Totally hereditarily normaloid operators and Weyl's theorem for an elementary operator

A Hilbert space operator T∈B(H) is hereditarily normaloid (notation: T∈HN) if every part of T is normaloid. An operator T∈HN is totally hereditarily normaloid (notation: T∈THN) if every invertible part of T is normaloid. We prove that THN-operators with Bishop's property (β), also THN-contractions with a compact defect operator such that and non-zero isolated eigenvalues of T are normal, are not supercyclic. Take A and B in THN and let dAB denote either of the elementary operators in B(B(H)): ΔAB and δAB, where ΔAB(X)=AXB−X and δAB(X)=AX−XB. We prove that if non-zero isolated eigenvalues of A and B are normal and , then dAB is an isoloid operator such that the quasi-nilpotent part H₀(dAB−λ) of dAB−λ equals ⁻¹(dAB−λ)(0) for every complex number λ which is isolated in σ(dAB). If, additionally, dAB has the single-valued extension property at all points not in the Weyl spectrum of dAB, then dAB, and the conjugate operator , satisfy Weyl's theorem.     

Dilation equations and Markov operators

Using the theory of Markov operators, we give a new proof of the known fact saying that for every positive integers N and k>1, and for every nonnegative reals c₀,…,cN satisfying the first sum rule the dilation equation

     

Nuclear matter test for a separable non-localN-N interaction

A nuclear matter test has been conducted on a separable non-localN-N interaction proposed by Sirohi and Srivastava. The potential had been constructed by fitting the phase-shifts. The results obtained compare with those obtained by Tabakin in each partial wave. The binding energy per particle and the symmetry energy coefficient obtained are 19.4 MeV and 66.5 MeV respectively atk _F=1.65 fm⁻¹, while the best estimated values for these quantities are 16 MeV and 30–35 MeV atk _F=1.5 fm⁻¹. Single particle potential generated out of this NLSI has in general the same shape as the one obtained through Tabakin potential. Finally as a test of non-locality the integrated photoabsorption cross-section parameterh has been calculated and the value of 1.03 agrees with other reported values.     

Method for construction of operators in Fock space

It is shown, by providing a general method for the construction that any Fock space linear operator defined on the dense linear manifold spanned by the particle number representation basis can be represented in terms of the annihilation and creation operators. The normal form of the representation is unique.     

Chiral SU(4) × SU(4) breaking: masses and decay constants of charmed hadrons

The (4, 4*) ⊕ (4*, 4) model of broken chiral SU (4) × SU (4) symmetry has been used to calculate the third-order coupling constants involving charmed and ordinary pseudoscalar mesons. These coupling constants are exploited to derive some interesting new relations among the masses and decay constants of these charmed particles. Using the known masses and decay constants as inputs, we exploit these relations to predict:F _D = −1·41F _π ,F _F = −1·13F _π ,F _D/F_F = 1·25,m(D _s) = 1·43 GeV,m(F _s) = 1·39 GeV andm(K _s) = 1·02 GeV.     

The ground state for sticky disks

It is proven that the ground state of the two-dimensional sticky potential is the triangular lattice.Research supported in part by NSF grant MCS 78-01520-A01.     

Covalence reduction factors of four-coordinated pseudo-tetrahedral paramagnetic compounds inD 2d symmetry

Theoretical expressions for the covalence reduction factors of orbital angular momentum and spin-orbit coupling in pseudo-tetrahedral four-coordinated paramagnetic complexes withD _2d symmetry, denoted ask's andR's respectively, have been derived. p ]The mixing coefficients in the antibonding MO's for the CuCl ₄ ^2- ion in three complexes are estimated using suitable approximations. It is shown thatk's must be less thanR's in Tinkham's approximation. Certain misconceptions existing in the literature regarding the value of the integral 〈p _u |???u|s〉 have been clarified.     

Absorption and laser excited fluorescence of Ho3+:LaF3

Pramana - The absorption and fluorescence spectra of Ho3+:LaF3, in the wavelength region from 4000 Å to 7500 Å have been reinvestigated incorporating polarization features, for the first...