In this paper, we derive eight basic identities of symmetry in three variables related to q-Euler polynomials and the q -analogue of alternating power sums. These and most of their corollaries are new, since there hav...In this paper, we derive eight basic identities of symmetry in three variables related to q-Euler polynomials and the q -analogue of alternating power sums. These and most of their corollaries are new, since there have been results only about identities of symmetry in two variables. These abundance of symmetries shed new light even on the existing identities so as to yield some further interesting ones. The derivations of identities are based on the p-adic integral expression of the generating function for the q -Euler polynomials and the quotient of integrals that can be expressed as the exponential generating function for the q -analogue of alternating power sums.展开更多
A reliable phenomenological analysis of superdeformed(SD)bands shows that the so-called 'identical' SD bands in general may have different bandhead moments of inertia (δJ_o/J_o≥10^(-2)). Because the dynamic ...A reliable phenomenological analysis of superdeformed(SD)bands shows that the so-called 'identical' SD bands in general may have different bandhead moments of inertia (δJ_o/J_o≥10^(-2)). Because the dynamic moment of inertia J varies with ω much faster than the kinematic moment of inertia J, and the ω variation of moments of inertia may be quite different for various SD bands, under certain conditions a near equality of J (hence E_γ) of two 'identical' SD bands may occur in certain frequency range (|δE_γ/E_γ|=|δJ/J|～10^(-3)), and the angular momentum alignments may appear to be approximately quantized. But the situation turns out to be different in other frequency regions. The present phenomenological analysis seems to be consistent with the configuration assignments made by the available microscopic theory in the framework of strong-coupling model. No pseudospin symmetry is involved in the present analysis.展开更多
文摘In this paper, we derive eight basic identities of symmetry in three variables related to q-Euler polynomials and the q -analogue of alternating power sums. These and most of their corollaries are new, since there have been results only about identities of symmetry in two variables. These abundance of symmetries shed new light even on the existing identities so as to yield some further interesting ones. The derivations of identities are based on the p-adic integral expression of the generating function for the q -Euler polynomials and the quotient of integrals that can be expressed as the exponential generating function for the q -analogue of alternating power sums.
文摘A reliable phenomenological analysis of superdeformed(SD)bands shows that the so-called 'identical' SD bands in general may have different bandhead moments of inertia (δJ_o/J_o≥10^(-2)). Because the dynamic moment of inertia J varies with ω much faster than the kinematic moment of inertia J, and the ω variation of moments of inertia may be quite different for various SD bands, under certain conditions a near equality of J (hence E_γ) of two 'identical' SD bands may occur in certain frequency range (|δE_γ/E_γ|=|δJ/J|～10^(-3)), and the angular momentum alignments may appear to be approximately quantized. But the situation turns out to be different in other frequency regions. The present phenomenological analysis seems to be consistent with the configuration assignments made by the available microscopic theory in the framework of strong-coupling model. No pseudospin symmetry is involved in the present analysis.
