The complex chaotic dynamics and multistability of financial system are some important problems in micro- and macroeconomic fields. In this paper, we study the influence of two-delay feedback on the nonlinear dynamics behavior of financial system, considering the linear stability of equilibrium point under the condition of single delay and two delays. The system undergoes Hopf bifurcation near the equilibrium point. The stability and bifurcation directions of Hopf bifurcation are studied by using the normal form method and central manifold theory. (...) The theoretical results are verified by numerical simulation. Furthermore, one feature of the proposed financial chaotic system is that its multistability depends extremely on the memristor initial condition and the system parameters. It is shown that the nonlinear dynamics of financial chaotic system can be significantly changed by changing the values of time delays. (shrink)

It is shown that $\operatorname{Con}(ZF)$ implies $\operatorname{Con}(ZFC$ + there exists a Dowker filter on ω2). The problem is also considered on higher cardinals.

According to Wittgenstein, philosophical puzzles are due to deep prejudices about language. In this collection of essays, in honour of Rush Rhees, philosophers investigate the hold such prejudices have on us in a number of closely related areas of philosophical enquiry.

In [Countable thin [Formula: see text] classes, Ann. Pure Appl. Logic 59 79–139], Cenzer, Downey, Jockusch and Shore proved the density of degrees containing members of countable thin [Formula: see text] classes. In the same paper, Cenzer et al. also proved the existence of degrees containing no members of thin [Formula: see text] classes. We will prove in this paper that the c.e. degrees containing no members of thin [Formula: see text] classes are dense in the c.e. degrees. We will (...) also prove that the c.e. degrees containing members of thin [Formula: see text] 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 113–130] for nonbranching degrees and [T. A. Slaman, The density of infima in the recursively enumerable degrees, Ann. Pure Appl. Logic 52 155–179] for branching degrees). (shrink)

Graphical AbstractGene editing with engineered nucleases introduce double-strand breaks that are repaired by error-prone nonhomologous end-joining (NHEJ). In article number 1900126, Sara G. Trimidal et al. propose that the length and type or resulting indels can now be controlled by editing with different engineered nucleases or by manipulating the expression of NHEJ genes.