Modulating the Photochemistry of Bipyridylic Compounds by Symmetric Substitutions

A quantum electronic study of the effect of substituents on (2,2′‐bipyridyl)‐3,3′‐diol and (2,2′‐bipyridyl)‐3,3′‐diamine is presented. A large difference in the photochemical behavior between the original and the substituted selected systems is expected. For the sake of simplicity, the study is restricted to the symmetrically bi‐substituted compounds: fluorine, the more electronegative atom and thus a strong σ‐acceptor but also a weak π‐donor group, and NO₂, a strong π‐acceptor substituent. Among the large set of compounds studied, two receive special attention: 5,5′‐dinitro‐(2,2′‐bipyridyl)‐3,3′‐diamine and 6,6′‐difluoro‐(2,2′‐bipyridyl)‐3,3′‐diol. While in the former case the nitro substitution transforms (2,2′‐bipyridyl)‐3,3′‐diamine, previously suggested to behave as a photomemory material, into a simple fluorescent species, the latter substitution turns (2,2′‐bipyridyl)‐3,3′‐diol into a fresh new candidate for a photomemory device.     

Bifurcations in parametric nonlinear programming

Bifurcation and continuation techniques are introduced as a class of methods for investigating the parametric nonlinear programming problem. Motivated by the Fritz John first-order necessary conditions, the parametric programming problem is first reformulated as a closed system of nonlinear equations which contains all Karush-Kuhn-Tucker and Fritz John points, both feasible and infeasible solutions, and relative minima, maxima, and saddle points. Since changes in the structure of the solution set and critical point type can occur only at singularities, necessary and sufficient conditions for the existence of a singularity are developed in terms of the loss of a complementarity condition, the linear dependence constraint qualification, and the singularity of the Hessian of the Lagrangian on a tangent space. After a brief introduction to elementary bifurcation theory, some simple singularities in this parametric problem are analyzed for both branching and persistence of local minima. Finally, a brief introduction to numerical continuation and bifurcation procedures is given to indicate how these facts can be used in a numerical investigation of the problem.This research was supported by the Air force Office of Scientific Research through grant number AFOSR-88-0059.     

Wick-Ordered Entire Functions of the Indefinite Metric Free Field

We present a simple and general method for constructing Wick-ordered entire functions of free fields with an indefinite metric, based on using an appropriate generalization of the Paley–Wiener–Schwartz theorem.     

Frobenius theorem for foliations on singular varieties

We generalize Frobenius singular theorem due to Malgrange, for a large class of codimension one holomorphic foliations on singular analytic subsets of ℂ ^N . This research was partially supported by Pronex.     

Isolated complex singularities and their CR links

In this paper, we discuss some recent studies on the complex structure of an isolated normal singularity by using the information from its link. We also give some open problems to be further pursued. Dedicated to Professor Sheng GONG on the occasion of his 75th birthday     

Singularities of Euler Flow? Not Out of the Blue!

Does three-dimensional incompressible Euler flow with smooth initial conditions develop a singularity with infinite vorticity after a finite time? This blowup problem is still open. After briefly reviewing what is known and pointing out some of the difficulties, we propose to tackle this issue for the class of flows having analytic initial data for which hypothetical real singularities are preceded by singularities at complex locations. We present some results concerning the nature of complex space singularities in two dimensions and propose a new strategy for the numerical investigation of blowup.     

Interior point algorithms for linear programming with inequality constraints

Interior methods for linear programming were designed mainly for problems formulated with equality constraints and non-negative variables. The formulation with inequality constraints has shown to be very convenient for practical implementations, and the translation of methods designed for one formulation into the other is not trivial. This paper relates the geometric features of both representations, shows how to transport data and procedures between them and shows how cones and conical projections can be associated with inequality constraints.     

二维圆柱坐标系中五角形共形网格算法

 时域有限差分（FDTD）算法求解电磁问题时，如果目标结构不能和传统网格体系共形，往往采用局部共形网格或非正交网格算法。详细讨论了二维圆柱坐标系中五角形共形网格算法，该算法能方便地对倾斜薄层媒质或电导率不均匀的倾斜媒质等复杂结构建模,并以锥形电磁脉冲天线为例，验证了该算法的有效性。     

Generic hypersurface singularities

The problem considered here can be viewed as the analogue in higher dimensions of the one variable polynomial interpolation of Lagrange and Newton. Let x₁,...,x _r be closed points in general position in projective spacePn, then the linear subspaceV ofH ⁰ (⨑ⁿ,O(d)) (the space of homogeneous polynomials of degreed on ⨑ⁿ) formed by those polynomials which are singular at eachx _i, is given by r(n + 1) linear equations in the coefficients, expressing the fact that the polynomial vanishes with its first derivatives at x₁,...,x _r. As such, the “expected” value for the dimension ofV is max(0,h ⁰(O(d))−r(n+1)). We prove thatV has the “expected” dimension for d≥5 (theorem A). This theorem was first proven in [A] using a very complicated induction with many initial cases. Here we give a greatly simplified proof using techniques developed by the authors while treating the corresponding problem in lower degrees.