An entropy-based uncertainty principle for a locally compact abelian group

We classify all functions on a locally compact, abelian group giving equality in an entropy inequality generalizing the Heisenberg Uncertainty Principle. In particular, for functions on a real line, we proof a conjecture of Hirschman published in 1957.     

Lévy processes and their subordination in matrix Lie groups

Lévy processes in matrix Lie groups are studied. Subordination (random time change) is used to show that quasi-invariance of the Brownian motion in a Lie group induces absolute continuity of the laws of the corresponding pure jump processes. These results are applied to several examples which are discussed in detail.     

Risk management of a bond portfolio using options

In this paper, we elaborate a formula for determining the optimal strike price for a bond put option, used to hedge a position in a bond. This strike price is optimal in the sense that it minimizes, for a given budget, either Value-at-Risk or Tail Value-at-Risk. Formulas are derived for both zero-coupon and coupon bonds, which can also be understood as a portfolio of bonds. These formulas are valid for any short rate model that implies an affine term structure model and in particular that implies a lognormal distribution of future zero-coupon bond prices. As an application, we focus on the Hull-White one-factor model, which is calibrated to a set of cap prices. We illustrate our procedure by hedging a Belgian government bond, and take into account the possibility of divergence between theoretical option prices and real option prices. This paper can be seen as an extension of the work of Ahn and co-workers [Ahn, D., Boudoukh, J., Richardson, M., Whitelaw, R., 1999. Optimal risk management using options. J. Financ. 54, 359-375], who consider the same problem for an investment in a share.     

A Fubini theorem

Let I₀ be the σ-ideal of subsets of a Polish group generated by Borel sets which have perfectly many pairwise disjoint translates. We prove that a Fubini-type theorem holds between I₀ and the σ-ideals of Haar measure zero sets and of meager sets. We use this result to give a simple proof of a generalization of a theorem of Balcerzak-Ros?anowski-Shelah stating that I₀ on N² strongly violates the countable chain condition.     

The structure of an Fe monolayer on the Ni (111) surface. A density-functional study using the generalized gradient approximation

Using a density-functional method that employs linear combinations of atomic orbitals as basis sets, nonlocal norm-conserving pseudopotentials and the generalized gradient approximation for exchange and correlation, we found that at 0 K the atoms of an Fe monolayer on the Ni (111) surface occupy hcp rather than fcc sites, in keeping with previous predictions made using the ab initio all-electron full-potential linearized augmented plane wave method with the local spin density approximation.     

The first <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript>-cohomology of some groups with one end

Let p be a real number greater than one. In this paper we study the vanishing and nonvanishing of the first L ^p -cohomology space of some groups that have one end. We also make a connection between the first L ^p -cohomolgy space and the Floyd boundary of the Cayley graph of a group. We apply the result about Floyd boundaries to show that there exists a real number p such that the first L ^p -cohomology space of a nonelementary hyperbolic group does not vanish. Received: 4 August 2006 Revised: 2 November 2006     

Synthesis and characterisation of bis(pentafluorophenyl)antimony(V) cations, [(C6F5)2SbL3]

Pentacoordinate complex cations of the general formula [(C₆F₅)₂SbL₃]³⁺ stabilized as solid salts in combination with tetraphenylborate (BPh₄), tetrafluorobroate (BF₄) anions, where L=DMSO, Ph₃AsO, PyO, DMF, α-, β- and γ-picoline have been isolated. The newly formed complexes were characterized by elemental analysis, molar conductance measurements, solid-state IR and and NMR. From these results, a five-fold coordination around antimony was required.     

Simultaneous determination of radionuclides separable into natural decay series by use of time-interval analysis

A delayed coincidence method, time-interval analysis (TIA), has been applied to successive 43/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">–43/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0"> decay events on the millisecond time-scale. Such decay events are part of the ²²⁰Rn43/xxlarge8594.gif" alt="rarr" align="BASELINE" BORDER="0">²¹⁶Po (T_1/2 145 ms) (Th-series) and ²¹⁹Rn43/xxlarge8594.gif" alt="rarr" align="BASELINE" BORDER="0">²¹⁵Po (T_1/2 1.78 ms) (Ac-series). By using TIA in addition to measurement of ²²⁶Ra (U-series) from 43/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">-spectrometry by liquid scintillation counting (LSC), two natural decay series could be identified and separated. The TIA detection efficiency was improved by using the pulse-shape discrimination technique (PSD) to reject 43/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-pulses, by solvent extraction of Ra combined with simple chemical separation, and by purging the scintillation solution with dry N₂ gas. The U- and Th-series together with the Ac-series were determined, respectively, from alpha spectra and TIA carried out immediately after Ra-extraction. Using the ²²¹Fr43/xxlarge8594.gif" alt="rarr" align="BASELINE" BORDER="0">²¹⁷At (T_1/2 32.3 ms) decay process as a tracer, overall yields were estimated from application of TIA to the ²²⁵Ra (Np-decay series) at the time of maximum growth. The present method has proven useful for simultaneous determination of three radioactive decay series in environmental samples.     

Wilson's functional equations on groups

We study properties of solutionsf, g, h C(G) of the functional equation

Maximal estimates on measure spaces for weak-type multipliers

We describe sufficient conditions for transferring from locally compact abelian groups to measure spaces the weak-type bounds of maximal operators defined by multipliers of weak type. This leads to homomorphism theorems for maximal multiplier operators. Communicated by Guido Weiss