Bi-Lipschitz geometry of weighted homogeneous surface singularities

We show that a weighted homogeneous complex surface singularity is metrically conical (i.e., bi-Lipschitz equivalent to a metric cone) only if its two lowest weights are equal. We also give an example of a pair of weighted homogeneous complex surface singularities that are topologically equivalent but not bi-Lipschitz equivalent.Comment: 5 pages. Added result that nonhomogeneous cyclic quotients are not conica

Solid-State Excitation Laser for Laser-Ultrasonics

The inspection speed of laser-ultrasonics compared with conventional ultrasonic testing is limited by the pulse repetition rate of the excitation laser. The maximum pulse repetition rate reported up to now for CO2-lasers, which are presently used for nearly all systems, is in the range of 400 Hz. In this paper a new approach based on a diode-pumped solid-state laser is discussed, which is currently being developed. This new excitation laser is designed for a repetition rate of 1 kHz and will operate at a mid-IR wavelength of 3.3 m. The higher repeti-tion rate enables a higher inspection speed, whereas the mid-IR wavelength anticipates a better coupling efficiency. The total power for pumping the laser crystals is transported via flexible optical fibres to the compact laser head, thus allowing operation on a robot arm. The laser head consists of a master oscillator feeding several lines of power amplifiers and in-cludes nonlinear optical wavelength conversion by an optical parametric process. It is char-acterized by a modular construction which provides optimal conditions for operation at high average power as well as for easy maintenance. These features will enable building reliable, long-lived, rugged, smart laser ultrasonic systems in futur

Revisiting the Equivalence Problem for Finite Multitape Automata

The decidability of determining equivalence of deterministic multitape automata (or transducers) was a longstanding open problem until it was resolved by Harju and Karhum\"{a}ki in the early 1990s. Their proof of decidability yields a co_NP upper bound, but apparently not much more is known about the complexity of the problem. In this paper we give an alternative proof of decidability, which follows the basic strategy of Harju and Karhumaki but replaces their use of group theory with results on matrix algebras. From our proof we obtain a simple randomised algorithm for deciding language equivalence of deterministic multitape automata and, more generally, multiplicity equivalence of nondeterministic multitape automata. The algorithm involves only matrix exponentiation and runs in polynomial time for each fixed number of tapes. If the two input automata are inequivalent then the algorithm outputs a word on which they differ

Quantum State Tomography Using Successive Measurements

We describe a quantum state tomography scheme which is applicable to a system described in a Hilbert space of arbitrary finite dimensionality and is constructed from sequences of two measurements. The scheme consists of measuring the various pairs of projectors onto two bases --which have no mutually orthogonal vectors--, the two members of each pair being measured in succession. We show that this scheme implies measuring the joint quasi-probability of any pair of non-degenerate observables having the two bases as their respective eigenbases. The model Hamiltonian underlying the scheme makes use of two meters initially prepared in an arbitrary given quantum state, following the ideas that were introduced by von Neumann in his theory of measurement.Comment: 12 Page

Changes in chemical composition of N. sitophila during the active growth phase

Changes in chemical composition during growt

A Redshift Survey of Nearby Galaxy Groups: the Shape of the Mass Density Profile

We constrain the mass profile and orbital structure of nearby groups and clusters of galaxies. Our method yields the joint probability distribution of the density slope n, the velocity anisotropy beta, and the turnover radius r0 for these systems. The measurement technique does not use results from N-body simulations as priors. We incorporate 2419 new redshifts in the fields of 41 systems of galaxies with z < 0.04. The new groups have median velocity dispersion sigma=360 km/s. We also use 851 archived redshifts in the fields of 8 nearly relaxed clusters with z < 0.1. Within R < 2 r200, the data are consistent with a single power law matter density distribution with slope n = 1.8-2.2 for systems with sigma < 470 km/s, and n = 1.6-2.0 for those with sigma > 470 km/s (95% confidence). We show that a simple, scale-free phase space distribution function f(E,L^2) ~ (-E)^(alpha-1/2) L^(-2 \beta) is consistent with the data as long as the matter density has a cusp. Using this DF, matter density profiles with constant density cores (n=0) are ruled out with better than 99.7% confidence.Comment: 22 pages; accepted for publication in the Astrophysical Journa

Design of a fault tolerant airborne digital computer. Volume 1: Architecture

This volume is concerned with the architecture of a fault tolerant digital computer for an advanced commercial aircraft. All of the computations of the aircraft, including those presently carried out by analogue techniques, are to be carried out in this digital computer. Among the important qualities of the computer are the following: (1) The capacity is to be matched to the aircraft environment. (2) The reliability is to be selectively matched to the criticality and deadline requirements of each of the computations. (3) The system is to be readily expandable. contractible, and (4) The design is to appropriate to post 1975 technology. Three candidate architectures are discussed and assessed in terms of the above qualities. Of the three candidates, a newly conceived architecture, Software Implemented Fault Tolerance (SIFT), provides the best match to the above qualities. In addition SIFT is particularly simple and believable. The other candidates, Bus Checker System (BUCS), also newly conceived in this project, and the Hopkins multiprocessor are potentially more efficient than SIFT in the use of redundancy, but otherwise are not as attractive

Quantum correlation games

A new approach to play games quantum mechanically is proposed. We consider two players who perform measurements in an EPR-type setting. The payoff relations are defined as functions of correlations, i.e. without reference to classical or quantum mechanics. Classical bi-matrix games are reproduced if the input states are classical and perfectly anti-correlated, that is, for a classical correlation game. However, for a quantum correlation game, with an entangled singlet state as input, qualitatively different solutions are obtained. For example, the Prisoners' Dilemma acquires a Nash equilibrium if both players apply a mixed strategy. It appears to be conceptually impossible to reproduce the properties of quantum correlation games within the framework of classical games

Thermodynamically self-consistent liquid state theories for systems with bounded potentials

The mean spherical approximation (MSA) can be solved semi-analytically for the Gaussian core model (GCM) and yields - rather surprisingly - exactly the same expressions for the energy and the virial equations. Taking advantage of this semi-analytical framework, we apply the concept of the self-consistent Ornstein-Zernike approximation (SCOZA) to the GCM: a state-dependent function K is introduced in the MSA closure relation which is determined to enforce thermodynamic consistency between the compressibility route and either the virial or energy route. Utilizing standard thermodynamic relations this leads to two different differential equations for the function K that have to be solved numerically. Generalizing our concept we propose an integro-differential-equation based formulation of the SCOZA which, although requiring a fully numerical solution, has the advantage that it is no longer restricted to the availability of an analytic solution for a particular system. Rather it can be used for an arbitrary potential and even in combination with other closure relations, such as a modification of the hypernetted chain approximation.Comment: 11 pages, 11 figures, submitted to J. Chem. Phy