Synthesis of α-Oxo and α-hydroxy-1-benzyl-1,4-dihydro-3(2H)-isoquinolinones

The reaction of some primary amines with the methyl 2-[(α-oxobenzyl)-(α-bromo)methyl]phenylacetate ( 5 ) afforded the isoquinolinones 7a-d , which in turn were hydrogenated to 10a-d . The synthesis of these compounds was designed on the basis of a potential depressant and antiinflammatory activity found in other structurally related compounds.     

Synthesis and characterization of 4-hydroxy-3-phenylprolines

4-Hydroxy-3-phenylprolines were synthesized via 1-acetyl-2,2-diethoxycarbonyl-2,3-dihydro-3-phenyl-1H-pyrrole. Reversed phase hplc resulted in the isolation of the products which were characterized by ¹H and ¹³C nmr spectroscopy.     

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).     

Fractal relaxed Dirichlet problems

Given aself similar fractal K ? ? ⁿ of Hausdorff dimension α>n?2, andc ₁>0, we give an easy and explicit construction, using the self similarity properties ofK, of a sequence of closed sets? _h such that for every bounded open setΩ?? ⁿ and for everyf ∈ L²(Ω) the solutions to $$\left\{ \begin{gathered} - \Delta u_h = f in \Omega \backslash \varepsilon _h \hfill \\ u_h = 0 on \partial (\Omega \backslash \varepsilon _h ) \hfill \\ \end{gathered} \right.$$ converge to the solution of the relaxed Dirichlet boundary value problem $$\left\{ \begin{gathered} - \Delta u + uc_1 \mathcal{H}_{\left| K \right.}^\alpha = f in \Omega \hfill \\ u = 0 on \partial \Omega \hfill \\ \end{gathered} \right.$$ (H _∣ ^α denotes the restriction of the α-dimensional Hausdorff measure toK). The condition α>n?2 is strict.