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In [Countable thin Π10 classes, Ann. Pure Appl. Logic59 (1993) 79–139], Cenzer, Downey, Jockusch and Shore proved the density of degrees (not necessarily c.e.) containing members of countable thin Π10 classes. In the same paper, Cenzer et al. also proved the existence of degrees containing no members of thin Π10 classes. We will prove in this paper that the c.e. degrees containing no members of thin Π10 classes are dense in the c.e. degrees. We will also prove that the c.e. degrees containing members of thin Π10 classes are dense in the c.e. degrees, improving the result of Cenzer et al. mentioned above. Thus, we obtain a new natural subclass of c.e. degrees which are both dense and co-dense in the c.e. degrees, while the other such class is the class of branching c.e. degrees (See [P. Fejer, The density of the nonbranching degrees, Ann. Pure Appl. Logic24 (1983) 113–130] for nonbranching degrees and [T. A. Slaman, The density of infima in the recursively enumerable degrees, Ann. Pure Appl. Logic52 (1991) 155–179] for branching degrees). [ABSTRACT FROM AUTHOR]

A correction is presented to the article "on the complexity of the successivity relation in computable linear orderings" that appeared in a previous issue.

Research in network controllability has mostly been focused on the effects of the network structure on its controllability, and some methods have been proposed to optimize the network controllability. However, they are all based on global structure information of networks. We propose two different types of methods to optimize controllability of a directed network by local structure information. Extensive numerical simulation on many modeled networks demonstrates that this method is effective. Since the whole topologies of many real networks are not visible and we only get some local structure information, this strategy is potentially more practical. [ABSTRACT FROM AUTHOR]

The optical properties of two series of azobenzene derivatives were modulated by backbone modifications with the density functional theory (DFT) calculations. Compared to the short-chain molecule, the chromophore with an elongated π-bridge exhibits a greater extent of charge transfer during one-photon excitation and hence possesses a larger molecular first hyperpolarizability (β0). Meanwhile, an evident red-shift in the maximum absorption was observed after extension of the π-conjugated backbone. The tendency of the static β0 value derived from the two-state model is consistent with the result of the calculation at M06-2X/6-311++G(d,p) level by means of analytical derivative method. The dynamic perturbations were revealed to cause the obvious enhancement of the first hyperpolarizability. The more closer the foundational wavelength to two times the value of the maximum absorption in one-photon transition, the larger βRHS value is observed for the chromophore. The nonlinear optical (NLO) properties augment with the introduction of the THF solvents by comparing the gas-phase values. With increasing the length of conjugated bridge, the dynamic βRHS value increases more rapidly in THF solution than in vacuum. In comparison with the short-chain molecule, the chromophore with an elongated 휋-bridge possesses a larger molecular first hyperpolarizability, accompanied by an evident red-shift in the maximum absorption. The dynamic perturbations were revealed to cause the obvious enhancement of the hyperpolarizability for various chromophores. Both the maximum absorption wavelength and the first hyperpolarizability augment by moving the molecules from the vacuum to THF solution. [ABSTRACT FROM AUTHOR]

In this paper, we solve a long-standing open question (see, e.g. Downey [6, Sec. 7] and Downey and Moses [11]), about the spectrum of the successivity relation on a computable linear ordering. We show that if a computable linear ordering $\mathcal{L}$ has infinitely many successivities, then the spectrum of the successivity relation is closed upwards in the computably enumerable Turing degrees. To do this, we use a new method of constructing $\Delta^0_3$-isomorphisms, which has already found other applications such as Downey, Kastermans and Lempp [9] and is of independent interest. It would seem to promise many further applications. [ABSTRACT FROM AUTHOR]