The one-body density-matrix elements obtained from the USDA Hamiltonian are used to calculate the electronnucleus scattering form factors for the 25 Mg nucleus. The longitudinal form factor calculations produce good agreements for all states in the first sequence whereas the shell-model predictions show a variation in results for the excitation states in the second sequence. The wave functions of radial single-particle matrix elements have been calculated with the Woods-Saxon, harmonic-oscillator, and Skyrme (Sk42) potentials. The results of the inelastic transverse form factors are in good agreement with the experimental data when using the Sk42 potential whereas the elastic magnetic scattering results show a significant difference in values compared with the experimental data. However the overall shape and other features of the form factors are satisfactory when using the harmonic-oscillator potential. The effective g factors were used as adjustable parameters in the OXBASH code to describe the core-polarization effects in the transverse form factor calculations with the use of a harmonic-oscillator size parameter in the elastic magnetic scattering.

The electric and magnetic transitions in the [Formula: see text]Mg nucleus are studied based on the calculations of the longitudinal and the transverse electron scattering form factors. The universal sd-shell model Hamiltonian (USDA) is used for calculations. The wave functions of radial single-particle matrix elements are calculated using the Skyrme potential. For the longitudinal form factors, a good agreement is obtained between the calculations and the experimental data. For the transverse form factors, the effective [Formula: see text] factors are made as adjustable parameters in order to describe the experimental data.

This paper studies the nonterminal complexity of weakly conditional grammars, and it proves that every recursively enumerable language can be generated by a weak conditional grammar with no more than seven nonterminals. Moreover, it is shown that the number of nonterminals in weakly conditional grammars without erasing rules leads to an infinite hierarchy of families of languages generated by weakly conditional grammars.Energy levels and the reduced probability of E2-transitions for Ytterbium isotopes with proton number Z = 70 and neutron numbers between 100 and 106 have been calculated through phenomenological (P hM ) and interacting boson (IBM − 1) models. The predicted low-lying levels (energies, spins and parities) and the reduced probability for E2-transitions results are reasonably consistent with the available experimental data.The predicted low-lying levels (gr-, β1-and γ1-band) by produced in the P hM are in good agreement with the experimental data comparison with those by IBM − 1 for all nuclei of interest. In addition, the phenomenological model was successful in predicted the β2-, β3-, β4-, γ2-and 1 + -band while it was a failure with IBM − 1. Also, the 3 +band is predicted by the IBM − 1 model for 172 Y b and 174 Y b nuclei. All calculations are compared with the available experimental data.

Nuclear excited states with T > 0 in sd even-even N=Z  nuclei have been studied by using shell model. The calculations have employed the USDB Hamiltonian in order to predict the energy levels, the reduced electric quadrupole transition probabilities and reduced magnetic dipole transition probabilities. The study also include the average number of nucleons in each sd- active orbitals. The results compared with available experimental data.  The comparison showed a good agreement between theoretical and experimental energy sates for most of the states studied in this work. On the other hand there was a difference between theoretical and experimental values of transition probabilities, but it can be said that it remained within the acceptable range of the difference.

The negative-parity states of 24Mg nucleus are investigated within the shell model. We are based on the calculations of energy levels, total squared form factors, and transition probability using the p-sd-pf (PSDPF) Hamiltonian in a large model space (0 + 1) hW. The comparison between the experimental and theoretical states showed a good agreement within a truncated model space. The PSDPF-based calculations successfully reproduced the data on the total squared form factors and transition probabilities of the negative-parity states in 24Mg nucleus. These quantities depend on the one-body density matrix elements that are obtained from the PSDPF Hamiltonian. The wave functions of radial one-particle matrix elements calculated with the harmonic-oscillator potential are suitable to predict experimental data by changing the center-of-mass corrections.

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