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.     

(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.     

Water Activities, Osmotic and Activity Coefficients and Some Correlation of Aqueous Mixtures of Alkaline-Earth and Ammonium Nitrates, NH4NO3-Y(NO3)2-H2O with Y ≡ Ba2+, Mg2+ and Ca2+ at T = 25 °C

The thermodynamic properties of the mixed aqueous electrolyte of ammonium and alkaline earth metal nitrates have been studied using the hygrometric method at 25?°C. The water activities of these {yNH₄NO₃+(1?y)Y(NO₃)₂}(aq) systems with Y ≡ Ba²⁺, Mg²⁺ and Ca²⁺ were measured at total molalities ranging from 0.10 mol?kg^?1 to saturation for different NH₄NO₃ ionic-strength fractions of y=0.20, 0.50 and 0.80. These data allow the calculation of osmotic coefficients. From these measurements, the ionic mixing parameters are determined and used to calculate the solute activity coefficients in the mixtures at different ionic-strength fractions. The results of these ternary solution measurements are compared with those for binary solutions of the alkaline earth nitrates of magnesium, calcium and barium with ammonium nitrates. The behavior of the aqueous electrolyte solutions containing mixtures of barium or calcium or magnesium with ammonium nitrates are correlated and show that ionic interactions are more important for the system containing Mg²⁺ than for Ca²⁺ or Ba²⁺. The trends are mainly due to the effects of the ionic size, polarizability and the hydration of the ions in these solutions.     

Synthesis,Crystal Structure,and Conductivity Investigation of a New Monophosphate: (2-CH3OC6H4CH2NH 3)H2PO4

Chemical preparation, crystal structure, thermogravimetric and differential analysis, solid state ³¹P MAS NMR characterization, and IR spectroscopic investigations are given for a new organic cation dihydrogenmonophosphate, (2-CH₃OC₆H₄CH₂NH₃)H₂PO₄. This compound is monoclinic C2/c, with unit cell parameters a = 27.740(8), b = 4.827(2), c = 16.435(3) Å, β = 93.79(2)°, V = 2196 (1) ų, Z = 8, and ρ = 1.422 g · cm^?3. The crystal structure has been determined and refined to R = 0.046 (Rw = 0.056), using 1,746 independent reflections with I > 3σ (I). Its atomic arrangement can be described by infinite polyanions [H₂PO₄] _n ^{n ?}, organized in ribbons alternating with organic cations. Strong hydrogen bonds connect the different components. Electrical conductivity measurements show that the [2-CH₃OC₆H₄CH₂NH₃]H₂PO₄ has a low ionic conductivity value at 403 K.     

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.