Computations of instanton invariants using Donaldson-Floer Theory

Summary We compute the Donaldson SU(2)-invariants of the double cover of ² branched over a smooth algebraic curve of degree eight. From this we deduce a formula for the relative invariants of the blow-up of the Gompf nucleusN ₂, and we show how this gives a blow-up formula for a class of 4-manifolds which includes essentially all the simply connected 4-manifolds known to have big diffeomorphism group. We apply the result on the nucleus also to prove a formula for the invariants of minimal simply connected elliptic surfaces which reduces the computation to the case of geometric genus one. In particular, we compute all the Donaldson invariants of minimal simply connected elliptic surfaces without multiple fibers. Our main tool is Donaldson-Floer theory.Oblatum IX-1993 & 26-IV-1994     

An exact algorithm for the capacitated shortest spanning arborescence

We are given a complete and loop-free digraphG=(V, A), whereV={1,...,n} is the vertex set,A={(i, j) :i, j V} the arc set, andr V is a distinguishedroot vertex. For each arc (i, j) A, letc _ij be the associatedcost, and for each vertexi, letq _i 0 be the associateddemand (withq _r =0). Moreover, a nonnegativebranch capacity, Q, is defined.A Capacitated Shortest Spanning Arborescence rooted at r (CSSA _r ) is a minimum cost partial digraph such that: (i) each vertexj r has exactly one entering arc; (ii) for each vertexj r, a path fromr toj exists; (iii) for each branch leaving vertexr, the total demand of the vertices does not exceed the branch capacity,Q. A variant of theCSSA _r problem (calledD-CSSA _r ) arises when the out-degree of the root vertex is constrained to be equal to a given valueD. These problems are strongly NP-hard, and find practical applications in routing and network design. We describe a new Lagrangian lower bound forCSSA _r andD-CSSA _r problems, strengthened in a cutting plane fashion by iteratively adding violated constraints to the Lagrangian problem. We also present a new lower bound based on projection leading to the solution of min-cost flow problems. The two lower bounds are then combined so as to obtain an overall additive lower bounding procedure. The additive procedure is then imbedded in a branch-and-bound algorithm whose performance is enhanced by means of reduction procedures, dominance criteria, feasibility checks and upper bounding. Computational tests on asymmetric and symmetric instances from the literature, involving up to 200 vertices, are given, showing the effectiveness of the proposed approach.     

Sobolev spaces associated to a polyhedron and Fourier integral operations inR n

The theory of the Sobolev spacesH _m ^p (R ⁿ ) (mR,p polyhedron in R ²ⁿ )of [BG]is revisited here in the frame of new classes of pseudodifferential operators related to the same polyhedron p.These operators generalize to corresponding classes of Fourier integral operators, for which we present the main lines of a symbolic calculus and results of continuity on the H _m ^p (R ⁿ ) spaces.     

Regio- and Stereochemical Aspects of the Palladium-Catalyzed Desilylation-Arylation of Substituted Vinylsilanes

The palladium-catalyzed desilylation-arylation of substituted vinylsilanes by p-iodoanisole in the presence of bidentate phosphine ligands is described. Apart from enhancing the rate of the reaction considerably, heteroatom-based functional groups in the vinylsilane moiety have a profound influence on the regiochemistry. A catalytic cycle for the chelation-controlled desilylation-arylation reaction involving five- and six-membered chelate rings is proposed.     

Preparation of lucifer yellow fluorescent liposomes: A method for cells' membrane labeling

This report describes a method to conjugate lucifer yellow to the external surface of liposomes. The heterobifunctional cross-linking reagentN-succinimidyl 3-(2-pyridyldithio)propionate has been used to activate DMPE molecules. The DMPE-dithiopyridine product has been mixed with DMPC to prepare liposome vesicles. These have been reduced by DTT and finally reacted with lucifer yellow-iodoacetamide to produce the fluorescence-labeled vesicles. The quenching of their fluorescence intensity by Kl is consistent with fully exposed fluorophores. The decay of the fluorescence intensity of the lipid-bound lucifer yellow is biexponential (₁=7.9 ns; ₂=1.1 ns), with a relative yield of 0.16. When the fluorescent liposomes are mixed with cells, the lucifer yellow-DMPE derivative is transferred. Boar spermatozoa and peripheral human blood lymphocytes have been used as cellular models. The extent of incorporation is dependent on the incubation time and temperature. At 36°C, lucifer yellow fluorescence appears in the spermatozoa cells after 10 min of incubation and reaches its maximum at about 60 min. The fluorescent phospholipid derivative seems to incorporate specifically into membrane structures. The highest labeling ratio is observed with integer, scarcely motile, spermatozoa. A poorer labeling yield (15%) is found with lymphocytes. Interestingly, photobleaching due to epiillumination of the labeled cells is apparently negligible and cells are clearly visible after irradiation times ranging from several minutes to few hours.A preliminary account of this work was presented at the Quarto Simposio su Biotecnologie Biochimiche, Capri, 28–30 June 1992.     

