A Bertini type theorem for pencils over finite fields

We study the question of finding smooth hyperplane sections to a pencil of hypersurfaces over finite fields.     

Permutation trinomials over Fq3

We consider four classes of polynomials over the fields ${\mathbb{F}}_{q^3}$, $q=p^h$, $p>3$, $f_1(x)=x^{q^2+q-1}+A{x}^{q^2-q+1}+Bx$, $f_2(x)=x^{q^2+q-1}+A{x}^{q^3-q^2+q}+Bx$, $f_3(x)=x^{q^2+q-1}+A{x}^{q^2}-Bx$, $f_4(x)=x^{q^2+q-1}+A{x}^q-Bx$, where $A,B\in {\mathbb{F}}_q$. We find sufficient conditions on the pairs $(A,B)$ for which these polynomials permute ${\mathbb{F}}_{q^3}$ and we give lower bounds on the number of such pairs.     

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.     

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。