Some applications of subordination theorems associated with fractional qq-calculus operator

summary:Using the operator $\frak {D}_{q,\varrho }^{m}(\lambda ,l)$, we introduce the subclasses $\frak {Y}^{*m}_{q,\varrho }(l,\lambda ,\gamma )$ and $\frak {K}^{*m}_{q,\varrho }(l,\lambda ,\gamma )$ of normalized analytic functions. Among the results investigated for each of these function classes, we derive some subordination results involving the Hadamard product of the associated functions. The interesting consequences of some of these subordination results are also discussed. Also, we derive integral means results for these classes

O(12) limit and complete classification of symmetry schemes in proton-neutron interacting boson model

It is shown that the proton-neutron interacting boson model (pnIBM) admits new symmetry limits with O(12) algebra which break F-spin but preserves the quantum number M_F. The generators of O(12) are derived and the quantum number `v' of O(12) for a given boson number N is determined by identifying the corresponding quasi-spin algebra. The O(12) algebra generates two symmetry schemes and for both of them, complete classification of the basis states and typical spectra are given. With the O(12) algebra identified, complete classification of pnIBM symmetry limits with good M_F is established.Comment: 22 pages, 1 figur

Bivariate tt-distribution for transition matrix elements in Breit-Wigner to Gaussian domains of interacting particle systems

Interacting many-particle systems with a mean-field one body part plus a chaos generating random two-body interaction having strength $\lambda$, exhibit Poisson to GOE and Breit-Wigner (BW) to Gaussian transitions in level fluctuations and strength functions with transition points marked by $\lambda=\lambda_c$ and $\lambda=\lambda_F$, respectively; $\lambda_F >> \lambda_c$. For these systems theory for matrix elements of one-body transition operators is available, as valid in the Gaussian domain, with $\lambda > \lambda_F$, in terms of orbitals occupation numbers, level densities and an integral involving a bivariate Gaussian in the initial and final energies. Here we show that, using bivariate $t$-distribution, the theory extends below from the Gaussian regime to the BW regime up to $\lambda=\lambda_c$. This is well tested in numerical calculations for six spinless fermions in twelve single particle states.Comment: 7 pages, 2 figure

Microscopic Nuclear Level Densities from Fe to Ge by the Shell Model Monte Carlo Method

We calculate microscopically total and parity-projected level densities for $\beta$-stable even-even nuclei between Fe and Ge, using the shell model Monte Carlo methods in the complete $(pf+0g_{9/2})$-shell. A single-particle level density parameter $a$ and backshift parameter $\Delta$ are extracted by fitting the calculated densities to a backshifted Bethe formula, and their systematics are studied across the region. Shell effects are observed in $\Delta$ for nuclei with Z=28 or N=28 and in the behavior of $A/a$ as a function of the number of neutrons. We find a significant parity-dependence of the level densities for nuclei with A \alt 60, which diminishes as $A$ increases.Comment: to be published in Phys. Lett. B; includes 5 eps figure

Some application of a generalized distribution series on certain class of analytic functions

In this search, we investigate a relation between generalized distribution series and particular subclasses of univalent functions. Further, we obtain the sufficient conditions for generalized distribution series ψ(τ,z) and ℳ*ψ(η,τ,z) belongs to ℒθ(A,B;γ). Also, we investigate some mapping properties for this class. Finally, we obtain some corollaries and consequences of the main results

Strength functions, entropies and duality in weakly to strongly interacting fermionic systems

We revisit statistical wavefunction properties of finite systems of interacting fermions in the light of strength functions and their participation ratio and information entropy. For weakly interacting fermions in a mean-field with random two-body interactions of increasing strength $\lambda$, the strength functions $F_k(E)$ are well known to change, in the regime where level fluctuations follow Wigner's surmise, from Breit-Wigner to Gaussian form. We propose an ansatz for the function describing this transition which we use to investigate the participation ratio $\xi_2$ and the information entropy $S^{\rm info}$ during this crossover, thereby extending the known behavior valid in the Gaussian domain into much of the Breit-Wigner domain. Our method also allows us to derive the scaling law for the duality point $\lambda = \lambda_d$, where $F_k(E)$, $\xi_2$ and $S^{\rm info}$ in both the weak ($\lambda=0$) and strong mixing ($\lambda = \infty$) basis coincide as $\lambda_d \sim 1/\sqrt{m}$, where $m$ is the number of fermions. As an application, the ansatz function for strength functions is used in describing the Breit-Wigner to Gaussian transition seen in neutral atoms CeI to SmI with valence electrons changing from 4 to 8