Gaussian heat kernel upper bounds via the Phragmen-Lindelof theorem

We prove that in the presence of L² Gaussian estimates, theso-called Davies–Gaffney estimates, on-diagonal upperbounds imply precise off-diagonal Gaussian upper bounds forthe kernels of analytic families of operators on metric measurespaces.     

Soft car sequencing with colors: Lower bounds and optimality proofs

This paper is a study of the car sequencing problem, when feature spacing constraints are soft and colors of vehicles are taken into account. Both pseudo-polynomial algorithms and lower bounds are presented for parts of the problem or family of instances. With this set of lower bounds, we establish the optimality (up to the first non-trivial criteria) of 54% of best known solutions for the benchmark used for the Roadef Challenge 2005. We also prove that the optimal penalty for a single ratio constraint N/P can be computed in O(P) and that determining the feasibility of a car sequencing instance limited to a pair of simple ratio constraints can be achieved by dynamic programming. Finally, we propose a solving algorithm exploiting these results within a local search approach. To achieve this goal, a new meta-heuristic (star relinking) is introduced, designed for the optimization of an aggregation of criteria, when the optimization of each single criterion is a polynomial problem.     

On the correlation structure of some random point processes on the line

The correlation structure of some remarkable point processes on the one-dimensional real line is investigated. More specifically, focus is on translation invariant determinantal, permanental and/or renewal point processes. In some cases, anomalous (non-Poissonian) fluctuations for the number of points in a large window can be observed. This may be read from the total correlation function of the point process. We try to understand when and why this occurs and what are the anomalous behaviors to be expected.From examples, it is shown that determinantal (fermion) point processes can be super-homogeneous (the number variance grows slower than the number mean) and even hyper-uniform (when variance growth saturates).Renewal point processes with bounded spacings variance are essentially Poissonian (the number variance grows like the number mean as in Poisson models).Under certain conditions, permanental (boson) point processes can be sub-homogeneous or critical (in the sense that the number variance grows faster than the number mean).We give several detailed examples illustrating these properties of interest together with unexpected behaviors.     

Topological Complexity of the Relative Closure of a Semi-Pfaffian Couple

Gabrielov introduced the notion of relative closure of a Pfaffian couple as an alternative construction of the o-minimal structure generated by Khovanskii’s Pfaffian functions. In this paper, we use the notion of format (or complexity) of a Pfaffian couple to derive explicit upper bounds for the homology of its relative closure. We consider both the singular and the Borel–Moore homology theories.     

A concise three-component synthesis of α-amino esters derived from phenylglycine and phenylalanine

α-Amino esters have been synthesized using a straightforward three-component reaction among preformed or in situ-generated aromatic or benzylic organozinc reagents, primary or secondary amines and ethyl glyoxylate. The procedure, which is characterized by its simplicity, allows the concise synthesis of phenylglycine and phenylalanine derivatives.     

Structure revision of plakotenin based on computational investigation of transition states and spectroscopic properties

We show that the previously [Tetrahedron Lett.1992, 33, 2579] proposed structure of natural plakotenin must be revised. Recently, the total synthesis of plakotenin was achieved via an intramolecular Diels-Alder reaction from a (E,E,Z,E)-tetraene as linear precursor. Using density functional theory, the computation of the four possible transition states for this reaction shows that the previously proposed structure could only have been formed via an energetically high-lying transition state, which is very unlikely. Instead, we suggest that the structure of plakotenin corresponds to the product formed via the lowest transition state. A comparison of experimental and theoretical optical rotation, circular dichroism, and two-dimensional nuclear Overhauser enhancement spectra conclusively proves that the structure of plakotenin is the one that is suggested by the transition state computations. Moreover, the simulation of the nuclear Overhauser enhancement spectra suggests that it is most likely that the misassignment of the (1)H chemical shifts of two methyl groups has led to the wrong structure prediction in the 1992 work. The previously proposed structure of iso-plakotenin remains unaffected by our structure revision, but the structures of homo- and nor-plakotenin must also be revised. The present work shows how the total synthesis of a natural product, together with the theoretical determination of the barrier heights of the reactions involved, can be of great help to assign its structure. It appears that intramolecular Diels-Alder reactions can be modeled accurately by today's first-principles methods of quantum chemistry.     

