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991.
The notion of broken k-diamond partitions was introduced by Andrews and Paule in 2007. For a fixed positive integer k, let \(\Delta _k(n)\) denote the number of broken k-diamond partitions of n. Recently, Paule and Radu conjectured two relations on \(\Delta _5(n)\) which were proved by Xiong and Jameson, respectively. In this paper, employing these relations, we prove that, for any prime p with \(p\equiv 1\ (\mathrm{mod}\ 4)\), there exists an integer \(\lambda (p)\in \{2,\ 3,\ 5,\ 6,\ 11\}\) such that, for \(n, \alpha \ge 0\), if \(p\not \mid (2n+1)\), then Moreover, some non-standard congruences modulo 11 for \(\Delta _5(n)\) are deduced. For example, we prove that, for \(\alpha \ge 0\), \(\Delta _5\left( \frac{11\times 5^{5\alpha }+1}{2}\right) \equiv 7\ (\mathrm{mod}\ 11)\).
相似文献
$$\begin{aligned} \Delta _5\left( 11p^{\lambda (p)(\alpha +1)-1} n+\frac{11p^{\lambda (p)(\alpha +1)-1}+1}{2}\right) \equiv 0\ (\mathrm{mod}\ 11). \end{aligned}$$
992.
Tiphaine Wong Lorette Brault Eric Gasparotto Romuald Valle Pierre-Yves Morvan Vincent Ferrires Caroline Nugier-Chauvin 《Molecules (Basel, Switzerland)》2021,26(15)
Marine polysaccharides are part of the huge seaweeds resources and present many applications for several industries. In order to widen their potential as additives or bioactive compounds, some structural modifications have been studied. Among them, simple hydrophobization reactions have been developed in order to yield to grafted polysaccharides bearing acyl-, aryl-, alkyl-, and alkenyl-groups or fatty acid chains. The resulting polymers are able to present modified physicochemical and/or biological properties of interest in the current pharmaceutical, cosmetics, or food fields. This review covers the chemical structures of the main marine polysaccharides, and then focuses on their structural modifications, and especially on hydrophobization reactions mainly esterification, acylation, alkylation, amidation, or even cross-linking reaction on native hydroxyl-, amine, or carboxylic acid functions. Finally, the question of the necessary requirement for more sustainable processes around these structural modulations of marine polysaccharides is addressed, considering the development of greener technologies applied to traditional polysaccharides. 相似文献
993.
Stefanie Scholtyssek Rameshwar Adhikari Volker Seydewitz Goerg Hannes Michler Eric Baer Anne Hiltner 《Macromolecular Symposia》2010,294(1):33-44
Nanostructured polymers and ultra-thin polymer layers are used more and more in technical applications like nanotechnology and microelectronics. Therefore, it is really important to understand the size-scale dependent properties as bulk polymers become thinner and more two-dimensional. Here the morphology as well as the macroscopic and the microscopic deformation behaviour of multilayered films of polypropylene (PP) and polystyrene (PS) have been investigated. For investigation different microscopic techniques and tensile testing were used. The films were prepared by multilayer coextrusion, whereas the composition of PP and PS and the film thickness – and therefore the thickness of each layer – varied. The thinnest calculated thickness of a single layer was about 5 nm. It is shown that the PP/PS films consist usually of homogeneous layers with only few defects. As the composition of PP/PS deviates strongly from 50/50 or the films get thinner the number of defects increases and the layered system turns to irregular lamellar system. In macroscopic tensile tests the small PS layers affect the elongation at break enormously: Most of the samples are brittle. For the films with a composition of PP/PS 90/10 and the film PP/PS 70/30 with a film thickness of 25 µm an elongation at break of 66% and higher could be reached. Transmission electron microscopy on these samples shows that the layers are characterized by plastic yielding in local deformation zones. 相似文献
994.
