Heisenberg-Pauli-Weyl Uncertainty Principle for the Spherical Mean Operator

The Heisenberg-Pauli-Weyl inequality is established for the Fourier transform associated with the spherical mean operator. Also, a generalization of this inequality is proved. Next, a local uncertainty principle is checked.     

Electronic structure and UV–Vis spectra simulation of square planar Bis(1-(4-methylphenylazo)-2-naphtol)-Transition metal complexes [M(L)2]x (M = Ni,Pd, Pt,Cu, Ag,and x = − 1, 0, + 1): DFT and TD-DFT study

Structural Chemistry - DFT/B3LYP calculations with full geometry optimizations have been carried out on 1-phenylazo-2-naphthol and their metal complexes of formula M(MePhNap)2 (M?=?Ni,...     

Integral representation for a class of vector valued operators

Let be a compact space and let , be a (real, for simplicity) Banach space. We consider the space of all continuous -valued functions on , with the supremum norm .

We prove in this paper a Bochner integral representation theorem for bounded linear operators

which satisfy the following condition:

where is the conjugate space of . In the particular case where , this condition is obviously satisfied by every bounded linear operator

and the result reduces to the classical Riesz representation theorem.

If the dimension of is greater than , we show by a simple example that not every bounded linear admits an integral representation of the type above, proving that the situation is different from the one dimensional case.

Finally we compare our result to another representation theorem where the integration process is performed with respect to an operator valued measure.

     

Electrophilicity parameters for sigma-complexation by uncharged electron-deficient aromatic and heteroaromatic structures

Using appropriate sets of reference nucleophiles, the reactivity of neutral electrophiles of widely different reactivity and structure has been ranked on the comprehensive electrophilicity scale of Mayr (Acc. Chem. Res., 2003, 36, 66), holding promise of a general rationalization of sigma-complexation processes and related SNAr substitutions.     

Synthesis,characterization and X-ray crystal structure of novel nickel Schiff base complexes and investigation of their catalytic activity in the electrocatalytic reduction of alkyl and aryl halides

Novel potentially bidentate NO Schiff base ligands, HL ¹ and HL ² derived from condensation reaction of 2′-methoxyphenyl-2-ethylamine with salicylaldehyde (HL ¹ ) and with 2-hydroxy-4-methoxybenzaldehyde (HL ² ), and their nickel complexes were synthesized and characterized by usual spectroscopic techniques such as FT-IR, UV–Vis, ¹H NMR, ¹³C NMR and elemental analysis. It was revealed that the bidentate Schiff base ligands coordinate with Ni(II) ions yielding mononuclear complexes with 1:2 (metal/ligand) stoichiometry. This result has been determined by using X-ray crystallographic technique of HL ² and the nickel complex derived from HL ¹ (Ni(II)-2L ¹ ). So, the structural studies showed that the two Ni(II) complexes adopt a square-planar geometry around the central metal ion. Cyclic voltammetry studies were investigated in 0.1 M TBAP in DMF solution and indicate that the nickel complexes show one reduction wave related to Ni(II)/Ni(I) redox couple. The electrocatalytical properties of these complexes were also studied in the same electrolyte medium. Their electrocatalytic performances have been tested toward the electroreduction reaction of bromocyclopentane and iodobenzene, showing a promoted activity in the case of the Ni(II)-2L ² complex.     

Theoretical study of the C3S molecule

For the most stable linear isomer of C₃S in its X¹Σ⁺ state a six-dimensional potential energy surface (PES) has been calculated ab initio by coupled cluster – connected triples (CCSD(T)) method. The analytic form of the PES has been transformed in a quartic force field in dimensionless normal coordinates and employed in calculations of spectroscopic constants using second-order perturbation theory. The PES and the full kinetic energy operator in internal coordinates have been used to calculate variationally the anharmonic ro-vibrational energies for J=0 and J=1. The two experimental band origins of C₃S observed in the gas phase, ν₁ and ν₁+ν₅−ν₅, agree very well with the theoretical values. The anharmonic ro-vibrational levels, including the bending modes up to 2200 cm⁻¹, are reported. The singlet ground state PES has a saddle point at about 1.25 eV above the linear minimum and two other higher lying cyclic local minima. The only dipole- and spin-allowed electronic transition between 0 and 5 eV is calculated to be the ¹Π−X¹Σ⁺ transition with a vertical transition energy of 353.2 nm in good agreement with the matrix value of 378 nm. The dissociative paths C + C₂S, C₂ + CS and C₃ + S of low lying singlet and triplet states have been investigated. Electronic Supplementary Material: Supplementary material is available in the online version of this article at dx.doi.org/10.1007/s00214-005-0683-7 Dedicated to Professor H. Stoll.     

Influence of non-proportional loading on ratcheting responses and simulations by two recent cyclic plasticity models

Aubin and her coworkers conducted a unique set of experiments demonstrating the influence of loading non-proportionality on ratcheting responses of duplex stainless steel. In order to further explore their new observation, a set of experiments was conducted on stainless steel (SS) 304L under various biaxial stress-controlled non-proportional histories. This new set of data reiterated Aubin and her coworkers’ observation and illustrated many new responses critical to model development and validation. Two recent and different classes of cyclic plasticity models, the modified Chaboche model proposed by Bari and Hassan and the version of the multi-mechanism model proposed by Taleb and Cailletaud, are evaluated in terms of their simulations of the SS304L non-proportional ratcheting responses. A modeling scheme for non-proportional ratcheting responses using the kinematic hardening rule parameters in addition to the conventionally used isotropic hardening rule parameter (yield surface size change) in the modified Chaboche model is evaluated. Strengths and weaknesses of the models in simulating the non-proportional ratcheting responses are identified. Further improvements of these models needed for improving the non-proportional ratcheting simulations are suggested in the paper.     

Martin boundaries for discrete Markov chains

In this paper we give explicit constructions of the Martin boundary for some discrete Markov chains. This construction is extended to the product of discrete Markov.chains     

Synthesis, Characterization and Electrochemical Behavior of CoII, NiII and CdII Complexes with N2O2 Donor Ligands Derived from 4,4′-Diaminobiphenyl and?2-Hydroxybenzaldehyde or?2,4-Dihydroxybenzaldehyde

The condensation of 2-hydroxybenzaldehyde or 2,4-dihydroxybenzaldehyde with 4,4′-diaminobiphenyl in absolute EtOH in a molar ratio 2:1 gave, respectively, the Schiff base ligands H₂L1 or H₂L2. The bases served as tetradentate ligands to coordinate Co^II, Ni^II and Cd^II chlorides, leading to complexes where the metal:ligand ratio is 2:1. All of the compounds were characterized by elemental analysis, infrared, electronic and mass spectroscopy, ¹H-n.m.r. and d.s.c. The cyclic voltammograms of the ligands and their complexes in DMF are discussed.