT) have attracted great attention due to the unique four-level energy states. Herein, we report the assembly of a Cd-L_F coordination polymer from purposely designed L_F(H₂hpi2cf) ligand, which can present switchable luminescence behavior by gain or loss protons originated in uncoordinated ESIPT sites and serve as acid-base vapor sensors. Fabricated into in-situ grown film or transparent ink by simple methods, Cd-L_F presents facile and portable amine sensor for food spoilage detection and fluorescent anti-counterfeiting ink applications.     

Palladium Catalyzed Cascade Azidation/Carbonylation of Aryl Halides with Sodium Azide for the Synthesis of Amides

Amide synthesis is one of the most important transformations in organic chemistry due to their ubiquitous presence in our daily life. In this communication, a palladium catalyzed cascade azidation/carbonylation of aryl halides for the synthesis of amides was developed. Both iodo- and bromobenzene derivatives were transformed to the corresponding amides using PdCl₂/xantphos as the catalyst system and sodium azide as the nitrogen-source. The reaction proceeds via a cascade azidation/carbonylation process. A range of alkyl and halogen substituted amides were prepared in moderate to good yields.     

Existence of homoclinic solutions for higher-order periodic difference equations with p-Laplacian

Using the critical point theory in combination with periodic approximations, we establish sufficient conditions on the existence of homoclinic solutions for higher-order periodic difference equations with p-Laplacian. Our results provide rather weaker conditions to guarantee the existence of homoclinic solutions and considerably improve some existing ones even for some special cases.     

Extremal Ranks of Some Nonlinear Matrix Expressions with Applications

In this paper, we establish a group of closed-form formulas for the maximal and minimal ranks of a nonlinear matrix expression with respect to two variant matrices by using a linearization method and some known formulas for extremal ranks of linear matrix expressions. In addition, by using some pure algebraic operations of matrices and their generalized inverses, we derive the maximal and minimal ranks of the above nonlinear matrix expression, where the two variant matrices are any solutions of two consistent matrix equations. As an application, we derive some sufficient and necessary conditions for the existence of the solution of a nonlinear matrix function.     

四元数体上Hermite矩阵的最小化问题

该文建立了四元数矩阵对的标准相关分解(CCD-Q). 借助CCD-Q, GSVD-Q 和有限维内积空间中的投影定理, 该文得到了基于四元数矩阵方程$AXB=C$的Hermite矩阵最小化问题解的表达式.