This paper is devoted to clarify the algorithmic definition of the weak stability boundary in the framework of the planar Restricted Three Body Problem. The role of the invariant hyperbolic manifolds associated to the central manifolds of the libration points L1 and L2, as boundary of the weak stability region, is shown.

We explain how any cofibrantly generated weak factorisation system on a category may be equipped with a universally and canonically determined choice of cofibrant replacement. We then apply this to the theory of weak ω-categories, showing that the universal and canonical cofibrant replacement of the operad for strict ω-categories is precisely Leinster’s operad for weak ω-categories.

Double no-touch options, contracts which pay out a fixed amount provided an underlying asset remains within a given interval, are commonly traded, particularly in FX markets. In this work, we establish model-free bounds on the price of these options based on the prices of more liquidly traded options (call and digital call options). Key steps are the construction of superand sub-hedging strateg...

In this paper we give a proof of the strong Goldbach conjecture by studying limit status of original continuous Godbach natural number sequence {3, 4, ..., GNL} generated by original continuous odd prime number sequence {3, 5, ..., p} when p → ∞, that is, GNL = p when p → ∞. It implies the weak Goldbach conjecture. If a prime p is defined as Goldbach prime when GNL = p then Goldbach prime is th...

The main object of this paper is to introduce a new concept of weak statistically Cauchy sequence in a normed space. It is shown that in a reflexive space, weak statistically Cauchy sequences are the same as weakly statistically convergent sequences. Finally, weak statistical convergence has been discussed in l p spaces. under the Creative Commons Attribution License, which permits unrestricted...

The slice condition and the more general weak slice conditions are geometric conditions on Euclidean space domains which have evolved over the last several years as a tool in various areas of analysis. This paper explores some of the finer distinctive properties of the various weak slice conditions.

A hierarchy of weak variants of Martin’s Axiom is extended and shown to be strict.