Quonic realization of the deformed Heisenberg-Weyl algebra

A consistent realization of an operatorial deformed Heisenberg-Weyl (HW) algebra is given. The explicit construction of the deformation matrix is discussed. The corresponding generalized Fock-like space is analyzed.     

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.     

The diagnonal multivariate natural exponential families and their classification

A natural exponential family (NEF)F in ? ⁿ ,n>1, is said to be diagonal if there existn functions,a ₁,...,a _n , on some intervals of ?, such that the covariance matrixV _F (m) ofF has diagonal (a ₁(m ₁),...,a _n (m _n )), for allm=(m ₁,...,m _n ) in the mean domain ofF. The familyF is also said to be irreducible if it is not the product of two independent NEFs in ? ^k and ? ^n-k , for somek=1,...,n?1. This paper shows that there are only six types of irreducible diagonal NEFs in ? ⁿ , that we call normal, Poisson, multinomial, negative multinomial, gamma, and hybrid. These types, with the exception of the latter two, correspond to distributions well established in the literature. This study is motivated by the following question: IfF is an NEF in ? ⁿ , under what conditions is its projectionp(F) in ? ^k , underp(x ₁,...,x _n )∶=(x ₁,...,x _k ),k=1,...,n?1, still an NEF in ? ^k ? The answer turns out to be rather predictable. It is the case if, and only if, the principalk×k submatrix ofV _F (m ₁,...,m _n ) does not depend on (m _k+1,...,m _n ).     

Eliminating Selective Dropping Attack in Mobile Ad Hoc Network

Wireless Personal Communications - In this paper, we propose a new reputation approach, called I-WD (improved WatchDog). We attempt to eliminate selective dropping attack that ensue when malicious...     

Investigation on corrosion inhibition and adsorption mechanism of azomethine derivatives at mild steel/0.5 ​M ​H2SO4 solution interface: Gravimetric,electrochemical, SEM and EDX studies

The inhibition performance of five azomethine derivatives such as: 1-(4-Methyloxy phenylimino)-1-(phenylhydrazono)-propan-2-one (SB₁), 1-(4-Methylphenylimino)-1-(phenylhydrazono) propan-2-one (SB₂), 1-(phenylimino)-1(phenylhydrazono)-propan-2-one (SB₃), 1-(4-Bromo phenylimino)-1(phenylhydrazono)-propan-2-one (SB₄) and 1-(4-Chlorophenylimino)-1(phenylhydrazono) -propan-2-on (SB₅) as corrosion inhibitors for mild steel in sulfuric acid 0.5 ?M were investigated using different methods. All experimental results demonstrate that these compounds are eficients inhibitors. The inhibition efficiencies ($IE$) increase with inhibitors concentration. At 7.5 $\times$ 10^?5 ?M, the $IE$ was 97.27%, 96.31%, 94.23%, 93.19 and 91.64% for SB₁, SB₂, SB₃, SB₄ and SB₅, respectively. The potentiodynamic polarization results indicated that all the studied inhibitors act as mixed type. The adsorption process on mild steel surface obeyed Langmuir isotherm. The associated activation parameters and thermodynamic have been calculated and discussed. The adsorbed film formed on the metal surface was characterized by SEM and EDX.     

(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.