On Markov's Undecidability Theorem for Integer Matrices

We study a problem considered originally by A. Markov in 1947: Given two finitely generated matrix semigroups, determine whether or not they contain a common element. This problem was proved undecidable by Markov for 4 x 4 matrices, even in a very restrict form, and for 3 x 3 matrices by Krom in 1981. Here we give a new proof in the 3 x 3 case which gives undecidability in an almost as restricted form as the result of Markov.     

Identification of hydrolysis products of AlCl(3)*6H(2)O in the presence of sulfate by electrospray ionization time-of-flight mass spectrometry and computational methods

ElectroSpray Ionization-Mass Spectrometry (ESI-MS) and computational methods (DFT, MP2, and COSMO) were used to investigate the hydrolysis products of aluminium chloride as a function of sulfate concentration at pH 3.7. With the aid of computational chemistry, structural information was deduced from the chemical compositions observed with ESI-MS. Many novel types of hydrolysis products were noted, revealing that our present understanding of aluminium speciation is too simple. The role of counterions was found to be critical: the speciation of aluminium changed markedly as a function of sulfate concentration. Ab initio calculations were used to reveal the energetically most favoured structures of aluminium sulfate anions and cations selected from the ESI-MS results. Several interesting observations were made. Most importantly, the bonding behaviour of the sulfate group changed as the number of aqua ligands increased. The accompanying structural rearrangement of the clusters revealed the highly active role of sulfate as a ligand. The gas phase calculations were expanded to the aquatic environment using a conductor-like screening model. As expected, the bonding behaviour of the sulfate group in the minimum energy structures was distinctly different in the aquatic environment compared to the gas phase. Together, these methods open a new window for research in the solution chemistry of aluminium species.     

Decidability of the binary infinite Post Correspondence Problem

We shall show that it is decidable for binary instances of the Post Correspondence Problem whether the instance has an infinite solution. In this context, a binary instance (h,g) consists of two morphisms h and g with a common two element domain alphabet. An infinite solution ω is an infinite word ω=a₁a₂… such that h(ω)=g(ω). This problem is known to be undecidable for the unrestricted instances of the Post Correspondence Problem.     

Identification and fragmentation of hydrolyzed aluminum species by electrospray ionization tandem mass spectrometry

Earlier characterization of some hydrolysis products of AlCl₃·6H₂O was confirmed by electrospray ionization tandem mass spectrometry with increasing collision energy of projectile ions. At lower collision energies, the aqua ligands were stripped off. At higher energies, two hydroxo groups formed a bridging oxo group with loss of one water molecule. Aluminum complexes could also capture aqua ligands in the collision chamber so long as the parent ion did not fragment, and the fragment ion spectra broadened toward higher m/z values. The chloro ligands were eliminated as hydrochloric acid. The aluminum cores remained highly intact. Copyright © 2004 John Wiley & Sons, Ltd.     

Convective stability of hot matter in ultrarelativistic heavy-ion collisions

The convective stability of strongly interacting matter undergoing hydrodynamic flow in ultrarelativistic heavy-ion collisions is studied in both the quark-gluon plasma and hadron gas phases. We find that this stability depends on the form of the initial conditions assumed for the hydrodynamic flow. In the case of initial conditions corresponding to partial transparency the flow of the quark-gluon plasma is stable whereas the flow of the hadron gas is convectively unstable. The timescale for hydrodynamic oscillations around the (stable or unstable) equilibrium state is found to be larger than the expected lifetime of the system, suggesting that the flow in either case is close to neutral convective equilibrium.     

Calculation of the O-H stretching vibrational overtone spectrum of the water dimer

The O-H stretching vibrational overtone spectrum of the water dimer has been calculated with the dimer modeled as two individually vibrating monomer units. Vibrational term values and absorption intensities have been obtained variationally with a computed dipole moment surface and an internal coordinate Hamiltonian, which consists of exact kinetic energy operators within the Born-Oppenheimer approximation of the monomer units. Three-dimensional ab initio potential energy and dipole moment surfaces have been calculated using the internal coordinates of the monomer units using the coupled cluster method including single, double, and perturbative triple excitations [CCSD(T)] with the augmented correlation consistent valence triple zeta basis set (aug-cc-pVTZ). The augmented correlation consistent valence quadruple zeta basis set (aug-cc-pVQZ), counterpoise correction, basis set extrapolation to the complete basis set limit, relativistic corrections, and core and valence electron correlations effects have been included in one-dimensional potential energy surface cuts. The aim is both to investigate the level of ab initio and vibrational calculations necessary to produce accurate results when compared with experiment and to aid the detection of the water dimer under atmospheric conditions.     

Preprocessing Strategies for Sparse Infrared Spectroscopy: A Case Study on Cartilage Diagnostics

The aim of the study was to optimize preprocessing of sparse infrared spectral data. The sparse data were obtained by reducing broadband Fourier transform infrared attenuated total reflectance spectra of bovine and human cartilage, as well as of simulated spectral data, comprising several thousand spectral variables into datasets comprising only seven spectral variables. Different preprocessing approaches were compared, including simple baseline correction and normalization procedures, and model-based preprocessing, such as multiplicative signal correction (MSC). The optimal preprocessing was selected based on the quality of classification models established by partial least squares discriminant analysis for discriminating healthy and damaged cartilage samples. The best results for the sparse data were obtained by preprocessing using a baseline offset correction at 1800 cm⁻¹, followed by peak normalization at 850 cm⁻¹ and preprocessing by MSC.     

Towards gadget-free internet services: A roadmap of the Naked world

This paper presents a roadmap for the transition from current gadget-centric digital services towards a gadget-free services environment called the Naked world. The main idea of the Naked world is that all the services which are currently provided by gadgets will be provided by the infrastructure, thus no gadgets will be needed to use any kind of digital services. When a user in the Naked world intends to use a service, the infrastructure senses the user, the nearby intelligent surrounding launches an interactive user interface, performs identification through biometric identities, provides the service, and then closes the session when the user finishes the job. Therefore, the Naked world comprises highly intelligent and context-aware interactive environments. The vision of the Naked world is an evolution towards a user-friendly and ubiquitously available digital services, which is naturally bounded by the technological advancement. Henceforth, this paper presents the essential technologies and functional requirements along with the current and forthcoming novel technological concepts and challenges for the realization of the Naked world.