线性常微分方程组解的特征数的估计

复数域上线性系统ｘ＝Ａ（ｔ）ｘ，当Ａ（ｔ）＝（ａｉｊ（ｔ））ｎ×ｎ具有（ｎ，Ｎ，ｒ） 差异性质且ｒｎ时，解的特征数ｊ有估计λｊ－ｌｉｍｔ→∞１ｔ∫ｔｔ０Ｒｅａｊ（τ）ｄτｎ－１ｒ＋１－ｎｌｉｍｔ→∞１ｔ∫ｔｔ０Ａ（τ）ｄτ，ｊ＝１，２，…，ｎ，其中Ａ（ｔ）＝ｍａｘ｛｜ａｉｊ（ｔ）｜：ｉ，ｊ＝１，２，…，ｎ，ｉ≠ｊ．｝     

Assessing the ability of chemical similarity measures to discriminate between active and inactive compounds

Summary A method for assessing the biological discriminating power of chemical similarity measures is presented. The main concern of this work was to develop an objective way of evaluating different similarity measures in terms of how well they distinguished between active and inactive compounds. In addition, we have explored the level of similarity required for optimal separation and commented on its implications for work in the field of chemical diversity studies. The results for one simple similarity measure showed that statistically significant separation could be achieved, and indicated a reasonable similarity value for future work.     

Designing and Synthesis of Novel Amidated Fentanyl Analogs

Some new amidated fentanyl (=N‐[1‐(2‐phenylethyl)piperidin‐4‐yl]‐N‐phenylpropanamide) analogs with a 4‐(N‐phenylamido)piperidine scaffold and additional amide bonds have been designed and synthesized through Ugi four‐component reaction (Ugi‐4CR). Good‐to‐high yields, diversity‐oriented synthesis, and possible applications in drug discovery are advantages of this approach.     

Xanthines as a scaffold for molecular diversity

Summary Xanthines represent a new, versatile scaffold for combinatorial chemistry. A five-step solid-phase synthesis of xanthine derivatives is described which includes alkylations, a nucleophilic displacement reaction at a heterocycle and a ring closure reaction by condensation of a nitroso function with an activated methylene group. The selected reaction sequence allows the production of a highly diverse small-molecule combinatorial compound library.     

Diversity oriented synthesis: substitution at C5 in unreactive pyrimidines by Claisen rearrangement and reactivity in nucleophilic substitution at C2 and C4 in pteridines and pyrido[2,3-d]pyrimidines

Diversity oriented synthesis of fused pyrimidines leads to scaffolds with many biological activities. In the case of the preparation of pyrido[2,3-d]pyrimidines from 2-alkylthiopyrimidines, the formation of a new carbon-carbon bond at C5 is required, a reaction, that is, very limited in scope. However Claisen type rearrangement of simple 4-allylic ethers affords C5 substituted pyrimidines readily; in cases with an ester substituent, rearrangement occurs at room temperature. Subsequent cyclisation to afford 6-methylpyrido[2,3-d]pyrimidin-7(8H)-ones was achieved in high yield. Using allylic ethers derived from 3-chloromethyl-4-arylbut-3-en-2-ones as substrates, a new titanium[IV]chloride catalysed reaction affording 6-arylmethyl-7-methylpyrido[2,3-d]pyrimidines was discovered. In contrast, 2-alkylthiopteridines are readily available. In both cases, substitution at C2 and C4 to generate diversity has been carried out and the reactivity compared; yields of substitution products were generally higher with pteridine substrates. In biological assays unexpected hits were found for activity against the Gram positive bacterium, Nocardia farcinia, and against the parasite Trypanosoma brucei brucei, illustrating the value of diversity oriented synthesis in the discovery of biologically active compounds.     

Diversity of Ligularia kanaitzensis in sesquiterpenoid composition and neutral DNA sequences

Twenty-six eremophilane-type sesquiterpenoids, including six new compounds, were isolated from the title species. One of the new compounds, kanaitzensol, suggested the presence of an enzyme for the conversion of eremophil-7(11)-en-8-one derivative to furanoeremophilanes. The plant was collected at 15 locations in Yunnan Province of China and found to be diverse with respect to its sesquiterpenoid composition. DNA sequencing also revealed a large intraspecific diversity of the plant.     

Complete synchronization induced by disorder in coupled chaotic lattices

The effect of phase disorder in external forces introduced into two-dimensional lattices of coupled chaotic pendulums is investigated. As the increase of the disorder, we find complete synchronization between the pendulums in each chain and different periodic synchronized patterns, while the chain remains asynchronous if all driving forces have the same phase. Applying the master stability function method, an analytic solution is given to support the numerical results. All these findings may provide further insight into chaos control and synchronization in nonlinear systems.     

Complex dynamics in the distribution of players’ scoring performance in Rugby Union world cups

The evolution of the scoring performance of Rugby Union players is investigated over the seven rugby world cups (RWC) that took place from 1987 to 2011, and a specific attention is given to how they may have been impacted by the switch from amateurism to professionalism that occurred in 1995. The distribution of the points scored by individual players, _Ps$P_s$, ranked in order of performance were well described by the simplified canonical law _Ps∝(r+?)^−α$P_s\propto {(r+?)}^{-\alpha }$, where r$r$ is the rank, and ?$?$ and α$\alpha$ are the parameters of the distribution. The parameter α$\alpha$ did not significantly change from 1987 to 2007 (α=0.92±0.03)$(\alpha =0.92\pm 0.03)$, indicating a negligible effect of professionalism on players’ scoring performance. In contrast, the parameter ?$?$ significantly increased from ?=1.32$?=1.32$ for 1987 RWC, ?=2.30$?=2.30$ for 1999 to 2003 RWC and ?=5.60$?=5.60$ for 2007 RWC, suggesting a progressive decrease in the relative performance of the best players. Finally, the sharp decreases observed in both α(α=0.38)$\alpha (\alpha =0.38)$ and ?(?=0.70)$?(?=0.70)$ in the 2011 RWC indicate a more even distribution of the performance of individuals among scorers, compared to the more heterogeneous distributions observed from 1987 to 2007, and suggest a sharp increase in the level of competition leading to an increase in the average quality of players and a decrease in the relative skills of the top players. Note that neither α$\alpha$ nor ?$?$ significantly correlate with traditional performance indicators such as the number of points scored by the best players, the number of games played by the best players, the number of points scored by the team of the best players or the total number of points scored over each RWC. This indicates that the dynamics of the scoring performance of Rugby Union players is influenced by hidden processes hitherto inaccessible through standard performance metrics; this suggests that players’ scoring performance is connected to ubiquitous phenomena such as anomalous diffusion.     

A hybrid metaheuristic method for the Maximum Diversity Problem

The Maximum Diversity Problem (MDP) consists in selecting a subset of m$m$ elements from a given set of n$n$ elements (n>m$n>m$) in such a way that the sum of the pairwise distances between the m$m$ chosen elements is maximized. We present a hybrid metaheuristic algorithm (denoted by MAMDP) for MDP. The algorithm uses a dedicated crossover operator to generate new solutions and a constrained neighborhood tabu search procedure for local optimization. MAMDP applies also a distance-and-quality based replacement strategy to maintain population diversity. Extensive evaluations on a large set of 120 benchmark instances show that the proposed approach competes very favorably with the current state-of-art methods for MDP. In particular, it consistently and easily attains all the best known lower bounds and yields improved lower bounds for 6 large MDP instances. The key components of MAMDP are analyzed to shed light on their influence on the performance of the algorithm.