Bi-Lipschitz parameterization of surfaces

We consider surfaces Z homeomorphic to the plane with complete, possibly singular Riemannian metrics. If we have _ZK⁺<2– for the positive and _ZK^–<C for the negative part of the integral curvature, then Z is L-bi-Lipschitz equivalent to ² with L depending only on >0 and C>0. This result implies a conjecture by J. Fu.Supported by NSF grant DMS-0200566.     

Palladium-catalyzed cross-coupling reactions and electrocyclizations—efficient combinations for new cascade reactions

Palladium-catalyzed cross-coupling reactions and electrocyclic transformations as well as cycloadditions can efficiently be combined in one-pot sequences to build up complex molecules from simple precursors. 1,3-Dicyclopropyl-1,2-propadiene (1) could be coupled to various aryl halides, and the 1,3,5-hexatrienes resulting after rearrangement were trapped with different dienophiles. Further exploration of the highly reactive building block bicyclopropylidene (8) demonstrates the combinatorial potential of the two reaction modes in terms of two different three-component reactions, and even a novel four-component reaction was readily developed. Additional increase of complexity was gained by combining an intramolecular Heck reaction with consecutive trapping by 8, which can be carried out with or without 6π-electrocyclization. Finally a Stille-Heck-coupling sequence of substituted 2-bromocycloalkenyl triflates with functionally substituted alkenylstannanes and acrylic esters led to highly substituted 1,3,5-hexatrienes, which smoothly underwent 6π-electrocyclization at elevated temperatures to yield bi- and tricyclic skeletons. With this methodology at hand, a new versatile access to steroid-analogues with a diene moiety in the B ring and a functionality at C-7 was developed.     

Synthesis of 3-aminolactams as X-Gly constrained pseudodipeptides and conformational study of a Trp-Gly surrogate

3-Amino-delta-valerolactams trans-11a-c were synthesized through conjugate addition and Curtius rearrangement and converted into Fmoc-[Trp-Gly], Fmoc-[Ile-Gly], and Fmoc-[Phe-Gly] pseudodipeptides. Conformational analyses of tripeptide analogues Ac-[Trp-Gly]-Leu-NH(2) 17a and 17b by NMR experiments and molecular modeling calculations showed that diastereomer 17a adopted a gamma-turn/distorted type II beta-turn structure, whereas diastereomer 17b adopted mainly a gamma-turn structure.     

Variability in goethite surface site density: evidence from proton and carbonate sorption

Goethite is a representative iron oxide in natural environments due to its abundance and thermodynamic stability and may be responsible for many surface-mediated processes, including ion retention and mobility in aqueous settings. A large variability in morphologies and specific surface areas of goethite crystals exists but little work has been done to compare surface reactivity between them. The present work offers experimental evidence for the existence of an inverse relationship between sorption capacity for protons and carbonate ions and specific surface area of goethite for three synthetic goethite preparations spanning surface area differences by a factor of 2. An explanation for this was found by assuming a variable reactive site density between preparations in direct relationship to their sorption capacity based on congruency of carbonate sorption computed on a per-site basis. Previous evidence of maximum sorption capacities supports this explanation, and site density ratios between the goethites studied here were obtained. Triple layer surface complexation modeling was successful in describing adsorption data for all goethite preparations using equal stoichiometries. A new formulation of standard state for activities of surface species based on a 1.0 mole fraction of sites on the solid allowed transformation of the conventional molar concentration-based affinity constants to values based on site occupancy. In this fashion, by applying the appropriate site density ratios, a single set of affinity constant values was found that described accurately the adsorption data for all preparations.     

Dynamics, Thermodynamics, and Time Asymmetry

There are two schools, or lines, of thoughtwhich attempt to unify the apparently divergent laws ofdynamics and thermodynamics and to explain the observedtime asymmetry of the universe and most of its subsystems in spite of the fact that thesesystems are driven by time-symmetric evolutionequations. They will be called the coarse-graining andthe extended dynamics schools (even if these names onlypartially describe their philosophy). The coarse-grainingschool obtains time asymmetry via a projection of thestate space onto a space of relevantstates. The corresponding projection of the primitivereversible evolution laws yields effective irreversibleevolution laws for the relevant states. Extendeddynamics always uses the same primitive reversibleevolution laws. But these laws (in adequate extensionsof the usual spaces where they are formulated)have a set of solutions S that can be decomposed intotwo subsets S₊ and S_- oftime-asymmetric solutions. Time asymmetry is establishedby choosing one of these two sets as the arena in which to formulate thetheory. This paper explains in the simplestself-contained and unbiased way the main characteristicsof both schools and points out the advantages anddisadvantages of each, in such a way as to make explicit thedebate between the schools. Some cosmological featuresof the theory are also considered, mainly the problem ofthe low-entropy initial state of the universe.     

