Solving stochastic programs with integer recourse by enumeration: A framework using Gröbner basis

In this paper we present a framework for solving stochastic programs with complete integer recourse and discretely distributed right-hand side vector, using Gröbner basis methods from computational algebra to solve the numerous second-stage integer programs. Using structural properties of the expected integer recourse function, we prove that under mild conditions an optimal solution is contained in a finite set. Furthermore, we present a basic scheme to enumerate this set and suggest improvements to reduce the number of function evaluations needed.     

Sarcophytolides G–L,New Biscembranoids from the Soft Coral Sarcophyton elegans

Six new biscembranoids, namely, sarcophytolides G–L ( 1 – 6 , resp.), together with six known analogs, were isolated from a marine soft coral Sarcophyton elegans. The structures of the new compounds were established on the basis of 1D‐ and 2D‐NMR (COSY, HSQC, HMBC, and NOESY) spectroscopic analysis together with the aid of MS, CD, and IR data. The unusual isobiscembranoid sarcophytolide G ( 1 ) was found for the first time in the genus Sarcophyton.     

An algorithm for the construction of convex hulls in simple integer recourse programming

We consider the objective function of a simple integer recourse problem with fixed technology matrix and discretely distributed right-hand sides. Exploiting the special structure of this problem, we devise an algorithm that determines the convex hull of this function efficiently. The results are improvements over those in a previous paper. In the first place, the convex hull of many objective functions in the class is covered, instead of only one-dimensional versions. In the second place, the algorithm is faster than the one in the previous paper. Moreover, some new results on the structure of the objective function are presented.     

Combining cationic ring‐opening polymerization and click chemistry for the design of functionalized polyurethanes

A straightforward strategy for the synthesis and functionalization of polyurethanes (PUs) via the use of alkyne‐functionalized polytetrahydrofuran (PTHF) diols is described. The alkyne groups have been introduced into the PTHF chains by the cationic ring‐opening copolymerization of tetrahydrofuran and glycidyl propargyl ether. These PTHF prepolymers were combined with 1,4‐butanediol and hexamethylene diisocyanate for the synthesis of linear PUs with latent functionalization sites. The polyether segments of the PUs have then been coupled with several types of functionalized azides by the copper‐catalyzed azide‐alkyne “click” chemistry, for example with phosphonium containing azides for their antibacterial properties. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Fragilolides A-Q,norditerpenoid and briarane diterpenoids from the gorgonian coral Junceella fragilis

Chemical investigation of the gorgonian coral Junceella fragilis resulted in the isolation of a new norditerpenoid fragilolide A (1), sixteen new briarane diterpenoids fragilolides B-Q (2–17), together with frajunolides H and N, and three known norcembranoids scabrolide D, sinuleptolide and 5-epi-sinuleptolide. The structures of new compounds were determined on the basis of extensive spectroscopic analysis, including the experimental and calculated ECD data and single-crystal X-ray diffraction for the configurational assignments. The structure of fragilolide A featured an unprecedented 4,13- and 7,11-fused tetracyclic norcembranoid, while the biogenetic relationships of the briarane analogues were postulated. Frajunolide H exerted significant inhibition against a panel of tumor cell lines, and six briarane diterpenoids (3, 6, 8, 12, 16, and frajunolide N) exhibited the inhibitory effects against the HBeAg express of hepatitis B virus in HepAD38 cells. In addition, sinuleptolide and 5-epi-sinuleptolide exerted the effects to inhibit NO production in RAW264.7 macrophage cells, in addition to the activation of ARE and the inhibition of NF-κB expression.     

Synthesis,Spectroscopy, Crystal Structure Determination,and Quantum Chemical Calculations of BODIPY Dyes with Increasing Conformational Restriction and Concomitant Red‐Shifted Visible Absorption and Fluorescence Spectra

Starting from the conformationally unconstrained compound 3,5‐di‐(2‐bromophenoxy)‐4,4‐difluoro‐8‐(4‐methylphenyl)‐4‐bora‐3a,4a‐diaza‐s‐indacene ( 1 ), two BODIPY dyes ( 2 and 3 ) with increasingly rigid conformations were synthesized in outstanding total yields through palladium catalyzed intramolecular benzofuran formation. Restricted bond rotation of the phenoxy fragments leads to dyes 2 and 3 , which absorb and fluoresce more intensely at longer wavelengths relative to the unconstrained dye 1 . Reduction of the conformational flexibility in 2 and 3 leads to significantly higher fluorescence quantum yields compared to those of 1 . X‐ray diffraction analysis shows the progressively more extended planarity of the chromophore in line with the increasing conformational restriction in the series 1 → 2 → 3 , which explains the larger red shifts of the absorption and emission spectra. These conclusions are confirmed by quantum chemical calculations of the lowest electronic excitations in 1 , 1a , 2 , 2a , 3 and dyes of related chemical structures. The effect of the molecular structure on the visible absorption and fluorescence emission properties of 1 , 1a , 2 , 2a , 3 has been examined as a function of solvent by means of the new, generalized treatment of the solvent effect (J. Phys. Chem. B 2009 , 113, 5951–5960). Solvent polarizability is the primary factor responsible for the small solvent‐dependent shifts of the visible absorption and fluorescence emission bands of these dyes.     

On the relation between complexity and uncertainty

In practical problem situations data are usually inherently unreliable. A mathematical representation of uncertainty leads to stochastic optimization problems. In this paper the complexity of stochastic combinatorial optimization problems is discussed. Surprisingly, certain stochastic versions of NP-hard determinstic combinatorial problems appear to be solvable in polynomial time.     

Improved Spectral Coverage and Fluorescence Quenching in Donor–acceptor Systems Involving Indolo[3‐2‐b]carbazole and Boron‐dipyrromethene or Diketopyrrolopyrrole

A novel π‐conjugated triad and a polymer incorporating indolo[3,2‐b]‐carbazole (ICZ) and 4,4‐difluoro‐4‐bora‐3a,4a‐diaza‐s‐indacene (BODIPY) were synthesized via a Sonogashira coupling. Compared to the parent BODIPY the absorption and fluorescence spectrum were for both compounds broader and redshifted. The redshift of the fluorescence and the decrease of the fluorescence quantum yield and decay time upon increasing solvent polarity were attributed to the formation of a partial charge‐transfer state. Upon excitation in the ICZ absorption band the ICZ fluorescence was quenched in both compounds mainly due to energy transfer to the BODIPY moiety. In a similar ICZ–π–DPP polymer (where DPP is diketopyrrolopyrrole), a smaller redshift of the absorption and fluorescence spectra compared to the parent DPP was observed. A less efficient quenching of the ICZ fluorescence in the ICZ–π–DPP polymer could be related to the unfavorable orientation of the transition dipoles of ICZ and DPP. The rate constant for energy transfer was for all compounds an order of magnitude smaller than predicted by Förster theory. While in a solid film of the triad a further redshift of the absorption maximum of nearly 100 nm was observed, no such shift was observed for the ICZ–π–BODIPY polymer.     

Subergane‐Type Sesquiterpenes from Gorgonian Coral Subergorgia suberosa with Antibacterial Activities

A new subergane‐type sesquiterpene, named epoxysubergorgic acid ( 1 ), along with seven known sesquiterpenes, were isolated from the gorgonian coral Subergorgia suberosa. The structure of the new compound was determined by extensive spectroscopic analyses. The previously uncertain absolute configuration of the known analogues 2 – 6 was determined on the basis of CD, Mosher's method, and through chemical conversions. All compounds were evaluated for antibacterial activities.