Azobenzene‐Functionalized Cage Silsesquioxanes as Inorganic–Organic Hybrid,Photoresponsive, Nanoscale,Building Blocks

Mono‐ and octa‐azobenzene‐functionalized cage silsesquioxanes were easily synthesized by the reaction of 4‐bromoazobenzene with monovinyl‐substituted octasilsesquioxane and cubic octavinylsilsesquioxane through the Heck coupling reaction. Excited‐state energies obtained from time‐dependent density functional theory (TDDFT) and the CAM‐B3LYP functional correlate very well with experimental trans–cis photoisomerization results from UV/Vis spectroscopy. These azobenzene‐functionalized cages exhibit good thermal stability and are fluorescent with maximum emission at approximately 400 nm, making them potential materials for blue‐light emission.     

Stable multi-sets

In this paper we introduce a generalization of stable sets: stable multi-sets. A stable multi-set is an assignment of integers to the vertices of a graph, such that specified bounds on vertices and edges are not exceeded. In case all vertex and edge bounds equal one, stable multi-sets are equivalent to stable sets.  For the stable multi-set problem, we derive reduction rules and study the associated polytope. We state necessary and sufficient conditions for the extreme points of the linear relaxation to be integer. These conditions generalize the conditions for the stable set polytope. Moreover, the classes of odd cycle and clique inequalities for stable sets are generalized to stable multi-sets and conditions for them to be facet defining are determined.  The study of stable multi-sets is initiated by optimization problems in the field of telecommunication networks. Stable multi-sets emerge as an important substructure in the design of optical networks. Received: February 14, 2001/Revised version: September 7, 2001     

Oligomeric guanidine synthesis assisted by TFA-sensitive arylsulfonylthiourea

Through arylsulfonyl activation of thiourea, efficient synthesis of oligomeric guanidines can be achieved in either solution or solid-phase. Incorporation of TFA-sensitive arylsulfonyl groups, such as Pbf, during the synthesis greatly simplifies deprotection procedures for obtaining the final oligomeric guanidine products.     

Minkowski-type and Alexandrov-Type Theorems for Polyhedral Herissons

Classical H. Minkowski theorems on existence and uniqueness of convex polyhedra with prescribed directions and areas of faces as well as the well-known generalization of H. Minkowski uniqueness theorem due to A.D. Alexandrov are extended to a class of nonconvex polyhedra which are called polyhedral herissons and may be described as polyhedra with injective spherical image.     

Guaranteed-accuracy approximation of reachable sets for a linear dynamic system subject to impulse actions

A method is proposed for approximating the reachable set of a dynamic system with a state space dimension no higher than six-eight considered on a finite time interval. The system is governed by linear differential equations with piecewise constant coefficients and impulse actions specified at prescribed times. The method is based on guaranteed-accuracy polyhedral approximations of reachable sets at researcher-specified times. Every approximation is constructed using the preceding one. A procedure is described for choosing parameters of the method that ensure the required accuracy with close-to-minimal time costs.     

Proof of the Mixing Theorem for Statistical Systems in Classical Physics

In a general measure-theoretic context, it is proved that the action of a stochastic map on a pair of probability distributions can be characterized by the criterion of decreasing mixing distance.     

Optimal node disjoint paths on partial 2-trees: A linear algorithm and polyhedral results

We present anO(p · n) algorithm for the problem of finding disjoint simple paths of minimum total length betweenp given pairs of terminals on oriented partial 2-trees withn nodes and positive or negative arc lengths. The algorithm is inO(n) if all terminals are distinct nodes. We characterize the convex hull of the feasible solution set for the casep=2.We gratefully acknowledge the referee's many helpful suggestions to improve the presentation of this paper.     

Thermal behaviour of a polyhedral oligomeric silsesquioxane with epoxy resin cured by diamines

A new material belongs to the family of polyhedral oligomeric silsesquioxanes, the 1-(3-glycidyl) propoxy-3,5,7,9,11,13,15-isobutylpentacyclo-[9.5.1.1(3,9).1(5,15).1(7,13)]octasiloxane (glycidylisobutyl-POSS) is characterized by differential scanning calorimetry, thermogravimetric analysis and atomic force microscopy. Epoxy systems based on diglycidyl ether of bisphenol A (DGEBA) cured with the diamines, 4,4'-diamine-diphenylmethane (DDM) and 1,4-phenylenediamine (pPDA), were kinetically studied by differential scanning calorimetry in isothermal and dynamic modes. The thermal behaviour of these systems as the glycidylisobutyl-POSS was added, is discussed later. This revised version was published online in July 2006 with corrections to the Cover Date.     

Synthetic studies of proanthocyanidins. Part 3: Stereoselective 3,4-cis catechin and catechin condensation by TMSOTf-catalyzed intramolecular coupling method

TMSOTf-catalyzed intramolecular condensation for catechin and epicatechin units are described. A potential electrophile and a nucleophile were connected with diester linkers and TMSOTf-catalyzed condensation was examined. In comparison with intermolecular catechin and catechin condensation, the intramolecular condensation required high reaction temperature and reversed 3,4-cis product was obtained. The condensed product was transformed into the natural 3,4-cis (+)-catechin-(4β→8)-(+)-catechin dimer.     

Representations of unbounded optimization problems as integer programs

Any optimization problem in a finite structure can be represented as an integer or mixed-integer program in integral quantities.We show that, when an optimization problem on an unbounded structure has such a representation, it is very close to a linear programming problem, in the specific sense described in the following results. We also show that, if an optimization problem has such a representation, no more thann+2 equality constraints need be used, wheren is the number of variables of the problem.We obtain a necessary and sufficient condition for a functionf:SZ, withS Z ⁿ , to have a rational model in Meyer's sense, and show that Ibaraki models are a proper subset of Meyer models.This research was supported by NSF Grant No. GP-37510X1 and ONR Contract No. N00014-75-C0621, NR047-048.