Phase diagrams of crystalline adducts containing two volatile components

The phase relationships in binary systems forming a crystalline addition compound are obtained by means of classical thermodynamic arguments for the case in which both components are volatile. This approach can be applied to inclusion compounds and to other low-stability addition compounds existing only in the solid phase. The results are consistent with those already known for clathrates containing a volatile guest and a non-volatile host, and for symmetric systems, such as racemic compounds. The temperature range in which the adduct undergoes a congruent sublimation depends on the ratio of the vapor pressures of the two components. A relation has been found to exist between the properties of the pure components, the melting behavior and the enthalpy of formation of the adduct.     

Direct mass spectrometry of polymers. XIII.. Thermal fragmentation processes in copoly-α-amino acids

The thermal fragmentation processes in L-Proline—Sarcosine and in L-Proline—L-Alanine copolymers have been investigated by direct pyrolysis—mass spectrometry. The mass spectral data show that proline—sarcosine copolymers decompose in three steps, yielding cyclic oligomers. The first step is characterized by the presence of the Sar—Sar, Sar—Pro, and Pro—Pro cyclic dimers. In the second step the formation of several series of cyclic oligomers up to nonamers—decamers can be observed, while the third step of thermal decomposition process leads to the almost exclusive formation of Pro—Pro cyclic dimer. The proline—alanine copolymers, instead, show a single-step thermal degradation process leading to the formation both of cyclic oligomers and compounds with olefin and nitrile end-groups. Our results show that the thermal decompostion of alanine units is affected by the neighboring units along the polymer chain. Sarcosine units act as thermally labile probes, causing the selective thermal cleavage of the Pro—Sar copolymer.     

Crystallizable elastomers by chemical modification of transtactic polydiolefins. Hydrochlorination

Solutions of crystalline, high-melting trans-1,4 polybutadiene (trans-PB), trans-1,4 mix 1,2 butadiene-piperylene copolymer (BPC, low piperylene content), and isotactic trans-1,4 piperylene (trans-PP) were partly hydrochlorinated under mild conditions with gaseous HCl. Glass transition and melting temperatures were strongly affected by the addition of HCl. Several hydrochlorinated trans-PB and -BPC were semicrystalline or amorphous elastomers, susceptible to reversible crystallization when stretched. The straininduced crystallinity was similar to that shown by trans-polybutadiene sequences, particularly in the form that is unstable in bulk at room temperature (form II). The addition of HCl to the asymmetric double bond in trans-PP occurs in a stereoselective way, according to ¹³C-NMR. under the experimental conditions of the present study the occurrence of side reactions was observed; these reactions decrease the polymer unsaturation to a lower level than that calculated by the amount of HCl added to the polymer.     

Palladium(II) and platinum(II)-C(3)-substituted 2,2′-bipyridines

Reaction of Pd(OAc)₂ with HL¹ and HL² (HL¹=6-iso-propyl-2,2-bipyridine; HL²=6-neo-pentyl-2,2-bipyridine), followed by treatment with LiCl or KI, gives [PdCl(L¹)]₂, (1), [PdCl(L²)]₂ (2), and [PdI(L²)]₂ (3), respectively. The chloride bridge in complexes1 and2 is split by PPh³ to give the mononuclear species PdCl(L¹)(PPh₃) (4) and PdCl(L²)(PPh₃) (5). Spectroscopic data provide evidence for coordination of the deprotonated ligands through a nitrogen and the C₍₃₎ atom of the 6-substituted pyridine. An analogous platinum complex PtCl(L³)(SMe₂) (6) (HL³=6-tert-butyl-2,2-bipyridine) was obtained from trans-PtClMe(SMe₂)₂ and HL³. The crystal structures of compounds1 and6 have been solved by X-ray diffraction analysis.Dipartimento di Chimica, Universita di Sassari, via Vienna 2, I-07100 Sassari, Italy; Dipartimento di Chimica Strutturale e Stereochimica Inorganica, Universita di Milano, Centro CNR, I-20133 Milano, Italy; Published in Khimiya Geterotsiklicheskikh Soedinenii, No. 8, pp. 1127–1137, August, 1999.     

Computer applications in food flavour research

Computer-assisted methods for improving research and production in a food-flavour company are described. Methods of experimental design are used in planning experiments. Special programs are used for identification of components through correlation of mass spectra and gas chromatographic retention indices, and for the design of new synthetic routes. In flavour creation, a data base containing qualitative and quantitative information on flavours, relevant legislation and organoleptic properties of components, can be searched selectively in attempts to improve flavours and to identify better combinations of substances. A computer-assisted production system is described which ensures complete qualitative and quantitative control.