Decomposition of Vocal Cycle Length Perturbations into Vocal Jitter and Vocal Microtremor, and Comparison of Their Size in Normophonic Speakers

A statistical method that enables raw vocal cycle length perturbations to be decomposed into perturbations ascribed to vocal jitter and vocal tremor is presented, together with a comparison of the size of jitter and tremor. The method is based on a time series model that splits the vocal cycle length perturbations into uncorrelated cycle-to-cycle perturbations ascribed to vocal jitter and supra-cycle perturbations ascribed to vocal tremor. The corpus was composed of 114 vocal cycle length time series for sustained vowels [a], [i], and [u] produced by 22 male and 16 female normophonic speakers. The results were the following. First, 100 out of 114 time series were decomposed successfully by means of the time series model. Second, vocal perturbations ascribed to tremor were significantly larger than perturbations ascribed to jitter. Third, the correlation between vocal jitter and vocal tremor was moderate, but statistically significant. Fourth, small but statistically significant differences were observed among the three vowel timbres in the relative jitter and the arithmetic difference of jitter and tremor. Fifth, the differences between male and female speakers were not statistically significant in the relative raw perturbations, the relative jitter, or the modulation level owing to tremor.     

On the existence of f-local subgroups in a group

We prove the existence of infinite subgroups with nontrivial locally finite radicals and of locally finite subgroups in the groups with almost finite almost solvable elements of prime orders and in the groups with generally finite elements.     

Efficient computation of mean drag for the subcritical flow past a circular cylinder using general Galerkin G2

General Galerkin (G2) is a new computational method for turbulent flow, where a stabilized Galerkin finite element method is used to compute approximate weak solutions to the Navier–Stokes equations directly, without any filtering of the equations as in a standard approach to turbulence simulation, such as large eddy simulation, and thus no Reynolds stresses are introduced, which need modelling. In this paper, G2 is used to compute the drag coefficient c_D for the flow past a circular cylinder at Reynolds number Re=3900, for which the flow is turbulent. It is found that it is possible to approximate c_D to an accuracy of a few percent, corresponding to the accuracy in experimental results for this problem, using less than 10⁵ mesh points, which makes the simulations possible using a standard PC. The mesh is adaptively refined until a stopping criterion is reached with respect to the error in a chosen output of interest, which in this paper is c_D. Both the stopping criterion and the mesh‐refinement strategy are based on a posteriori error estimates, in the form of a space–time integral of residuals times derivatives of the solution of a dual problem, linearized at the approximate solution, and with data coupling to the output of interest. Copyright © 2008 John Wiley & Sons, Ltd.     

Variations of Robin capacity and applications

We obtain some estimates for the distortions of the moduli of quadrilaterals, the reduced moduli, and Robin capacities depending on the variation of the boundary of a domain. We show that for sufficiently smooth variations of the boundary the corresponding variations of the moduli and capacities are proportional to the area of the variable part of the domain in some extremal metric. We apply these results to studying the generalized Lavrent’ev problem of finding the shape of an infinitely thin airfoil of given length with the maximal aerodynamical lift under some restriction on the curvature of the airfoil.     

Thermodynamics of wurtzite GaN from first-principle calculation

The density function perturbation theory (DFPT) is employed to study the linear thermal expansion and heat capacity at constant pressure (with the quasiharmonic approximation) for wurtzite GaN. The calculated results of linear thermal expansion coefficient and heat capacity at constant pressure are compared with the available experimental data in a wide temperature range. Generally these properties calculated agree well with experimental data except at high temperature, thus it suggests the thermal expansion and heat capacity can be well calculated from this first-principle approach.     

Observability of elastic vibrations of a beam

The observability problem for beam vibrations described by a fourth-order partial differential equation with various boundary conditions is considered. Dynamic observability problems are solved in terms of boundary conditions and observations of the beam state at certain fixed instants of time.     

A POSTERIORI ESTIMATOR OF NONCONFORMING FINITE ELEMENT METHOD FOR FOURTH ORDER ELLIPTIC PERTURBATION PROBLEMS

In this paper, we consider the nonconforming finite element approximations of fourth order elliptic perturbation problems in two dimensions. We present an a posteriori error estimator under certain conditions, and give an h-version adaptive algorithm based on the error estimation. The local behavior of the estimator is analyzed as well. This estimator works for several nonconforming methods, such as the modified Morley method and the modified Zienkiewicz method, and under some assumptions, it is an optimal one. Numerical examples are reported, with a linear stationary Cahn-HiUiard-type equation as a model problem.     

THE OPTIMAL CONVERGENCE ORDER OF THE DISCONTINUOUS FINITE ELEMENT METHODS FOR FIRST ORDER HYPERBOLIC SYSTEMS

In this paper, a discontinuous finite element method for the positive and symmetric, first-order hyperbolic systems （steady and nonsteady state） is constructed and analyzed by using linear triangle elements, and the O（h^2）-order optimal error estimates are derived under the assumption of strongly regular triangulation and the Ha-regularity for the exact solutions. The convergence analysis is based on some superclose estimates of the interpolation approximation. Finally, we discuss the Maxwell equations in a two-dimensional domain, and numerical experiments are given to validate the theoretical results.     

Smooth and path connected Banach submanifold Σ r of B(E,F) and a dimension formula in B(ℝ n ,ℝ m )

Given two Banach spaces E,F, let B(E,F) be the set of all bounded linear operators from E into F, Σ _r the set of all operators of finite rank r in B(E,F), and Σ _r ^# the number of path connected components of Σ _r . It is known that Σ _r is a smooth Banach submanifold in B(E,F) with given expression of its tangent space at each A ∈ Σ _r . In this paper,the equality Σ _r ^# = 1 is proved. Consequently, the following theorem is obtained: for any nonnegative integer r, Σ _r is a smooth and path connected Banach submanifold in B(E,F) with the tangent space T _A Σ _r = {B ∈ B(E,F): BN(A) ⊂ R(A)} at each A ∈ Σ _r if dim F = ∞. Note that the routine method can hardly be applied here. So in addition to the nice topological and geometric property of Σ _r the method presented in this paper is also interesting. As an application of this result, it is proved that if E = ℝ ⁿ and F = ℝ ^m , then Σ _r is a smooth and path connected submanifold of B(ℝ ⁿ , ℝ ^m ) and its dimension is dimΣ _r = (m+n)r−r ² for each r, 0 <- r < min {n,m}. Supported by the National Science Foundation of China (Grant No.10671049 and 10771101).     

Logarithmic asymptotics for a single-server processing distinguishable sources

We consider a single-server first-in-first-out queue fed by a finite number of distinct sources of jobs. For a large class of short-range dependent and light-tailed distributed job processes, using functional large deviation techniques we prove a large deviation principle and logarithmic asymptotics for the joint waiting time and queue lengths distribution. We identify the paths that are most likely to lead to the rare events of large waiting times and long queue lengths. A number of examples are presented to illustrate salient features of the results.