Bernabé L. Rivas Julio Sánchez S. Amalia Pooley Luis Basaez Eduardo Pereira Christophe Bucher Guy Royal Eric Saint Aman Jean-Claude Moutet 《Macromolecular Symposia》2010,296(1):416-428
Arsenic species can be removed from aqueous solutions using the liquid-phase polymer-based retention, LPR, technique. The LPR technique removes ionic species by functional groups of water-soluble polyelectrolytes (WSP) and then using a ultrafiltration membrane that does not let them pass through the membrane, thus separating them from the solution. The ability of WSP with groups (R)4N+X− to remove arsenate ions using LPR was studied. The interaction and arsenate anion retention capacity depended on: pH, the quaternary ammonium group's counter ion, and the ratio polymer: As(V), using different concentrations of As(V). Water-soluble polychelates were also used for one-step retention of As(III) in solution. The complex of poly(acrylic acid)-Sn, 10 and 20 wt-% of metal gave a high retention of As(III) species at pH 8, although the molar ratio polychelate: As(III) was 400:1. The enrichment method was used to determine the maximum retention capacity (C) for arsenate anions in aqueous solutions at pH 8. In similar conditions, the values of C were 142 mg g−1 for P(ClAETA) and 75 mg g−1 for P(SAETA). The combined treatment of arsenic aqueous solutions by electrocatalytic oxidation (EO) to convert the species of As(III) to As(V) with the LPR technique quantitatively removed arsenic. 相似文献
995.
Nguyen Vi Cao Emmanuel Fragnière Jacques-Antoine Gauthier Marlène Sapin Eric D. Widmer 《European Journal of Operational Research》2010
Research shows that the success of marriages and other intimate partnerships depends on objective attributes such as differences in age, cultural background, and educational level. This article proposes a mathematical approach to optimizing marriage by allocating spouses in such a way as to reduce the likelihood of divorce or separation. To produce our optimization model, we use the assumption of a central “agency” that would coordinate the matching of couples. Based on a representative and longitudinal sample of 1074 cohabiting and married couples living in Switzerland, we estimate various objective functions corresponding to age, education, ethnicity, and prior divorce concerning every possible combination of men and women. Our results show that the current state of marriages or partnerships is well below the social optimum. We reallocate approximately 68% of individuals (7 out of 10) to a new couple that we posit has a higher likelihood of survival. From this selection of new partners, we obtain our final “optimal” solutions, with a 21% reduction in the objective function. 相似文献
996.
Fluorescence methodologies have been utilized to examine micropolarity, intramolecular motion, and singlet quenching in the intraparticle void volume of zeolites X, Y, and ultrastable Y (USY) interfaced with bathing polar solvents. Micropolarity was assessed from the 3-to-1 band ratio (III/I) of the fluorescence spectrum of pyrene (PY) and from lambda(max) of the fluorescence spectrum of 1-pyrenecarboxaldehyde (1-PCA). In zeolites bathed in anhydrous solvents, both PY and 1-PCA reported increased micropolarity according to the trend USY < bulk solvent < NaX approximately NaY. For example, in NaY (USY), III/I ranged from 0.44 (0.98) in acetonitrile to 0.52 (1.34) in n-hexanol, compared to 0.60, 1.06, and 1.62 in bulk acetonitrile (ACN), n-hexanol, and n-hexane, respectively. The polarity studies reveal that the ionic nature of NaX and NaY and the hydrophobic nature of USY strongly influence the microenvironment of the arene despite the presence of desorbing polar solvents. Constraints on intramolecular motion were examined in polar-solvated NaX through measurements of the fluorescence lifetime of trans-stilbene. Lifetimes ranged from 113 ps in NaX-ACN to 671 ps in NaX-tert-butyl alcohol. The latter value is close to that observed in bulk glycerol. Diffusion-controlled quenching of PY fluorescence by O2 and a series of nitrocompounds dissolved in solvents bathing the zeolite was examined by a time-resolved approach. For all of the quenchers and solvents studied, quenching was more efficient in USY compared to NaX and NaY. Interestingly, the rate of O2 quenching in