Echolocation range of captive and free-ranging baiji (Lipotes vexillifer), finless porpoise (Neophocaena phocaenoides), and bottlenose dolphin (Tursiops truncatus).

The interclick intervals of captive dolphins are known to be longer than the two-way transit time between the dolphin and a target. In the present study, the interclick intervals of free-ranging baiji, finless porpoises, and bottlenose dolphins in the wild and in captivity were compared. The click intervals in open waters ranged up to 100-200 ms, whereas the click intervals in captivity were in the order of 4-28 ms. Echolocation of free-ranging dolphins appears to adapt to various distance in navigation or ranging, sometimes up to 140 m. Additionally, the difference of waveform characteristics of clicks between species was recognized in the frequency of maximum energy and the click duration.     

Signals in chaos: A method for the cancellation of deterministic noise from discrete signals

In this paper we describe a method for separating a combination of a chaotic time series and a discrete-valued signal. The method uses a feedback technique stabilised using knowledge of the chaotic system and the discrete nature of the signal. It is not based on a linearization of the dynamics, and therefore, unlike previously proposed separation methods, does not require that the signal be small. Nor does it make any assumptions about the relative timescales of the signal and the chaotic time series.     

Dynamical symmetries inq-deformed quantum mechanics

The dynamical algebra of theq-deformed harmonic oscillator is constructed. As a result, we find the free deformed Hamiltonian as well as the Hamiltonian of the deformed oscillator as a complicated, momentum dependent interaction Hamiltonian in terms of the usual canonical variables. Furthermore we construct a welldefined algebraSU _q(1,1) with consistent conjugation properties and comultiplication. We obtain non lowest weight representations of this algebra.     

Convective Heat Transfer past Small Cylindrical Bodies

Convective heat transfer from an array of small, cylindrical bodies of arbitrary shape in an unbounded, two-dimensional domain is a singular perturbation problem involving an infinite logarithmic expansion in the small parameter ε, representing the order of magnitude of the size of the bodies. Using the method of matched asymptotic expansions, we formulate a hybrid asymptotic-numerical method to solve for the dimensionless, steady-state temperature. We assume that the velocity field of the fluid surrounding the bodies is arbitrary but known. From our asymptotic solution for an arbitrary velocity field, we present the results for two special cases: a uniform flow field and a simple shear flow field. We demonstrate the asymptotic results of the hybrid method through a number of examples and, in a particular case, we compare these results to an exact analytical solution.     

Enumeration of three-dimensional convex polygons

A self-avoiding polygon (SAP) on a graph is an elementary cycle. Counting SAPs on the hypercubic lattice ℤ ^d withd≥2, is a well-known unsolved problem, which is studied both for its combinatorial and probabilistic interest and its connections with statistical mechanics. Of course, polygons on ℤ ^d are defined up to a translation, and the relevant statistic is their perimeter. A SAP on ℤ ^d is said to beconvex if its perimeter is “minimal”, that is, is exactly twice the sum of the side lengths of the smallest hyper-rectangle containing it. In 1984, Delest and Viennot enumerated convex SAPs on the square lattice [6], but no result was available in a higher dimension. We present an elementar approach to enumerate convex SAPs in any dimension. We first obtain a new proof of Delest and Viennot's result, which explains combinatorially the form of the generating function. We then compute the generating function for convex SAPs on the cubic lattice. In a dimension larger than 3, the details of the calculations become very cumbersome. However, our method suggests that the generating function for convex SAPs on ℤ ^d is always a quotient ofdifferentiably finite power series.     

Polling systems in heavy traffic: Exhaustiveness of service policies

We study the expected delay in cyclic polling models with general ‘branching-type’ service disciplines. For this class of models, which contains models with exhaustive and gated service as special cases, we obtain closed-form expressions for the expected delay under standard heavy-traffic scalings. We identify a single parameter associated with the service discipline at each queue, which we call the ‘exhaustiveness’. We show that the scaled expected delay figures depend on the service policies at the queues only through the exhaustiveness of each of the service disciplines. This implies that the influence of different service disciplines, but with the same exhaustiveness, on the expected delays at the queues becomes the same when the system reaches saturation. This observation leads to a new classification of the service disciplines. In addition, we show monotonicity of the scaled expected delays with respect to the exhaustiveness of the service disciplines. This induces a complete ordering in terms of efficiency of the service disciplines. The results also lead to new rules for optimization of the system performance with respect to the service disciplines at the queues. Further, the exact asymptotic results suggest simple expected waiting-time approximations for polling models in heavy traffic. Numerical experiments show that the accuracy of the approximations is excellent for practical heavy-traffic scenarios. This revised version was published online in June 2006 with corrections to the Cover Date.     

Effective potentials and Bogoliubov’s quasi-averages

The effective potential method, used in quantum field theory to study spontaneous symmetry violation, is discussed from the point of view of Bogoliubov’s quasi-averaging procedure. It is shown that the effective potential method is a disguised type of this procedure. The catastrophe theory approach to the study of phase transitions is discussed and the existence of the potentials used in that approach is proved from the statistical point of view. It is shown that in the case of broken symmetry, the nonconvex effective potential is not a Legendre transform of the generating functional for connected Green’s functions. Instead, it is a part of the potential used in catastrophe theory. The relationship between the effective potential and the Legendre transform of the generating functional for connected Green’s functions is given by Maxwell’s rule. A rigorous rule for evaluating quasi-averaged quantities within the framework of the effective potential method is established. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 113, No. 1, pp. 149–161, October, 1997.     

Orbifolds, Sheaves and Groupoids

We characterize orbifolds in terms of their sheaves, and show that orbifolds correspond exactly to a specific class of smooth groupoids. As an application, we construct fibered products of orbifolds and prove a change-of-base formula for sheaf cohomology.