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Let P(z) be a polynomial of degree n having no zeros in |z| < k where k ≥ 1. Then it is known that for every real or complex number α with |α| ≥ 1, max |z|=1 |DαP(z)| ≤ n (|α| + k/1 + k) max |z|=1 |P(z)|, where DαP(z) = nP(z) + (α - z)P' (z) denotes the polar derivative of the polynomial P(z) of degree n with respect to a point α ∈ ℂ. In this paper, by a simple method, a refinement of the above inequality and other related results are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some refinements of a well-known result of Eneström-Kakeya concerning the bounds for the moduli of the zeros of polynomials with complex coefficients which among other things are also improved upon some known results in this direction. [ABSTRACT FROM AUTHOR]

The electric quadrupole transition rates for the high-spin yrast states of l04Pd have been measured by using the Doppler-shift attenuation method. These values decrease with the increase of angular momentum, which can be associated with the phenomenon of antimagnetic rotation. In the present work, a numerical calculation based on the semiclassical particle plus rotor model for antimagnetic rotation has been employed, giving a good description of the experimental Routhian and the transition rates and providing conclusive evidence of antimagnetic rotation in a nucleus other than cadmium. [ABSTRACT FROM AUTHOR]

For the class of Lacunary polynomials P(z) = anzn + Σnυ=μ an-υ zn-υ, 1 ⩽ μ ⩽ n, of degree n having all their zeros in ∣z∣ ⩽ k where k ⩽ 1; Aziz and Shah [6] proved for each r > 0 n{2π∫0 ∣ P (eiθ) ∣r dθ}1/r ⩽ {2π∫0 ∣ 1 + kμ eiθ ∣r dθ}1/r max ∣ P' (z)∣./∣z∣=1 In this paper, we extend above inequality to the polar derivative thereby establish some refinements and generalizations of some known polynomial inequalities concerning the polar derivative of a polynomial with restricted zeros. [ABSTRACT FROM AUTHOR]

For polynomial P(z) of degree at most n which does not vanish in ∣z∣ < 1, it was recently formulated by Shah and Liman [19, Integral estimates for the family of B-operators, Operators and Matrices, 5(2011), 79 - 87] that for every R ≧ 1, p ≧ 1, ... where B is a Bn-operator with parameters λ0; λ1; λ2 in the sense of Rahman [13], σ(z) = Rz and Φ(λ0; λ1; λ2)= λ0; λ1n2/2+n3(n-1) Unfortunately the proof of this result is not correct. In this paper, we present certain more general sharp Lp-inequalities for Bn-operators which not only provide a correct proof of the above inequality as a special case but also extend them for 0 ≦ p < 1 as well. [ABSTRACT FROM AUTHOR]

Abstract: The negative-parity yrast band of 110Ag has been extended significantly and the lifetimes of the high spin levels of this band have been measured. The experimentally observed level scheme and measured electromagnetic transition rates have been compared with the theoretical predictions of a model with two quasiparticles coupled to a triaxially deformed core. This calculation successfully reproduces the energy spectra and electromagnetic transition rates beyond . These observations indicate that the principal axis of rotation is responsible for the generation of high angular momentum states along the yrast cascade in 110Ag. In all the other lighter isotopes, these states are generated through titled axis rotation. Thus, 110Ag is the first nucleus where the boundary between tilted and principal axis rotation could be established. [Copyright &y& Elsevier]

The basis space in the triaxial projected shell model (TPSM) approach is generalized for odd–odd nuclei to include two-neutron and two-proton configurations on the basic one-neutron coupled to one-proton quasiparticle state. The generalization allows to investigate odd–odd nuclei beyond the band crossing region and as a first application of this development, high-spin band structures recently observed in odd–odd 194 - 200 Tl isotopes are investigated. In some of these isotopes, the doublet band structures observed after the band crossing have been conjuctured to arise from the spontaneous breaking of the chiral symmetry. The driving configuration of the chiral symmetry in these odd–odd isotopes is one-proton and three-neutrons rather than the basic one-proton and one-neutron as already observed in many other nuclei. It is demonstrated using the TPSM approach that energy differences of the doublet bands in 194 Tl and 198 Tl are, indeed, small. However, the differences in the calculated transition probabilities are somewhat larger than what is expected in the chiral symmetry limit. Experimental data on the transition probabilities is needed to shed light on the chiral nature of the doublet bands. [ABSTRACT FROM AUTHOR]

In this paper, by using standard techniques we shall obtain a result that gives regions containing all the zeros of a polynomial with real coefficients. Our result not only generalizes several well-known results concerning the location of zeros of polynomials but also yields an answer to a question raised by Professor N. K. Govil. We also obtain a similar result for analytic functions. In addition to this, we show by examples that our result gives better information about the bounds of zeros of polynomials than some known results. [ABSTRACT FROM AUTHOR]

The positive-parity band of 106Ag has been extended up to I = 25 ħ and the lifetimes of the high spin levels of this band have been measured. The deduced transition rates decrease with increasing spin until I = 21 ħ. Beyond this spin, the observed transition rates are substantially small and remain nearly constant. This is a novel observation for a shears band. The observed features have been described within the framework of the shears mechanism with a principle axis cranking calculation. [ABSTRACT FROM AUTHOR]

The negative parity non-yrast band of 106Ag has been studied to investigate the falling trend in magnetic dipole transition rates. In this context, the level lifetimes of the excited levels of this band have been measured using the Doppler shift attenuation method. The comparison of the experimental Routhian and the transition rates with the numerical results of the shears mechanism with the principal axis cranking calculation indicates that this band is generated due to the shears mechanism involving the three proton hole configuration. [ABSTRACT FROM AUTHOR]

A positive parity sequence of Δ I = 2 γ transitions has been identified above I π = 9 / 2 + state (E x = 2019 keV) in 115Sb through in-beam γ ray spectroscopic technique. Rotational features of this sequence are found similar to a low- K decoupled band. Observation of this newly identified low- K decoupled band, along with the earlier reported strongly coupled high- K band in this nucleus, provides the first experimental evidence for prolate-oblate shape coexistence associated with g 9 / 2 proton-hole configuration around Z = 50 shell closure. Experimental results are reproduced reasonably well in the frameworks of the projected shell model and the total Routhian surface calculations. [ABSTRACT FROM AUTHOR]

A theory for a system clustering under gravity is developed for the clustering parameter b(n, T), in terms of a partial differential equation using thermodynamic technique. Various solutions of the differential equation relate b(n, T) with density n and temperature T of the gravitating system. The physical validity of various solutions of b(n, T) on the basis of certain boundary conditions and probability density distribution function is discussed. Results indicate that the clustering parameter depends on the specific combination nT-3. The theory also provides a new insight into gravitational clustering. [ABSTRACT FROM AUTHOR]