Maximum norms of random sums and transient pattern formation

Many interesting and complicated patterns in the applied sciences are formed through transient pattern formation processes. In this paper we concentrate on the phenomenon of spinodal decomposition in metal alloys as described by the Cahn-Hilliard equation. This model depends on a small parameter, and one is generally interested in establishing sharp lower bounds on the amplitudes of the patterns as the parameter approaches zero. Recent results on spinodal decomposition have produced such lower bounds. Unfortunately, for higher-dimensional base domains these bounds are orders of magnitude smaller than what one would expect from simulations and experiments. The bounds exhibit a dependence on the dimension of the domain, which from a theoretical point of view seemed unavoidable, but which could not be observed in practice.

In this paper we resolve this apparent paradox. By employing probabilistic methods, we can improve the lower bounds for certain domains and remove the dimension dependence. We thereby obtain optimal results which close the gap between analytical methods and numerical observations, and provide more insight into the nature of the decomposition process. We also indicate how our results can be adapted to other situations.

     

An integrated console for capsule-based,automated organic synthesis

The current laboratory practices of organic synthesis are labor intensive, impose safety and environmental hazards, and hamper the implementation of artificial intelligence guided drug discovery. Using a combination of reagent design, hardware engineering, and a simple operating system we provide an instrument capable of executing complex organic reactions with prepacked capsules. The machine conducts coupling reactions and delivers the purified products with minimal user involvement. Two desirable reaction classes – the synthesis of saturated N-heterocycles and reductive amination – were implemented, along with multi-step sequences that provide drug-like organic molecules in a fully automated manner. We envision that this system will serve as a console for developers to provide synthetic methods as integrated, user-friendly packages for conducting organic synthesis in a safe and convenient fashion.

Using a combination of reagent design, hardware engineering, and a simple operating system we provide an instrument capable of executing complex organic reactions using prepacked capsules with minimal user involvement.     

β-Lactam Derivatives as Enzyme Inhibitors: Peptidic Derivatives of ( RS )-2-Oxo-4-phenylazetidine-1-alkanoic Acids

4-Phenylazetidine-2-one was transformed into 4-phenylazetidine-1-alkanoic acids, which were reacted in the presence of diphenylphosphoroazidate with amino acid esters and dipeptide esters yielding β-lactam peptides with different spacers between the lactam ring and the peptide moiety. All structures were established by elementary analyses, HPLC, optical rotation, and spectroscopic data and all new compounds were tested as inhibitors of PPE using standard procedures. Four compounds exhibited a weak activity compared with the standard inhibitor trifluoroacetyl-l-val-l-tyr-l-val.     

PHOTOSENSITIZATION OF MELANIN: AN ELECTRON SPIN RESONANCE STUDY OF SENSITIZED RADICAL PRODUCTION AND OXYGEN CONSUMPTION

Abstract Rose Bengal is shown to photosensitize free-radical production and oxygen consumption in solutions of melanin from autooxidation of 3,4-dihydroxyphenylalanine (DOPA). In anaerobic solutions the sensitizer enhances rates of free-radical production by up to a factor of 20. In aerobic solutions, rates of oxygen consumption can be increased by a factor of several hundred. The reactions appear to involve the triplet state of the sensitizer. The effect of the sensitizer in increasing oxygen consumption is quenched by low concentrations of azide and enhanced by D₂O, suggesting that a singlet oxygen mechanism is involved.     

A convenient synthesis of 1,3-oxazolidin-4-ones and 1,3-oxazin-4-ones

1,3-Oxazolidin-4-ones and 1,3-oxazin-4-ones were synthesized by formal cyclocondensation of imines with α- or β-hydroxy acids.     

Synthesis of (-)-2s,3s, 11s,12r-2,3,11,12-tetraphenyl[18]crown-6

The synthesis of ( - ) 2S,3S,11S,12R-2, 3,11,12-tetraphenyl [18]-crown-6 from (-)-1S,2S-hydrobenzoin and meso-hydrobenzoin is described. Chemical shifts and vicinal coupling constants of the benzylic protons in the 2 S, 3 S and 11 S,12 R substructures in the free ligands and in complexes with KSCN and 1-phenylethylammonium bromides and a brief discussion of the related conformational changes are also presented. A detailed procedure for the resolution of racemic hydrobenzoin is given.     

Diastereoselective cascade synthesis of azabicyclo[3.1.0]hexanes from acyclic precursors

The diastereoselective synthesis of azabicyclo[3.1.0]hexanes bearing different substituents on all positions of the cyclopropane ring has been achieved in moderate to good yields.     

Total synthesis of the ramoplanin A2 and ramoplanose aglycon

A convergent total synthesis of the ramoplanin A2 and ramoplanose aglycon is disclosed. Three key subunits composed of residues 3-9 (heptapeptide 15), pentadepsipeptide 26, and pentapeptide 34 (residues 10-14) were prepared, sequentially coupled, and cyclized to provide the 49-membered depsipeptide core of the aglycon. Key to the preparation of the pentadepsipeptide 26 incorporating the backbone ester was the asymmetric synthesis of an orthogonally protected L-threo-beta-hydroxyasparagine and the development of effective and near-racemization free conditions for esterification of its hindered alcohol (EDCI, DMAP, 0 degrees C). The coupling sites were chosen to maximize the convergency of the synthesis including that of the three subunits, to prevent late stage racemization of carboxylate-activated phenylglycine-derived residues, and to enlist beta-sheet preorganization of an acyclic macrocyclization substrate for 49-membered ring closure. As such, macrocyclization at the chosen Phe(9)-D-Orn(10) site may benefit from both beta-sheet preorganization as well as closure at a D-amine terminus. Deliberate late stage incorporation of the subunit bearing the labile depsipeptide ester and a final stage Asn(1) side chain introduction provides future access to analogues of the aglycons which themselves are reported to be equally potent or more potent than the natural products in antimicrobial assays.     

Numerische Ermittlung quasikonformer Abbildungen mit finiten Elementen

Summary In this note we consider so called p-analytic mappings of simply or doubly connected domains on rectangles or circular rings. Real and imaginary parts of the mappings can be described by minimal-principles. By minimizing the corresponding functionals in a class of linear or bilinear finite elements we obtain an approximation of the mapping and also upper and lower bounds for the p-module of a domain with polygonal boundary. Error bounds are given for smooth and for piecewise constant functionsp. We present numerical experiments.