Fonctions de partitions à parité périodique

Let be the set of positive integers and a subset of . For , let denote the number of partitions of n with parts in . In the paper J. Number Theory 73 (1998) 292, Nicolas et al. proved that, given any and , there is a unique set , such that is even for n>N. Soon after, Ben Saïd and Nicolas (Acta Arith. 106 (2003) 183) considered , and proved that for all k≥0, the sequence is periodic on n. In this paper, we generalise the above works for any formal power series f in with f(0)=1, by constructing a set such that the generating function of is congruent to f modulo 2, and by showing that if f=P/Q, where P and Q are in with P(0)=Q(0)=1, then for all k≥0 the sequence is periodic on n.     

Synthesis,proton NMR stereochemical study and diels-alder reaction of (E)-7-arylidene-2H,6H-naphtho[1,8-bc]furan-2,6-diones

7-Arylidene-2H,6H-naphtho[1,8-bc]furan-2,6-diones 3 were prepared by a retro-Diels-Alder reaction of the corresponding dihydro 1,3-oxazines 2 or in a one pot synthesis from 6-hydroxy-2H-naphtho[1,8-bc]furan-2-one 1 . Their E configuration was established from the chemical shift's values of the vinylic proton and by ¹H nmr NOE difference spectroscopy. Cycloadditions of 3b upon styrene or stilbene were catalyzed by boron trifluoride etherate. The cycloadducts were obtained with the relative trans configuration.     

Study of the cis-trans isomerization of enalapril by reversed-phase liquid chromatography

Enalapril is a dipeptidic angiotensin converting enzyme inhibitor. It exists as a mixture of two conformers in solution with respect to the peptide bond involving the proline amino group. The RPLC of such products may yield peak splitting or multiple peaks as a result of the slow kinetics of the conformation change. In this study, the influence of the flow-rate, pH, temperature, organic modifier and counter ion on the peak shape and the separation of the cis and trans conformers are examined qualitatively by HPLC. It appears that decrease of relaxation time for isomerization with concomitant improvement in peak shape is favoured by a decrease in pH and flow-rate, increase of temperature, choice of organic solvent (nature, amount) and cationic counter ion concentration in the mobile phase. The elution order of the isomers was dependent on the nature of the organic modifier whereas the separation selectivity was improved by an increase of pH or the addition of a negatively charged counter ion. In addition, an NMR investigation on enalapril is described.     

Etude des equilibres solide-liquide des systems MIPO3Sm(PO3)3 (MI = Li,Na, Ag)

The M^IPO₃Sm(PO₃)₃(M^I = Li, Na, Ag) systems were studied. Differential thermal analysis and X-ray diffraction were used to investigate the liquidus and solidus relations. Three compounds LiSm(PO₃)₄, NaSm(PO₃)₄, and AgSm(PO₃)₄ were obtained which melt incongruently at 1248, 1143, and 1078 K, respectively. These compounds are isomorphous with their homologs LiLn(PO₃)₄, NaLn(PO₃)₄, AgLn(PO₃)₄ (Ln = Ce, La, Nd). They belong to the monoclinic system. The LiSm(PO₃)₄ unit cell parameters refined by least squares method are a = 16.43(3) Å, b = 7.16(1) Å, c = 9.65(3) Å, β = 125,9°(1), with the space group $\text{C2}\text{c}$ and Z = 4. NaSm(PO₃)₄ and AgSm(PO₃)₄ are isotypic; they cristallize in the $\text{P2}{}_1\text{c}$ space group, Z = 4; their unit cell parameters are, respectively, a = 12.18(1) Å, b = 13.05(1) Å, c = 7.25(5) Å, β = 126,53°(4), $\text{a = 12.25(1)}\text{A}\text{?}$, b = 13.06(1) Å, c = 7.201(9) Å, β = 126,57°(7). The ir spectra of the last two compounds indicate that these phosphates are chain phosphates.     

