APPROXIMATION PROPERTIES OF rth ORDER GENERALIZED BERNSTEIN POLYNOMIALS BASED ON q-CALCULUS

In this paper we introduce a generalization of Bernstein polynomials based on q calculus. With the help of Bohman-Korovkin type theorem, we obtain A-statistical approximation properties of these operators. Also, by using the Modulus of continuity and Lipschitz class, the statistical rate of convergence is established. We also gives the rate of A-statistical convergence by means of Peetre＇s type K-functional. At last, approximation properties of a rth order generalization of these operators is discussed.

Systematic study of rotational energy formulae for superdeformed bands in La and Ce isotopes

The experimental rotational spectra of superdeformed（SD） bands of 130La, 131Ce（1,2）, 132Ce（1,2,3） and133 Ce（1,2,3） in the A～130 mass region are systematically analyzed with the four parameter formula, power index formula, nuclear softness formula, and VMI model. It is observed that out of all the formulae, the four parameter formula suits best for the study of the 130La, 131Ce（1,2）, 132Ce（2,3） and 133Ce（1,2,3） SD bands. The four parameter formula works efficiently in determining the band head spin of the 130La, 131Ce（1,2） 132Ce（2,3） and 133Ce（1,2,3） SD bands. Good agreement is seen between the calculated and observed transition energies whenever the accurate spin is assigned. In 132Ce（1）, the power index formula is found to work better than the other three formulae. The dynamic moment of inertia is also calculated for all the formulae and its variation with the rotational frequency is investigated.

Band head spin determination of triaxial superdeformed bands in ^163,164,165Lu through two-parameter formulae

The two-parameter formulae, i.e. the nuclear softness formula and the power index formula, have been used to obtain the band head spin （I0） of the triaxial superdeformed （SD） bands in ^163Lu（1,2,3,4）, ^164Lu（1,2,3） and ^165Lu（1,2,3）, in the A - 160 mass region. The least squares fitting approach is used. The values of the root mean square （RMS） deviation among the computed and the measured experimental transition energies are obtained by calculating the model parameters. Whenever accurate spins are available, superb agreement is shown between the determined and the measured experimental transition energies. In comparison to the power index formula, the values of band head spin （I0） of the triaxial SD bands in ^163Lu（1,2,3,4）, ^164Lu（1,2,3） and ^165Lu（1,2,3） obtained by the nuclear softness formula are closer to the experimental data. The lowest RMS deviation is also achieved by the nuclear softness formula. Hence, the nuclear softness formula works well for obtaining the band head spin （I0） for the triaxial SD bands in ^163Lu（1,2,3,4）, ^164Lu（1,2,3） and ^165Lu（1,2,3） in the A-160 mass region. The dynamic moment of inertia against hω is also studied.

Systematic study of kinematic and dynamic moments of inertia of superdeformed bands with NpNn scheme

The systematics of kinematic moment of inertia J and dynamic moment of inertia J of superdeformed（SD） bands in A -130, 150, 190 mass regions have been studied. We have obtained the values of J^（1） and J^（2）for all the SD bands observed in the A-130, 150, 190 mass regions by using the experimental intraband E2 transition energies. The result of this work includes the variation of J with the product of valence proton and neutron numbers（NpNn）. The phenomenon of band mixing has been observed in the A -130, 150 mass regions and band crossing has been observed in the A-190 mass region. The systematics also includes the variation of J with the product of valence proton and neutron numbers（NpNn）. Evidence of staggering behaviour has been observed in all three A-130, 150 and 190 mass regions. We present for the first time the variation of J^（1）and J^（2）of SD bands in the A-130, 150, 190 mass regions with NpNn.

Band head spin assignment of superdeformed bands in Hg isotopes through power index formula

The power index formula has been used to obtain the band head spin(I0) of all the superdeformed(SD) bands in Hg isotopes. A least squares fitting approach is used. The root mean square deviations between the determined and the observed transition energies are calculated by extracting the model parameters using the power index formula. Whenever definite spins are available, the determined and the observed transition energies are in accordance with each other. The computed values of dynamic moment of inertia J~((2)) obtained by using the power index formula and its deviation with the rotational frequency is also studied. Excellent agreement is shown between the calculated and the experimental results for J~((2)) versus the rotational frequency. Hence, the power index formula works very well for all the SD bands in Hg isotopes expect for195Hg(2, 3, 4).