Pomeranchuk-like theorems on integrated cross sections and average spin polarization parameters

Pomeranchuk-like theorems on the integrated cross sections and on the average spin polarization parameters of different meson-baryon reactions are obtained by using the improvements of the usual triangular isospin inequalities on integrated cross sections.     

A linear filtering problem in complete correlated actions

In the last paper, the geometry of the Sz.-Nagy-Foia model for contraction operators on Hilbert spaces was used to advantage in several problems of multivariate analysis. The lifting of intertwining operators, one of the basic results from the Sz.-Nagy-Foia theory, is now recognized as the most adequate operatorial form of the deep classical results of the extrapolation theory. The labeling of the exact intertwining dilations given by [1]Acta Sci. Math. (Szeged) 40 9–32] and the recursive methods used there open a broad perspective for using the Sz.-Nagy-Foia model in multivariate filtering theory. In this paper, using the notion of correlated action (see [5 and 6] Rev. Roumaine Math. Pures Appl. 23, No. 9 1393–1423]) as a time domain, a linear filtering problem is formulated and its solution in terms of the coefficients of the analytic function which factorizes the spectral distribution of the known data and the coefficients of an analytic function which describes the cross correlations is given. In some special cases it is shown that the filter coefficients can be determined using recursive methods from the intertwining dilation theory, of the autocorrelation function of the known data and an intertwining operator, interpreted as the initial estimator given by the prior statistics.     

Approximating the Partition Function of Morse Oscillators

A simple method is proposed leading to reasonable approximations of the partition function of Morse oscillators in terms of elementary functions.     

Making decisions in the absence of clear facts

Bennis and O’Toole [Bennis, W.G., O’Toole, J., 2005. How business schools lost their way. Harvard Business Review 83, 96–104] have recently argued that decision makers need guidance in ‘making decisions in the absence of clear facts’. As such, decision makers must be able to resourcefully use whatever limited information is available and advantageously portray its implications. Based on recently published theory which directly addresses this requirement, this paper demonstrates, through a practical example, how decision makers can make systemic decisions in situations characterized by extremely limited information and, furthermore, what form such decisions can take. Evidence is provided, therefore, that operational research can effectively address what appears to be a gap in management training.     

Novel ring-cleaving reaction of 4-nitro-1,1,2,2,9,9,10,10-octafluoro[2.2]paracyclophane with nucleophiles

When 4-nitro-AF4 is treated with nucleophiles such as alkoxides and cyanide, a novel ring opening, cyclophane destroying reaction is observed whereby, via an S_NAr mechanism, the nucleophile attacks the bridgehead aryl carbon vicinal to the nitro group with subsequent aryl-CF₂ bond cleavage.     

Temperature induced rotation in a [4.4]cyclophane

The synthesis, the X-ray, NMR and molecular modeling structure determination of a new orthopara[4.4]cyclophane are reported. The similarity of the π(CO)-π(Ar) driven conformational equilibrium of this compound to the work of an amusement ride machinery is also revealed.     

The next generation of C2-symmetric ligands: A di-N-heterocyclic carbene (NHC) ligand and the synthesis and X-ray characterization of mono- and dinuclear rhodium(I) and iridium(I) complexes

A new C₂-symmetric chelating di-N-heterocyclic carbene (NHC) ligand is reported. The stable free di-carbene (+/−)[DEAM-BY] (3) forms upon treating the imidazolium salt (+/−)[DEAM-BI][OTf]₂ (2) with potassium bis-trimethylsilylamide (where DEAM-BY = trans-9,10-dihydro-9,10-ethanoanthracene-11,12-bis(1-benzyl)imidaz-2-ylidene and DEAM-BI = trans-9,10-dihydro-9,10-ethanoanthracene-11,12-bis(1-benzyl)imidazolium). Metalation reactions of 2 with [Rh(COD)Cl]₂ and [Ir(COD)Cl]₂ are carried out under mild conditions to produce either mono- or bimetallic complexes. Each compound is characterized by NMR spectroscopy, combustion analysis, and single-crystal X-ray crystallography.     

Anharmonic stabilization of the high-pressure simple cubic phase of calcium

The phonon spectrum of the high-pressure simple cubic phase of calcium, in the harmonic approximation, shows imaginary branches that make it mechanically unstable. In this Letter, the phonon spectrum is recalculated by using density-functional theory ab initio methods fully including anharmonic effects up to fourth order at 50 GPa. Considering that the perturbation theory cannot be employed with imaginary harmonic frequencies, a variational procedure based on the Gibbs-Bogoliubov inequality is used to estimate the renormalized phonon frequencies. The results show that strong quantum anharmonic effects make the imaginary phonons become positive even at zero temperature so that the simple cubic phase becomes mechanically stable, as experiments suggest. Moreover, our calculations find a superconducting T(c) in agreement with experiments and predict an anomalous behavior of the specific heat.