Theoretical Design of Biodegradable Phthalic Acid Ester Derivatives in Marine and Freshwater Environments

The biodegradability of phtalic acid esters in marine and freshwater environments was characterized by their binding free energy with corresponding degrading enzymes. According to comprehensive biodegradation effects weights, the binding free energy values were converted into dimensionless efficacy coefficient using ratio normalization method. Then, considering comprehensive dual biodegradation effects value and the structural parameters of PAEs in both marine and freshwater environments, a 3D-QSAR pharmacophore model was constructed, five PAE derivatives (DBP−COOH, DBP−CHO, DBP−OH, DINP−NH₂, and DINP−NO₂) were screened out based on their environmental friendliness, functionality and stability. The prediction of biodegradation effects on five PAE derivatives by biodegradation models in marine and freshwater environment increased by 15.90 %, 15.84 %, 27.21 %, 12.33 %, and 8.32 %, and 21.57 %, 15.21 %, 20.99 %, 15.10 %, and 9.74 %, respectively. By simulating the photodegradation path of the PAE derivative molecular, it was found that DBP−OH can generate ^.OH and provides free radicals for the photodegradation of microplastics in the environment.     

Minimal Ellipsoid Circumscribing a Polytope Defined by a System of Linear Inequalities

In this paper, we will propose algorithms for calculating a minimal ellipsoid circumscribing a polytope defined by a system of linear inequalities. If we know all vertices of the polytope and its cardinality is not very large, we can solve the problem in an efficient manner by a number of existent algorithms. However, when the polytope is defined by linear inequalities, these algorithms may not work since the cardinality of vertices may be huge. Based on a fact that vertices determining an ellipsoid are only a fraction of these vertices, we propose algorithms which iteratively calculate an ellipsoid which covers a subset of vertices. Numerical experiment shows that these algorithms perform well for polytopes of dimension up to seven.     

A characterization of adding machine maps

Let f :X→X be a continuous map of a compact metric space to itself. We prove that f is topologically conjugate to an adding machine map if and only if X is an infinite minimal set for f and each point of X is regularly recurrent. Moreover, if X is an infinite minimal set for f and one point of X is regularly recurrent, then f is semiconjugate to an adding machine map.     

非线性控制系统的最小实现

对于那些由代数微分方程描述的具有输入输出关系的非线性控制系统，本文采用两种方法讨论了其最小实现问题：一种方法是直接计算系统的特征列；另一种方法则采用了本原元定理．两种方法给出的最小实现所需的状态变量最小数目是相等的．文中的大量代数与微分运算则可利用数学机械化来完成     

The set of toric minimal log discrepancies

We describe the set of minimal log discrepancies of toric log varieties, and study its accumulation points. This work is supported by a 21st Century COE Kyoto Mathematics Fellowship, and a JSPS Grant-in-Aid No 17740011.     

Achievable sets, brambles, and sparse treewidth obstructions

One consequence of the graph minor theorem is that for every k there exists a finite obstruction set Obs(TW?k). However, relatively little is known about these sets, and very few general obstructions are known. The ones that are known are the cliques, and graphs which are formed by removing a few edges from a clique. This paper gives several general constructions of minimal forbidden minors which are sparse in the sense that the ratio of the treewidth to the number of vertices n does not approach 1 as n approaches infinity. We accomplish this by a novel combination of using brambles to provide lower bounds and achievable sets to demonstrate upper bounds. Additionally, we determine the exact treewidth of other basic graph constructions which are not minimal forbidden minors.     

Codimension-one minimal projections onto Haar subspaces

Let H_n be an n-dimensional Haar subspace of and let H_n−1 be a Haar subspace of H_n of dimension n−1. In this note we show (Theorem 6) that if the norm of a minimal projection from H_n onto H_n−1 is greater than 1, then this projection is an interpolating projection. This is a surprising result in comparison with Cheney and Morris (J. Reine Angew. Math. 270 (1974) 61 (see also (Lecture Notes in Mathematics, Vol. 1449, Springer, Berlin, Heilderberg, New York, 1990, Corollary III.2.12, p. 104) which shows that there is no interpolating minimal projection from C[a,b] onto the space of polynomials of degree n, (n2). Moreover, this minimal projection is unique (Theorem 9). In particular, Theorem 6 holds for polynomial spaces, generalizing a result of Prophet [(J. Approx. Theory 85 (1996) 27), Theorem 2.1].     

The Pharmacophore Hypothesis of Novel Inhibitors for Aurora A Kinase

A three-dimensional pharmacophore model was developed from a series of inhibitors of Aurora A kinase to discover new potent anti-cancer agents using the HypoGen module in the Catalyst software. The pharmacophore model was developed based on the structure of 20 currently available inhibitors, which were carefully selected from the literature. The best hypothesis （Hypo 1） was defined by four features： one hydrogen-bond donor and three hy- drophobic points, with the best correlation coefficient of 0.909, the lowest rms deviation of 1.563, and the highest cost difference of 99.075. The Hypo 1 was then validated by a test set consisting of 24 compounds and by a cross-validation of 95% confidence level through randomizing the data using the CatScramble program, which suggested that a predictive pharmacophore model had been successfully obtained.     

Agonist–PPARγ interactions: Molecular modeling study with docking approach

Docking simulation of 18 agonists with the ligand binding pocket (LBP) of PPARγ has been performed. The binding conformations and binding affinities of these agonists were obtained by use of the flexible docking protocol FlexX. Test compound calculations indicated that FlexX can reproduce the binding conformation of the crystal structure (root mean square deviation = 1.43 Å); moreover, the predicted binding affinities correlate well with the activities of these agonists. The interaction model and pharmacophore of PPARγ agonists were derived and the difference in biologic activities of these agonists can be well explained. The PPARγ agonists must have both polar head and the hydrophobic tail, which form hydrogen bonds and hydrophobic contacts with hydrophilic and hydrophobic regions of the LBP of PPARγ, respectively. In addition, a suitable linker is also necessary. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 405–410, 2003     

An improved nicotinic pharmacophore and a stereoselective CoMFA-model for nicotinic agonists acting at the central nicotinic acetylcholine receptors labelled by [3H]-N-methylcarbamylcholine

A study of a series of compounds with agonistic effect at the alpha4beta2 nicotinic acetylcholine receptors resulted in an improved pharmacophore model as well as a CoMFA model. The pharmacophore was composed of three pharmacophoric elements: (1) a site point (a) corresponding to a protonated nitrogen atom, (2) a site point (b) corresponding to an electronegative atom capable of forming a hydrogen bond, and (3) the centre of a heteroaromatic ring or a C=O bond (c). The pharmacophoric elements were related by the following parameters: (a-b) 7.3-8.0 A, (a-c) 6.5-7.4 A, and the angle between the two distance vectors (delta bac) 30.4-35.8 degrees. In addition to this, a stereoselective CoMFA model was developed, which showed good predictability even for compound classes not present in the training set.