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.     

Yields and average cross sections of recoil charged particle induced reactions on11B,12C,13C,14N,16O and18O

The yield and average cross section for the reactions¹¹B(p, n)¹¹C,¹²C(p, )¹³N,¹³C(p, n)¹³N, ₁₂ ¹² C(d, n)¹³N,¹⁴N(p, )¹¹C,¹⁶O(p, )¹³N,¹⁶O(d, n)¹⁷F,¹⁶O(t, n)¹⁸F, and¹⁸O(p, n)¹⁸F have been measured in different compounds. The charged particles were created in the samples themselves either through recoil by scattering of 14 MeV neutrons off hydrogen and deuterium, or by the (n, t) reaction on⁶Li using thermal neutrons. The yields of reactions¹²C(d, n);¹⁶O(p, );¹⁶O(t, n) and¹⁸O(p, n) have been measured using proton, deuteron and triton spectra generated by 14 MeV neutrons in the reactions D(n, p)2n;⁶Li(n, d);⁷Li(n, d) and¹⁰B(n, d);⁷Li(n, t) and¹⁰B(n, t), respectively.     

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...     

Light Emission and Scanning Electron Microscopic Characterization of Porous Silicon

Optical emission resulting from sputtered species during ion bombardment of porous and oxidized porous silicon targets has been studied. Samples were bombarded with 5‐keV Kr⁺ ions at an incidence angle of 70 degrees, and the light emitted was analyzed over the wavelength range 200–300 nm. The surface morphology was investigated, and the micrographs revealed grooves parallel to the plane of incidence when the porosity was surprisingly observed in the grooves under each pore. The results are discussed as a function of the incidence angle and the porosity of the silicon targets.     

Theoretical study of selenium and tellurium impurities in (ZnO)6 clusters using DFT and TDDFT

Zinc oxide (ZnO) nanostructures have attracted much interest due to their potential applications in various fields including optoelectronics, glass industries, and solar cells. These compounds hold the promise of creating new materials that can advance energy technologies. In this work, a series of (ZnO)₆ clusters with selenium and tellurium applied as substitutional impurities has been studied. The investigated structures have been produced through the doping of (ZnO)₆ clusters by replacing an oxygen atom with a selenium or a tellurium atom at each time. The ground state geometric parameters of (ZnO)₆ structures, containing selenium or tellurium atoms as substitutional impurities, were calculated using density functional theory (DFT) with B3LYP and LanL2DZ basis set. Excited state energies and absorption wavelengths were computed using time‐dependent‐DFT (TDDFT). For the calculation of emission wavelengths, Hartree–Fock configuration interaction singles (HF/CIS) has been used in order to perform the excited state geometry optimization. This work led to some important results that can be helpful for developing novel THz sensitive materials and imaging detectors that may be an alternative to x‐rays detectors for radiology as well as for the development of solar cells and electroluminescent diodes. Zinc oxide (ZnO) nanostructures have attracted growing interest due to their potential applications in many technological fields, including optoelectronics, the glass industry, and energy. The presence of impurities, in particular selenium and tellurium, in ZnO‐based clusters can affect their structural and spectroscopic properties. Some of these doped nanostructures have favorable Terahertz emission characteristics that make them good candidates for applications in biology and medicine.     

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.     

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.