Comments on the design of chemical libraries for screening

Different representations of molecules, based ondistinct sets of properties can yield differentperspectives of the issues involved in library design.In particular, different chemical representations cangive rise to very different estimates of requiredlibrary sizes. We provide a preliminary mathematicalframework that examines the size of libraries requiredto adequately sample the spaces corresponding to somecommonly used property sets. Introduction ofconformational flexibility is also discussed as ameans of increasing coverage of chemical libraries,while at the same time considering the thermodynamicconsequences of flexibility upon detectable activity.Our theoretical analysis reveals that the propertyspaces currently in use are extremely large andunlikely to provide adequate discrimination amongcompounds.     

Carleson conditions for asymptotic weights

The doubling and conditions are characterized in terms of convolution with rapidly decreasing kernels. The Carleson-measure criterion for of Fefferman, Kenig, and Pipher is extended to the case when all bounds become optimally small in the asymptotic limit.

     

Hausdorff Measures and Capacities for Increase Times of Stable Processes

Let X be a real-valued stable process. It is known that X possesses increase times iff (X ₁ > 0) > ([1]). In that case, we specify the exact Hausdorff function of the set of increase times, and characterize the subsets of [0,+) which contain increase times in terms of their capacity.     

Grand canonical distribution for multicomponent system in the collective variables method

The collective variables method with a reference system is developed for the case of the grand canonical ensemble for a multicomponent continuous system. The method is used to investigate phase transitions in a binary system. For a binary symmetrical system the relations between microscopic parameters determining the alternation of gas-liquid and separation phase transitions are found. The functional of the grand partition function of the symmetrical mixture is examined in the framework of parameters containing the separation point. The system is described with two sets of collective variables: _k, a set connected with the gas-liquid critical point, andc _k, a set connected with the separation phenomenon. The fourfold basic density measure is constructed inc _k-variable phase space which contains the variablec _v connected with the order parameter of the system. It is shown that the problem can be reduced to the 3D Ising model in an external field.     

Large deviations for empirical measures of switching diffusion processes with small parameters

We consider the asymptotic property of the diffusion processes with Markovian switching. For a general case, we prove a large deviation principle for empirical measures of switching diffusion processes with small parameters.     

初中生环境素养调查及思考

在初中生环境素养调查的基础上,对当前初中生环境素养状况进行统计和分析,并提出相应的建议和措施:创新环境教育实施模式,提高环境教育实施效率;提供系统培训,加强校际合作;建立家校联系合作,提高家长环境素养;创新评价体系,挂钩升学条件。     

化学用语中易读错字的调查与分析

通过问卷和访谈调查,调研了目前中学化学教师与化学师范生在化学元素、化合物、化学教学用语中存在的易读错字情况,并根据调查结果提出相应培训措施和可行的记忆策略。     

Transitions to Equilibrium State in Classical φ4 Lattice

Statistical behavior of a classical φ⁴ Hamiltonian lattice is investigated from microscopic dynamics. The largest Lyapunov exponent and entropies are considered for manifesting chaos and equipartition behaviors of the system. It is found, for the first time, that for any large while finite system size there exist two critical couplings for the transitions to equipartitions, and the scaling behaviors of these lower and upper critical couplings vs. the system size are numerically obtained.     

Determination of Spherical Area Measures by Means of Dilation Volumes

For a large class of compact sets X in ℝ^d which can be represented as finite unions of sets of positive reach, the spherical area measure of order d — 1 is determined by the volumes of dilations of X with infinitesimal multiples of all rotations of a suitable convex test set. For spherical area measures of lower orders, a similar result is obtained by approximating the set X by the closures of the complements of close parallel bodies.     

A matrix method for estimating the Liapunov exponent of one-dimensional systems

Let : [0, 1][0, 1] be a piecewise monotonie expanding map. Then admits an absolutely continuous invariant measure. A result of Kosyakin and Sandler shows that can be approximated by a sequence of absolutely continuous measures _n invariant under piecewise linear Markov maps _itn. Each _itn is constructed on the inverse images of the turning points of . The easily computable measures _n are used to estimate the Liapunov exponent of . The idea of using Markov maps for estimating the Liapunov exponent is applied to both expanding and nonexpanding maps.