The Bertini irreducibility theorem for higher codimensional slices

In [3], Poonen and Slavov recently developed a novel approach to Bertini irreducibility theorems over an arbitrary field, based on random hyperplane slicing. In this paper, we extend their work by proving an analogous bound for the dimension of the exceptional locus in the setting of linear subspaces of higher codimensions.     

On uniform propagation of chaos

In this paper we obtain a time-uniform propagation estimate for a system of interacting diffusion processes. Using a well defined metric function h , our result guarantees a time-uniform estimate for the convergence of a class of interacting stochastic differential equations towards their mean field limit, under conditions that ensure that the decay associated to the internal dynamics term dominates the interaction and noise terms. Our result should have diverse applications, particularly in neuroscience, and allows for models more elaborate than the one of Wilson and Cowan. In particular, the internal dynamics need not be that of linear decay.     

Anharmonic force fields of cis- and trans-S1 C2H2

We calculate second-order vibrational perturbation theory (VPT2) anharmonic force fields for the cis and trans conformers of S₁ C₂H₂, and compare the results to experiment. The vibrational assignments of recently observed levels belonging to the cis well are of particular interest. A refined estimate of the cis origin position (44,870?±?10?cm^?1) is proposed, and preliminary low-energy fits to the global J?=?K?=?0 trans level structure are also described. The performance of perturbation theory in this isomerizing system is examined, and both surprising successes and failures are encountered. We examine these and their causes, and offer practical suggestions for avoiding the pitfalls of applying perturbation theory to systems with large amplitude motions.     

Some useful integer arrays for the teaching of generalization skills

Teachers of first-year college mathematics and engineering courses must often spend considerable time reviewing material originally taught in high school. Instead of this being a mere exercise in repetition, this article suggests that such a review can enrich and revitalize by unifying some of the subjects that need to be re-taught. In the example presented, the subjects in question are absolute values, graphs and solutions of equations, and domains of definition. These are unified by the problem of finding an analytic expression for a square and triangle and their interiors. In the course of the development, basic notions such as the additive property of areas and convexity are introduced. The approach presented in the article was tried with secondary school teachers participating in professional development workshops and with students at a technical college; the teachers and students responded enthusiastically to the material.     

外电场对2-氟-5-溴吡啶分子结构与电子光谱影响的研究

采用密度泛函B3LYP方法，在6-311++g(3df,3pd)基组水平上优化了不同外电场下2-氟-5-溴吡啶分子的基态稳定构型、电偶极矩和分子的总能量，在此基础上利用杂化CIS方法研究了外电场下2-氟-5-溴吡啶分子的前9个激发态的激发能、波长和振子强度受外电场的影响规律。结果表明：5C-9Br和3C-10F间键长受到X轴向外场影响最大，随着外电场的继续增加，可能最先趋于断裂；在外电场F=-0.005a.u.时总能量达到最大，而偶极矩达到最小；LUMO能级受外场影响较大，HOMO能级受外电场影响较小；激发波长、振子强度也受外电场影响，但随电场变化比较复杂。     

Rovibrational and energetic analysis of the hydroxyethynyl anion (CCOH−)

For the first time, high-level structural and rovibrational data are provided for the hyroxyethynyl anion, CCOH^?. CCOH^? is a promising molecule for interstellar detection even though no new anions have been observed in the interstellar medium for the past half-decade. The large dipole moment of the corresponding neutral radical may be key for its creation as has been hypothesised and supported for other anions known to exist in various astronomical environments. Highly accurate quartic force fields are employed where previous benchmarks have produced spectroscopic constants and anharmonic vibrational frequencies within 20 MHz and 1 cm^?1, respectively, of experiment. This same approach is applied here for CCOH^? and its deuterated isotopologue with the goal of assisting laboratory experiments and/or astronomical observers in the potential detection of this anion.     

Nonstationarity and related measures for time‐dependent hartree–fock and multiconfigurational models

Based on an earlier article (Eberly and Singh, Phys. Rev. D 1973 , 7, 359) and related works on short‐time evolution, this article proposes a many‐electron formulation for the nonstationarity degree which can be assigned to quantum system at each time point. The key measure introduced, , is a nonstationarity index that can be thought of as an inverse nominal lifetime at each instance of time. The index is directly computed from the time derivative of one‐electron density matrix and is a size‐consistent quantity. In this article, the approach is developed for the time‐dependent Hartree–Fock (TDHF), single‐excitation (TDCIS), and time‐dependent full configuration interaction (TDFCI) models. As a rule, nonstationarity effects are more pronounced in correlated electron systems, and a joint analysis of and the multiconfigurational character of wave functions apparently provide a deeper insight into dynamical molecular processes. The performed calculations on small molecules in laser fields show a preference for the TDCIS model when comparing TDCIS and TDHF with the “exact” TDFCI model. © 2013 Wiley Periodicals, Inc.