Analytical solutions for a doubly driven two-level atom

We have deduced analytical solutions of an energy level diagram of the doubly driven/dressed atom for a two-level atom exposed to a strong near-resonant bichromatic laser field in a special case, i.e., the bichromatic field with frequencies ω1 and ω2, and Rabi frequencies ?1 and ?2, in which the first coupling field of ?1 acts on the bare atomic levels, and then the resulting singly dressed states are driven by the second coupling field of ?2, thus resulting in the doubly dressed atom.We have measured the probe absorption spectra of a doubly driven two-level atom. The system consists of 52S1/2, F= 2 and 5~2P_(3/2), F'= 3 states of ~(87)Rb atoms in a magneto-optical trap(MOT) as well as the cooling/trapping beams and an additional coupling field. As for the spectroscopic properties of the doubly driven two-level atom, theoretical analytical solutions are in general agreement with the experimental spectrum as a whole.     

New behaviors of α-particle preformation factors near doubly magic 100Sn

The \begin{document}$ \alpha $\end{document}-particle preformation factors of nuclei above doubly magic nuclei \begin{document}$ ^{100} $\end{document}Sn and \begin{document}$ ^{208} $\end{document}Pb are investigated within the generalized liquid drop model. The results show that the \begin{document}$ \alpha $\end{document}-particle preformation factors of nuclei near self-conjugate doubly magic \begin{document}$ ^{100} $\end{document}Sn are significantly larger than those of analogous nuclei just above \begin{document}$ ^{208} $\end{document}Pb, and they will be enhanced as the nuclei move towards the \begin{document}$ N = Z $\end{document} line. The proton–neutron correlation energy \begin{document}$ E_{p-n} $\end{document} and two protons–two neutrons correlation energy \begin{document}$ E_{2p-2n} $\end{document} of nuclei near \begin{document}$ ^{100} $\end{document}Sn also exhibit a similar situation, indicating that the interactions between protons and neutrons occupying similar single-particle orbitals could enhance the \begin{document}$ \alpha $\end{document}-particle preformation factors and result in superallowed \begin{document}$ \alpha $\end{document} decay. This also provides evidence of the significant role of the proton–neutron interaction on \begin{document}$ \alpha $\end{document}-particle preformation. Also, the linear relationship between \begin{document}$ \alpha $\end{document}-particle preformation factors and the product of valence protons and valence neutrons for nuclei around \begin{document}$ ^{208} $\end{document}Pb is broken in the \begin{document}$ ^{100} $\end{document}Sn region because the \begin{document}$ \alpha $\end{document}-particle preformation factor is enhanced when a nucleus near \begin{document}$ ^{100} $\end{document}Sn moves towards the \begin{document}$ N = Z $\end{document} line. Furthermore, the calculated \begin{document}$ \alpha $\end{document} decay half-lives fit well with the experimental data, including the recent observed self-conjugate nuclei \begin{document}$ ^{104} $\end{document}Te and \begin{document}$ ^{108} $\end{document}Xe [Phys. Rev. Lett. 121, 182501 (2018)].     

Doubly Periodic Wave Solutions of Jaulent-Miodek Equations Using Variational Iteration Method Combined with Jacobian-function Method

One of the advantages of the variational iteration method is the free choice of initial guess. In this paper we use the basic idea of the Jacobian-function method to construct a generalized trial function with some unknown parameters. The Jaulent-Miodek equations are used to illustrate effectiveness and convenience of this method, some new explicit exact travelling wave solutions have been obtained, which include bell-type soliton solution, kink-type soliton solutions, solitary wave solutions, and doubly periodic wave solutions.     

弦图子类的全控制函数

本文首先证明了k-全控制问题和符号全控制问题在双弦图上均为NP-完全的.其次,在强消去序已给定的强弦图上,给出了求解符号全控制、负全控制、k-全控制和k-全控制问题的统一的O(m+n)时间算法.     

There exists no (15,5,4) RBIBD

An (n, M, d)_q code is a q‐ary code of length n, cardinality M, and minimum distance d. We show that there exists no (15,5,4) resolvable balanced incomplete block design (RBIBD) by showing that there exists no (equidistant) (14,15,10)₃ code. This is accomplished by an exhaustive computer search using an orderly algorithm combined with a maximum clique algorithm. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 227–232, 2001     

Geometric quantities of lower doubly excited bound states of helium

Expectation values of single electron and interelectronic geometric quantities such as $\langle r\rangle$, $\langle r_{12}\rangle$, $\langle r_<\rangle$, $\langle r_>\rangle$, $\langle \cos\theta_{12}\rangle$ and $\langle \theta_{12}\rangle$ are calculated for doubly excited $2{\rm p}n{\rm p}\,{}^1P^{\,\rm e}\,(3\leq n\leq5),\, 2{\rm p}n{\rm p}\,{}^3\!P^{\,\rm e}\,(2\leq n\leq5)$ and $2{\rm p}n{\rm d}\,{}^{1,3}D^{\,\rm o}\,(3\leq n\leq5)$ states of helium using Hylleraas-$B$-spline basis set. The energy levels converge to at least 10 significant digits in our calculations. The extrapolated values of geometric quantities except for $\langle \theta_{12}\rangle$ reach 10 significant digits as well; $\langle \theta_{12}\rangle$ reaches at least 7 significant digits using a multipole expansion approach. Our results provide a precise reference for future research.     

Jordan Algebras and Dual Affine Connections on Symmetric Cones

We study dually flat structures on symmetric cones associated with Jordan algebras. We give an interpretation of connections, a geometrical concept, in terms of Jordan algebras and show a relation between doubly autoparallel submanifolds and Jordan subalgebras.     

EXISTENCE OF THREE-FOLD BIBDs WITH BLOCK-SIZE SEVEN

Hanani discussed the existence of balanced incomplete block designs B[7,3;ν] leaving seven open cases of v , five of which were solved by Greig and Yin and Wu. In this paper we shall deal with the last two cases and then complete the existence question.     

α‐Resolvable group divisible designs with block size three

A group divisible design GD(k,λ,t;tu) is α‐resolvable if its blocks can be partitioned into classes such that each point of the design occurs in precisely α blocks in each class. The necessary conditions for the existence of such a design are λt(u ? 1) = r(k ? 1), bk = rtu, k|αtu and α|r. It is shown in this paper that these conditions are also sufficient when k = 3, with some definite exceptions. © 2004 Wiley Periodicals, Inc.     

Exponentially Many Hadamard Designs

If there is a Hadamard design of order n, then there are at least 2^{8n−16−9log n} non-isomorphic Hadamard designs of order 2n. Mathematics Subject Classificaion 2000: 05B05