(m‐CH3C6H4NH3)6P6O18

In hexakis(m‐toluidinium) cyclo­hexaphosphate, 6C₇H₁₀N⁺·­P₆O₁₈^6?, the atomic arrangement is typical of a layer structure. Layers including the centrosymmetric P₆O₁₈ ring anions develop around the (100) planes at x = . The hydrogen‐bond distribution is described.     

An efficient novel synthesis of beta-(azuleno[1,2-b]benzothienyl)- and beta-(azuleno[2,1-b]benzothienyl)-alpha,beta-unsaturated ketones by the tropylium ion-mediated intramolecular furan ring-opening reaction and X-ray investigation of methyl ketone derivative

Intramolecular reaction of 2-tropylio-3-(5-substituted 2-furyl)benzothiophenes (3), prepared from the corresponding 2-cycloheptatrienyl-3-(5-substituted 2-furyl)benzothiophenes (2), afforded the beta-(azuleno[1,2-b]benzothienyl)-alpha,beta-unsaturated ketones (4), which are otherwise difficult to obtain, in moderate yields. The reaction involves a ring-opening process of the furan ring by intramolecular attack of the tropylium ion onto the 2-position of the furan ring. Similarly, beta-(azuleno[2,1-b]benzothienyl)-alpha,beta-unsaturated ketones (8) were obtained from the corresponding 3-tropylio-2-(5-substituted 2-furyl)benzothiophenes (7) albeit in lower yields. The molecular and crystal structures of the methyl ketone derivative, 8a, are discussed on the basis of X-ray structure analysis.     

Ce-promoted Fe–Cu–ZSM-5 catalyst: SCR-NO activity and hydrothermal stability

Research on Chemical Intermediates - Fe–Cu–ZSM-5 and Ce–Fe–Cu–ZSM-5 solids prepared using solid-state ion exchange method (SSIE) were tested in the NH3–SCR of NO...     

A noncontact atomic force microscope in air using a quartz resonator and the FM detection method

Noncontact imaging was successfully performed with the quartz resonator in air by using the FM detection method. A constant frequency shift mode was used. The frequency shift was about -30 mHz, which was induced by the attractive force gradient. A noncontact image of the Si(111) atomic step was obtained with vertical and lateral resolutions of 0.8 Å and 60 Å.     

Antibacterial, Anti-Chlamydial, and Cytotoxic Activities of a Marine Snail (Hexaplex trunculus) Phospholipase A2: an In Vitro Study

In order to report pharmacological characterization of marine snail (Hexaplex trunculus) hepatopancreatic phospholipase A₂ (mSDPLA₂), we have talked for the first time the antimicrobial activity against different pathogenic bacterial strains, anti-chlamydial activity as well as its cytotoxic activity against McCoy cell lines. mSDPLA₂, showed a high level of activity towards Gram-positive bacteria as Staphylococcus aureus and Staphylococcus epidermidis. Whereas Gram-negative bacteria, unfortunately, exhibited a higher resistance, mSDPLA₂ was also found to have a strong cytotoxic activity, causing significant morphological alterations of the McCoy cell lines surfaces and to be a hinder to the proliferation. Moreover, mSDPLA₂ proved to have a very potent anti-chlamydial activity. Over 95?% inhibition of chlamydial inclusions were obtained at a concentration of 10???g/ml of mSDPLA₂ after 24?h postinfection. Interestingly, at a concentration of 10???g/ml of mSDPLA₂, the proliferation of McCoy cells was not affected. Approximately 50?% inhibition of cell growth was obtained with a concentration of 37???g/mL of mSDPLA₂. mSDPLA₂ could be considered as an excellent candidate for the development of a new anti-infective agent. This enzyme showed significant antimicrobial activities.     

Approximation of the unsteady Brinkman‐Forchheimer equations by the pressure stabilization method

In this work, we propose and analyze the pressure stabilization method for the unsteady incompressible Brinkman‐Forchheimer equations. We present a time discretization scheme which can be used with any consistent finite element space approximation. Second‐order error estimate is proven. Some numerical results are also given.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1949–1965, 2017