On the Landau-Teller approximation for energy exchanges with fast degrees of freedom

We revisit the Landau-Teller heuristic approach to adiabatic invariants and, following Rapp, use it to investigate the energy exchanges between the different degrees of freedom, in simple Hamiltonian systems describing the collision of fast rotating or vibrating molecules with a fixed wall. We critically compare the theoretical results with particularly accurate numerical computations (quite small energy exchanges, namely of one part over 10³⁰, are measured).     

Studies on the Enzymatic Acylation of Quinic Acid,Shikimic Acid,Shikimic Acid,and Their Derivatives in Organic Solvents

Quinic acid ( 1a ), shikimic acid ( 2 ), and their derivatives were acylated in organic solvents by several lipases and by the protease subtilisin Carlsberg. The most satisfactory results were obtained with methyl (or benzyl) quinate ( 7a (or 8a )) and lipase from Chromobacterium viscosum adsorbed on Celite, which showed an overshelming preference towards the acylation of OH–C(4). Under optimized conditions, the syntehtically useful 4-O -acetylquinate 8d was isolated in ca. 90% yield. On the other hand, acylation of methyl shikimate ( 10a ) showed no regioselectivity with any of the enzymes tested. A possible rationale for the different behavior of Chromobacterium viscosum lipase towards 7a and 10a is given, comparing the conformations of these two molecules, as deducted from ¹H-NMR and molecular-mechanics calculation.     

Effects of heat treatment on the aggregation and charging of Stöber-type silica

Measuring and modeling the surface charge of clays, and more especially smectites, has become an important issue in the use of bentonites as a waste confinement material aimed at retarding migration of water and solutes. Therefore, many studies of the acid-base properties of montmorillonite have appeared recently in the literature, following older studies principally devoted to cation exchange. It is striking that beyond the consensus about the complex nature of the surface charge of clays, there are many discrepancies, especially concerning the dissociable charge, that prevents intercomparison among the published data. However, a general trend is observed regarding the absence of common intersection point on raw titration curves at different ionic strengths. Analysis of the literature shows that these discrepancies originate from the experimental procedures for the preparation of the clays and for the quantification of their surface charge. The present work is an attempt to understand how these procedures can impact the final results. Three critical operations can be identified as having significant effects on the surface properties of the studied clays. The first one is the preparation of purified clay from the raw material: the use of acid or chelation treatments, and the repeated washings in deionized water result in partial dissolution of the clays. Then storage of the purified clay in dry or wet conditions strongly influences the equilibria in the subsequent experiments respectively by precipitation or enhanced dissolution. The third critical operation is the quantification of the surface charge by potentiometric titration, which requires the use of strong acids and bases. As a consequence, besides dissociation of surface sites, many secondary titrant consuming reactions were described in the literature, such as cation exchange, dissolution, hydrolysis, or precipitation. The cumulated effects make it difficult to derive proper dissociation constants, and to build adequate models. The inadequation of the classical surface complexation models to describe the acid-base behavior of clays is illustrated by the electrokinetic behavior of smectites, which is independent from the pH and the ionic strength. Therefore, there is still a need on one hand for accurate data recorded in controlled conditions, and on the other hand for new models taking into account the complex nature of the charge of clays.     

Development of a multiplexed microbioreactor system for high-throughput bioprocessing

A multiplexed microbioreactor system for parallel operation of multiple microbial fermentation is described. The system includes miniature motors for magnetic stirring of the microbioreactors and optics to monitor the fermentation parameters optical density (OD), dissolved oxygen (DO), and pH, in-situ and in real time. The microbioreactors are fabricated out of poly(methylmethacrylate)(PMMA) and poly(dimethylsiloxane)(PDMS), and have a working volume of 150 microl. Oxygenation of the cells occurs through a thin PDMS membrane at the top of the reactor chamber. Stirring is achieved with a magnetic spin bar in the reactor chamber. Parallel microbial fermentations with Escherichia coli are carried out in four stirred microbioreactors and demonstrate the reproducible performance of the multiplexed system. The profiles for OD, DO, and pH compare favourably to fermentations performed in bioreactor systems with multiple bench-scale reactors. Finally, the multiplexed system is used to compare two different reactor designs, demonstrating that the reproducibility of the system permits the quantification of microbioreactor performance.