Representing homology classes by locally flat 2-spheres

We prove an existence result for topologically locally flat embeddings of 2-spheres in simply connected 4-manifolds. This topological result is deduced from a splitting theorem for pointed Hermitian modules over a cyclic group ring. A stability result for such modules is also proved. This applies to the isotopy classification of locally flat embeddings.Partially supported by the NSF.     

Improved convergence in orbital localization methods

A new method for choosing the rotation angle in the usual indirect localization procedure consisting of the iterative use of 2 × 2 rotation matrices is suggested. Calculations reported here obtaining the localized orbitals of the water molecule show this new method to converge much more quickly and to a significantly better numerical value of the localization criterion than previous methods.     

New heuristics for total tardiness minimization in a flexible flowshop

This paper analyses the total tardiness minimization in a flowshop with multiple processors at each stage. While there is considerable research to minimize the makespan, very little work is reported on minimizing the total tardiness for this problem. This research focuses on heuristic methods that consider this environment as a series of parallel machine problems. New dispatching rules are introduced. One of the proposed rules is able to deal with jobs that will come afterwards and not only the available jobs at the decision time. Dispatching rules are also associated with classical (forward and backward) and new list scheduling algorithms. A special scheduling algorithm able to deal with idle times is proposed. Computational experiments in a set of 4,320 literature instances show that the developed heuristics are competitive and outperforms their classical counterparts.     

Implied Volatility of Leveraged ETF Options

Abstract

This paper studies the problem of understanding implied volatilities from options written on leveraged exchanged-traded funds (LETFs), with an emphasis on the relations between LETF options with different leverage ratios. We first examine from empirical data the implied volatility skews for LETF options based on the S&P 500. In order to enhance their comparison with non-leveraged ETFs, we introduce the concept of moneyness scaling and provide a new formula that links option implied volatilities between leveraged and unleveraged ETFs. Under a multiscale stochastic volatility framework, we apply asymptotic techniques to derive an approximation for both the LETF option price and implied volatility. The approximation formula reflects the role of the leverage ratio, and thus allows us to link implied volatilities of options on an ETF and its leveraged counterparts. We apply our result to quantify matches and mismatches in the level and slope of the implied volatility skews for various LETF options using data from the underlying ETF option prices. This reveals some apparent biases in the leverage implied by the market prices of different products, long and short with leverage ratios two times and three times.     

The convergence of chaotic integrals

We review the convergence of chaotic integrals computed by Monte Carlo simulation, the trace method, dynamical zeta function, and Fredholm determinant on a simple one-dimensional example: the parabola repeller. There is a dramatic difference in convergence between these approaches. The convergence of the Monte Carlo method follows an inverse power law, whereas the trace method and dynamical zeta function converge exponentially, and the Fredholm determinant converges faster than any exponential. (c) 1997 American Institute of Physics.     

Conway–Kochen and the Finite Precision Loophole

Recently Cator and Landsman made a comparison between Bell’s Theorem and Conway and Kochen’s Strong Free Will Theorem. Their overall conclusion was that the latter is stronger in that it uses fewer assumptions, but also that it has two shortcomings. Firstly, no experimental test of the Conway–Kochen Theorem has been performed thus far, and, secondly, because the Conway–Kochen Theorem is strongly connected to the Kochen–Specker Theorem it may be susceptible to the finite precision loophole of Meyer, Kent and Clifton. In this paper I show that the finite precision loophole does not apply to the Conway–Kochen Theorem.     

Some more examples of monotonically Lindelöf and not monotonically Lindelöf spaces

A space is monotonically Lindelöf (mL) if one can assign to every open cover U a countable open refinement r(U) (still covering the space) so that r(U) refines r(V) whenever U refines V. Some examples of mL and non-mL spaces are considered. In particular, it is shown that the product of a mL space and the convergent sequence need not be mL, that some L-spaces are mL, and that Cp(X) is mL only for countable X.     

Rigidity of certain finite group actions on the complex projective plane

Partially supported by NSERC grant A4000