USY-MeOH was only 12 times lower than that in bulk MeOH. In contrast, in NaY-MeOH and NaX-MeOH the rate of O2 quenching was too low to be measured. The rate constants in these systems were therefore taken as the rate constant for diffusion-controlled quenching of trapped electrons measured previously. These values were 600 times and 10(5) times lower than the rate of fluorescence quenching in USY-MeOH, respectively. The O2 quenching studies show that dispersive interactions of polar solvents with the cavity walls dominate in USY because of the hydrophobic nature of the USY surface. In NaX and NaY, stronger ion-dipole and hydrogen bonding interactions dominate and lead to more restricted access and lowered quenching efficiency. Perrin (or static) quenching of pyrene fluorescence was also examined to infer the concentration of nitromethane (NM) in the void volume of NaX and NaY bathed in MeOH, ACN, or H2O. The results indicate that access of NM to the interior of NaY is more inhibited in ACN compared to MeOH, presumably because of the higher dipole moment of ACN and its resulting stronger association with the zeolite surface. At similar levels of static quenching equated to a similar NM concentration in the zeolite, dynamic quenching by NM varied by no more than a factor of 2 in all systems compared. This implies that the rate of NM diffusion in solvated zeolite interiors is similar regardless of zeolite or solvent properties. In contrast to O2 diffusion in zeolites, NM exhibits a high dipole moment and can therefore migrate through polar-solvated zeolite apertures by adsorbing to the zeolite. Overall, the results of this study show a close relationship between the behavior of probes and quenchers in the confines of polar-solvated zeolite interiors and the chemical properties of the zeolite. Differences between weakly and strongly interacting surfaces are revealed clearly in the results. 相似文献
997.
[reaction: see text] A general approach to the tricyclic core of the icetexane natural products via the cycloisomerization of alkynyl indenes using GaCl(3) is presented. This strategy provides an efficient synthesis of the natural product salviasperanol and sets the stage for access to other members of this family of diterpenoids. 相似文献
998.
Takami T Arnold DP Fuchs AV Will GD Goh R Waclawik ER Bell JM Weiss PS Sugiura K Liu W Jiang J 《The journal of physical chemistry. B》2006,110(4):1661-1664
Initial stages of two-dimensional crystal growth of the double-decker sandwich complex Lu(Pc*)2 [Pc* = 2,3,9,10,16,17,23,24-octakis(octyloxy)phthalocyaninato] have been studied by scanning tunneling microscopy at the liquid/solid interface between 1-phenyloctane and highly oriented pyrolytic graphite. High-resolution images strongly suggest alignment of the double-decker molecules into monolayers with the phthalocyanine rings parallel to the surface. Domains were observed with either hexagonal or quadrate packing motifs, and the growing interface of the layer was imaged. Molecular resolution was achieved, and the face of the phthalocyanine rings appeared as somewhat diffuse circular features. The alkyl chains are proposed to be interdigitating to maintain planar side-by-side packing. 相似文献
999.
A series of six 2,5-disubstituted adjacent bis(tetrahydrofuran) stereoisomers with trans/erythro/cis, trans/threo/trans, or cis/threo/cis relative stereochemistry have been synthesized from known dihydroxycyclooctenes via ring opening/cross metathesis and Pd(0)-mediated asymmetric double cycloetherification. The stereochemistry of four of these isomers has been found in the biologically active annonaceous acetogenin natural products. [reaction: see text]. 相似文献
1000.
Cyclopentadienyl half-sandwich ruthenium complexes have been demonstrated to be promising scaffolds as protein kinase inhibitors. In order to rapidly identify derivatives which display modified pharmacological properties, we developed the synthesis of an organoruthenium compound bearing an N-succinimidyl ester at the cyclopentadienyl moiety. The quenching of this activated ester with a library of primary amines, followed by testing of the resulting amide library, led to the identification of organometallic Pim-1 and GSK-3 inhibitors with improved potencies and kinase selectivities. [structure: see text]. 相似文献