On Dual Gabor Frame Pairs Generated by Polynomials

We provide explicit constructions of particularly convenient dual pairs of Gabor frames. We prove that arbitrary polynomials restricted to sufficiently large intervals will generate Gabor frames, at least for small modulation parameters. Unfortunately, no similar function can generate a dual Gabor frame, but we prove that almost any such frame has a dual generated by a B-spline. Finally, for frames generated by any compactly supported function φ whose integer-translates form a partition of unity, e.g., a B-spline, we construct a class of dual frame generators, formed by linear combinations of translates of φ. This allows us to chose a dual generator with special properties, for example, the one with shortest support, or a symmetric one in case the frame itself is generated by a symmetric function. One of these dual generators has the property of being constant on the support of the frame generator.     

Optimal decision under ambiguity for diffusion processes

In this paper we consider stochastic optimization problems for an ambiguity averse decision maker who is uncertain about the parameters of the underlying process. In a first part we consider problems of optimal stopping under drift ambiguity for one-dimensional diffusion processes. Analogously to the case of ordinary optimal stopping problems for one-dimensional Brownian motions we reduce the problem to the geometric problem of finding the smallest majorant of the reward function in a two-parameter function space. In a second part we solve optimal stopping problems when the underlying process may crash down. These problems are reduced to one optimal stopping problem and one Dynkin game. Examples are discussed.     

Optimal stopping of strong Markov processes

We characterize the value function and the optimal stopping time for a large class of optimal stopping problems where the underlying process to be stopped is a fairly general Markov process. The main result is inspired by recent findings for Lévy processes obtained essentially via the Wiener–Hopf factorization. The main ingredient in our approach is the representation of the β$\beta$-excessive functions as expected suprema. A variety of examples is given.     

No Arbitrage and the Growth Optimal Portfolio

Abstract

Recently, several papers have expressed an interest in applying the Growth Optimal Portfolio (GOP) for pricing derivatives. We show that the existence of a GOP is equivalent to the existence of a strictly positive martingale density. Our approach circumvents two assumptions usually set forth in the literature: 1) infinite expected growth rates are permitted and 2) the market does not need to admit an equivalent martingale measure. In particular, our approach shows that models featuring credit constrained arbitrage may still allow a GOP to exist because this type of arbitrage can be removed by a change of numéraire. However, if the GOP exists the market admits an equivalent martingale measure under some numéraire and hence derivatives can be priced. The structure of martingale densities is used to provide a new characterization of the GOP which emphasizes the relation to other methods of pricing in incomplete markets. The case where GOP denominated asset prices are strict supermartingales is analyzed in the case of pure jump driven uncertainty.     

Atomic scale Kelvin probe force microscopy studies of the surface potential variations on the TiO2(110) surface

From an interplay of simultaneous Kelvin probe force microscopy and noncontact atomic force microscopy we study atomic-scale variations in the electronic surface potential on TiO(2)(110). Both imaging channels reveal an atomic contrast reflected by the geometry and charged state of the alternating rows of Ti and O surface atoms. From a thorough cross-section analysis we add significant trust to the concept of a local contact potential difference, and determine from this the chemical identity of individual surface species and their role in setting up the local surface potential.     

Drug-loaded nano/microbubbles for combining ultrasonography and targeted chemotherapy

A new class of multifunctional nanoparticles that combine properties of polymeric drug carriers, ultrasound imaging contrast agents, and enhancers of ultrasound-mediated drug delivery has been developed. At room temperature, the developed systems comprise perfluorocarbon nanodroplets stabilized by the walls made of biodegradable block copolymers. Upon heating to physiological temperatures, the nanodroplets convert into nano/microbubbles. The phase state of the systems and bubble size may be controlled by the copolymer/perfluorocarbon volume ratio. Upon intravenous injections, a long-lasting, strong and selective ultrasound contrast is observed in the tumor volume indicating nanobubble extravasation through the defective tumor microvasculature, suggesting their coalescence into larger, highly echogenic microbubbles in the tumor tissue. Under the action of tumor-directed ultrasound, microbubbles cavitate and collapse resulting in a release of the encapsulated drug and dramatically enhanced intracellular drug uptake by the tumor cells. This effect is tumor-selective; no accumulation of echogenic microbubbles is observed in other organs. Effective chemotherapy of the MDA MB231 breast cancer tumors has been achieved using this technique.     

Characterizations of modalities and lex modalities

A reflective subuniverse in homotopy type theory is an internal version of the notion of a localization in topology or in the theory of ∞-categories. Working in homotopy type theory, we give new characterizations of the following conditions on a reflective subuniverse L: (1) the associated subuniverse $L^{\prime }$ of L-separated types is a modality; (2) L is a modality; (3) L is a lex modality; and (4) L is a cotopological modality. In each case, we give several necessary and sufficient conditions. Our characterizations involve various families of maps associated to L, such as the L-étale maps, the L-equivalences, the L-local maps, the L-connected maps, the unit maps ${\eta }_X$, and their left and/or right orthogonal complements. More generally, our main theorem gives an overview of how all of these classes related to each other. We also give examples that show that all of the inclusions we describe between these classes of maps can be strict.     

The retro Grignard addition reaction revisited: the reversible addition of benzyl reagents to ketones

The Grignard addition reaction is known to be a reversible process with allylic reagents, but so far the reversibility has not been demonstrated with other alkylmagnesium halides. By using crossover experiments it has been established that the benzyl addition reaction is also a reversible transformation. The retro benzyl reaction was shown by the addition of benzylmagnesium chloride to di-tert-butyl ketone followed by exchange of both the benzyl and the ketone moiety with another substrate. Similar experiments were performed with phenylmagnesium bromide and tert-butylmagnesium chloride, but in these two cases the Grignard addition reaction did not show any sign of a reverse transformation.     

Inexpensive and rapid hydrogenation catalyst from CuSO4/CoCl2 — Chemoselective reduction of alkenes and alkynes in the presence of benzyl protecting groups

The simple reduction of a number of alkenes and alkynes was performed with a typical reaction time of 20?min using a copper-cobalt catalytic system. The reduction did not cleave benzyl protecting groups which are usually vulnerable to catalytic hydrogenation reactions. The catalyst can be prepared in situ by reduction of the inexpensive precursor salts CuSO₄ and CoCl₂ with NaBH₄. Sodium borohydride was also used as an easily handled hydrogen source for the catalytic reductions. No pressure, heating or inert atmosphere is required and purification/catalyst removal is achieved using extraction procedures, making this approach simple and efficient.