The α-decay half-lives of recently synthesized superheavy nuclei (SHN) are investigated by employing a unified fission model (UFM) and Royer’s analytical formula (2000 J. Phys. G: Nucl. Part. Phys. 26 1149). The good agreement with the experimental data indicates the UFM and the analytical formula are useful tools to investigate these α-decays. A modified formula is proposed for determining the spontaneous fission half-lives based on Swiatecki’s formula, including the microscopic shell correction and isospin effect.The spontaneous fission half-lives for heavy and SHN in regions from Th to Fl are calculated systematically. Experimental data are well reproduced by the modified Swiatecki formula. The competition between α-decay and spontaneous fission is analyzed in detail and the decay modes are predicted for the unknown cases.

In the present paper, we establish necessary and sufficient conditions for the functions $x^\alpha\bigl\lvert\psi^{(i)}(x+\beta)\bigr\lvert$ and $\alpha\bigl\lvert\psi^{(i)}(x+\beta)\bigr\lvert-x\bigl\lvert\psi^{(i+1)}(x+\beta)\bigr\lvert$ respectively to be monotonic and completely monotonic on $(0,\infty)$, where $i\in\mathbb{N}$, $\alpha>0$ and $\beta\ge0$ are scalars, and $\psi^{(i)}(x)$ are polygamma functions.Comment: 14 page

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BiHom-Novikov agebra is a generalized Hom-Novikov algebra endowed with two commuting multiplicative linear maps. The main purpose of this paper is to show that two classes of BiHom-Novikov algebras can be constructed from BiHom-commutative algebras together with derivations and BiHom-Novikov algebras with Rota-Baxter operators, respectively. We show that quadratic BiHom-Novikov algebras are associative algebras and the sub-adjacent BiHom-Lie algebras of BiHom-Novikov algebras are 2-step nilpotent. Moreover, we develop the 1-parameter formal deformation theory of BiHom-Novikov algebras

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