Enhancement of poly(vinyl ester) solubility in supercritical CO2 by partial fluorination: the key role of polymer-polymer interactions

An enhancement of poly(vinyl ester) solubility in supercritical carbon dioxide (sc-CO(2)) can be achieved by decreasing the strength of the polymer-polymer interactions. To demonstrate this, a library of statistical copolymers of vinyl acetate and vinyl trifluoroacetate was synthesized by RAFT/MADIX polymerization with varying compositions at a given number-average molecular weight. These copolymers exhibited unprecedentedly low cloud-point pressures in sc-CO(2) at 40 °C compared with previously reported poly(vinyl esters). Surface tension measurements combined with a computational approach evidenced the prominent role played by polymer-polymer interactions.     

Deprotonative metalation of aromatic compounds using mixed lithium–iron combinations

The deprotonation of 2-methoxypyridine was attempted using putative (TMP)₃FeLi prepared from different iron sources. Using iodine to intercept the metalated 2-methoxypyridine, the best result was obtained from FeBr₂ (1 equiv) using THF at room temperature; nevertheless, in addition to the expected iodide, the corresponding 2,2′-dimer was obtained (86% total yield). The origin of the competitive formation of the 2,2′-dimer was not identified but mechanisms were suggested to explain its formation. It was observed that the nature of the electrophile employed to trap the 3-metalated 2-methoxypyridine has a strong impact on this dimer formation, the latter being favored using iodine (35% yield), but also benzophenone (28%), benzoyl chloride (22%), methyl iodide (27%), allyl bromide (15%), benzyl bromide (41%), and tetramethylthiuram disulphide (36%); for this reason, the yields of the expected derivatives were only 51, 15, 62, 0, <5, 18, and 0%, respectively. In contrast, using aldehydes readily led to the expected pyridine alcohols without dimerization (59% yield using 3,4,5-trimethoxybenzaldehyde and 66% yield using pivalaldehyde). 2,6-Dimethoxypyridine (in 68% yield), anisole (47%), 2,4-dimethoxypyrimidine (50% at C5 and 3% at C6), 2-fluoropyridine (64%), and thiophene (49%) were similarly converted into the corresponding alcohols after subsequent trapping with pivalaldehyde. Using iodine to trap the 2-metalated anisole did not lead to dimer formation, and 2-iodoanisole was isolated in 71% yield.     

Stereochemical effect revealed in self-assemblies based on archaeal lipid analogues bearing a central five-membered carbocycle: a SAXS study

The relative stereochemistry (cis or trans) of a 1,3-disubstituted cyclopentane unit in the middle of tetraether archaeal bipolar lipid analogues was found to have a dramatic influence on their supramolecular self-assembly properties. SAXS studies of two synthetic diastereomeric archaeal lipids bearing two lactosyl polar head groups at opposite ends revealed different lyotropic behaviors. The cis isomer led to L(c)-L(α)-Q(II) transitions whereas the trans isomer retained an L(α) phase from 20 to 100 °C. These main differences originate from the conformational equilibrium (pseudorotation) of 1,3-disubstituted cyclopentanes. Indeed, this pseudorotation exhibits quite similar orientations of the two substituents in a trans isomer whereas several orientations of the two alkyl chains are expected in a cis-1,3-dialkyl cyclopentane, thus authorizing more conformational flexibility in the lipid packing.     

Synthetic Studies toward C‐Glucosidic Ellagitannins: A Biomimetic Total Synthesis of 5‐O‐Desgalloylepipunicacortein A

C‐glucosidic ellagitannins constitute a subclass of bioactive polyphenolic natural products with strong antioxidant properties, as well as promising antitumoral and antiviral activities that are related to their capacity to interact with both functional and structural proteins. To date, most synthetic efforts toward ellagitannins have concerned glucopyranosic species. The development of a synthetic strategy to access C‐glucosidic ellagitannins, whose characteristic structural feature includes an atropoisomeric hexahydroxydiphenoyl (HHDP) or a nonahydroxyterphenoyl (NHTP) unit that is linked to an open‐chain glucose core by a C‐aryl glucosidic bond, is described herein. The total synthesis of the biarylic HHDP‐containing 5‐O‐desgalloylepipunicacortein A ( 1 β ) was achieved by either using the natural ellagic acid bis‐lactone as a precursor of the requested HHDP unit or by implementing an atroposelective intramolecular oxidative biarylic coupling to forge this HHDP unit. Both routes converged in the penultimate step of this synthesis to enable a biomimetic formation of the key C‐aryl glucosidic bond in the title compound.