597 research outputs found
Convergent Asymptotic Expansions of Charlier, Laguerre and Jacobi Polynomials
Convergent expansions are derived for three types of orthogonal polynomials:
Charlier, Laguerre and Jacobi. The expansions have asymptotic properties for
large values of the degree. The expansions are given in terms of functions that
are special cases of the given polynomials. The method is based on expanding
integrals in one or two points of the complex plane, these points being saddle
points of the phase functions of the integrands.Comment: 20 pages, 5 figures. Keywords: Charlier polynomials, Laguerre
polynomials, Jacobi polynomials, asymptotic expansions, saddle point methods,
two-points Taylor expansion
Multi-point Taylor Expansions of Analytic Functions
Taylor expansions of analytic functions are considered with respect to
several points, allowing confluence of any of them. Cauchy-type formulas are
given for coefficients and remainders in the expansions, and the regions of
convergence are indicated. It is explained how these expansions can be used in
deriving uniform asymptotic expansions of integrals. The method is also used
for obtaining Laurent expansions in several points as well as Taylor-Laurent
expansions.Comment: 20 pages, 7 figures. Keywords: multi-point Taylor expansions,
Cauchy's theorem, analytic functions, multi-point Laurent expansions, uniform
asymptotic expansions of integral
Two-point Taylor Expansions of Analytic Functions
Taylor expansions of analytic functions are considered with respect to two
points. Cauchy-type formulas are given for coefficients and remainders in the
expansions, and the regions of convergence are indicated. It is explained how
these expansions can be used in deriving uniform asymptotic expansions of
integrals. The method is also used for obtaining Laurent expansions in two
points.Comment: 14 pages, 10 figure
Computer based human-centered display system
A human centered informational display is disclosed that can be used with vehicles (e.g. aircraft) and in other operational environments where rapid human centered comprehension of an operational environment is required. The informational display integrates all cockpit information into a single display in such a way that the pilot can clearly understand with a glance, his or her spatial orientation, flight performance, engine status and power management issues, radio aids, and the location of other air traffic, runways, weather, and terrain features. With OZ the information is presented as an integrated whole, the pilot instantaneously recognizes flight path deviations, and is instinctively drawn to the corrective maneuvers. Our laboratory studies indicate that OZ transfers to the pilot all of the integrated display information in less than 200 milliseconds. The reacquisition of scan can be accomplished just as quickly. Thus, the time constants for forming a mental model are near instantaneous. The pilot's ability to keep up with rapidly changing and threatening environments is tremendously enhanced. OZ is most easily compatible with aircraft that has flight path information coded electronically. With the correct sensors (which are currently available) OZ can be installed in essentially all current aircraft
The Bayesian Mutation Sampler Explains Distributions of Causal Judgments
One consistent finding in the causal reasoning literature is that causal judgments are rather variable. In particular, distributions of probabilistic causal judgments tend not to be normal and are often not centered on the normative response. As an explanation for these response distributions, we propose that people engage in ‘mutation sampling’ when confronted with a causal query and integrate this information with prior information about that query. The Mutation Sampler model (Davis & Rehder, 2020) posits that we approximate probabilities using a sampling process, explaining the average responses of participants on a wide variety of tasks. Careful analysis, however, shows that its predicted response distributions do not match empirical distributions. We develop the Bayesian Mutation Sampler (BMS) which extends the original model by incorporating the use of generic prior distributions. We fit the BMS to experimental data and find that, in addition to average responses, the BMS explains multiple distributional phenomena including the moderate conservatism of the bulk of responses, the lack of extreme responses, and spikes of responses at 50%.</p
Asymptotic behaviour of three-dimensional singularly perturbed convection–diffusion problems with discontinuous data
AbstractWe consider three singularly perturbed convection–diffusion problems defined in three-dimensional domains: (i) a parabolic problem −ϵ(uxx+uyy)+ut+v1ux+v2uy=0 in an octant, (ii) an elliptic problem −ϵ(uxx+uyy+uzz)+v1ux+v2uy+v3uz=0 in an octant and (iii) the same elliptic problem in a half-space. We consider for all of these problems discontinuous boundary conditions at certain regions of the boundaries of the domains. For each problem, an asymptotic approximation of the solution is obtained from an integral representation when the singular parameter ϵ→0+. The solution is approximated by a product of two error functions, and this approximation characterizes the effect of the discontinuities on the small ϵ− behaviour of the solution and its derivatives in the boundary layers or the internal layers
Dressed test particles, oscillation centres and pseudo-orbits
A general semi-analytical method for accurate and efficient numerical
calculation of the dielectrically screened ("dressed") potential around a
non-relativistic test particle moving in an isotropic, collisionless,
unmagnetised plasma is presented. The method requires no approximations and is
illustrated using results calculated for two cases taken from the MSc thesis of
the first author: test particles with velocities above and below the ion sound
speed in plasmas with Maxwellian ions and warm electrons. The idea that the
fluctuation spectrum of a plasma can be described as a superposition of the
fields around \emph{non-interacting} dressed test particles is an expression of
the quasiparticle concept, which has also been expressed in the development of
the oscillation-centre and pseudo-orbit formalisms.Comment: 14 pages to Plasma Physics and Controlled Fusion for publication with
a cluster of papers associated with workshop Stability and Nonlinear Dynamics
of Plasmas, October 31, 2009 Atlanta, GA on occasion of the 65th birthday of
R.L. Dewar. Version 2: Reference [27] added in Sec. 5. Version 3: Revised in
response to referee
The Schrodinger equation with Hulthen potential plus ring-shaped potential
We present the solutions of the Schrdinger equation with the
Hulthn potential plus ring-shape potential for states
within the framework of an exponential approximation of the centrifugal
potential.Solutions to the corresponding angular and radial equations are
obtained in terms of special functions using the conventional Nikiforov-Uvarov
method. The normalization constant for the Hulthn potential is also
computed.Comment: Typed with LateX,12 Pages, Typos correcte
Power Utility Maximization in Discrete-Time and Continuous-Time Exponential Levy Models
Consider power utility maximization of terminal wealth in a 1-dimensional
continuous-time exponential Levy model with finite time horizon. We discretize
the model by restricting portfolio adjustments to an equidistant discrete time
grid. Under minimal assumptions we prove convergence of the optimal
discrete-time strategies to the continuous-time counterpart. In addition, we
provide and compare qualitative properties of the discrete-time and
continuous-time optimizers.Comment: 18 pages, to appear in Mathematical Methods of Operations Research.
The final publication is available at springerlink.co
Reproducibility and validity of a diet quality index for children assessed using a FFQ
The diet quality index (DQI) for preschool children is a new index developed to reflect compliance with four main food-based dietary guidelines for preschool children in Flanders. The present study investigates: (1) the validity of this index by comparing DQI scores for preschool children with nutrient intakes, both of which were derived from 3d estimated diet records; (2) the reproducibility of the DQI for preschoolers based on a parentally reported forty-seven-item FFQ DQI, which was repeated after 5 weeks; (3) the relative validity of the FFQ DQI with 3d record DQI scores as reference. The study sample included 510 and 58 preschoolers (2-5-6.5 years) for validity and reproducibility analyses, respectively. Increasing 3d record DQI scores were associated with decreasing consumption of added sugars, and increasing intakes of fibre, water, Ca and many micronutrients. Mean FFQ DQI test-retest scores were not significantly different: 72 (so 11) v. 71 (Si) 10) (P-=0-218) out of a maximum of 100. Mean 3d record DQI score (66 (so 10)) was significantly lower than mean FFQ DQI (71 (so 10);
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