Showing 41 - 50 of 94 Items
Kernel functions on domains with hyperelliptic double
Date: 1977-01-01
Creator: William H. Barker
Access: Open access
- Iii this paper we show that the structure of the Bergman and Szegö kernel functions is especially simple on domains with hyperelliptic double. Each such domain is conformally equivalent to the exterior of a system of slits taken from the real axis, and on such domains the Bergman kernel function and its adjoint are essentially the same, while the Szegö kernel function and its adjoint are elementary and can be written in a closed form involving nothing worse than fourth roots of polynomials. Additionally, a number of applications of these results are obtained. © 1977 American Mathematical Society.
Noether’s theorem for plane domains with hyperelliptic double
Date: 1977-01-01
Creator: William H. Barker
Access: Open access
- This paper is motivated by the observation that Noether’s theorem for quadratic differentials fails for hyperelliptic Riemann surfaces. In this paper we provide an appropriate substitute for Noether’s theorem which is valid for plane domains with hyperelliptic double. Our result is somewhat more explicit than Noether’s, and, in contrast with the case of nonhyperelliptic surfaces, it provides a basis for the (even) quadratic differentials which holds globally for all domains with hyperelliptic double. An important fact which plays a significant role in these considerations is that no two normal differentials of the first kind can have a common zero on a domain with hyperelliptic double. © 1977 Pacific Journal of Mathematics. All rights reserved.
Demonstration of Dispersive Rarefaction Shocks in Hollow Elliptical Cylinder Chains
Date: 2018-05-11
Creator: H. Kim, E. Kim, C. Chong, P. G. Kevrekidis, J., Yang
Access: Open access
- We report an experimental and numerical demonstration of dispersive rarefaction shocks (DRS) in a 3D-printed soft chain of hollow elliptical cylinders. We find that, in contrast to conventional nonlinear waves, these DRS have their lower amplitude components travel faster, while the higher amplitude ones propagate slower. This results in the backward-tilted shape of the front of the wave (the rarefaction segment) and the breakage of wave tails into a modulated waveform (the dispersive shock segment). Examining the DRS under various impact conditions, we find the counterintuitive feature that the higher striker velocity causes the slower propagation of the DRS. These unique features can be useful for mitigating impact controllably and efficiently without relying on material damping or plasticity effects.
Wave transmission in time- and space-variant helicoidal phononic crystals
Date: 2014-11-04
Creator: F. Li, C. Chong, J. Yang, P. G. Kevrekidis, C., Daraio
Access: Open access
- We present a dynamically tunable mechanism of wave transmission in one-dimensional helicoidal phononic crystals in a shape similar to DNA structures. These helicoidal architectures allow slanted nonlinear contact among cylindrical constituents, and the relative torsional movements can dynamically tune the contact stiffness between neighboring cylinders. This results in cross-talking between in-plane torsional and out-of-plane longitudinal waves. We numerically demonstrate their versatile wave mixing and controllable dispersion behavior in both wavenumber and frequency domains. Based on this principle, a suggestion toward an acoustic configuration bearing parallels to a transistor is further proposed, in which longitudinal waves can be switched on and off through torsional waves.
The validity of the kdv approximation in case of resonances arising from periodic media
Date: 2011-11-15
Creator: Christopher Chong, Guido Schneider
Access: Open access
- It is the purpose of this short note to discuss some aspects of the validity question concerning the Korteweg-de Vries (KdV) approximation for periodic media. For a homogeneous model possessing the same resonance structure as it arises in periodic media we prove the validity of the KdV approximation with the help of energy estimates. © 2011 Elsevier Inc.
Sensitivity Analysis of Basins of Attraction for Nelder-Mead
Date: 2022-01-01
Creator: Sonia K. Shah
Access: Open access
- The Nelder-Mead optimization method is a numerical method used to find the minimum of an objective function in a multidimensional space. In this paper, we use this method to study functions - specifically functions with three-dimensional graphs - and create images of the basin of attraction of the function. Three different methods are used to create these images named the systematic point method, randomized centroid method, and systemized centroid method. This paper applies these methods to different functions. The first function has two minima with an equivalent function value. The second function has one global minimum and one local minimum. The last function studied has several minima of different function values. The systematic point method is a reliable method in particular scenarios but is extremely sensitive to changes in the initial simplex. The randomized centroid method was not found to be useful as the basin of attraction images are difficult to understand. This made it particularly troublesome to know when the method was working effectively and when it was not. The systemized centroid method appears to be the most precise and effective method at creating the basin of attraction in most cases. This method rarely fails to find a minimum and is particularly adept at finding global minima more effectively compared to local minima. It is important to remember that these conclusions are simply based off the results of the methods and functions studied and that more effective methods may exist.
From local to global behavior in competitive Lotka-Volterra systems
Date: 2003-01-01
Creator: E. C. Zeeman, M. L. Zeeman
Access: Open access
- In this paper we exploit the linear, quadratic, monotone and geometric structures of competitive Lotka-Volterra systems of arbitrary dimension to give geometric, algebraic and computational hypotheses for ruling out nontrivial recurrence. We thus deduce the global dynamics of a system from its local dynamics. The geometric hypotheses rely on the introduction of a split Liapunov function. We show that if a system has a fixed point p ∈ int R+n and the carrying simplex of the system lies to one side of its tangent hyperplane at p, then there is no nontrivial recurrence, and the global dynamics are known. We translate the geometric hypotheses into algebraic hypotheses in terms of the definiteness of a certain quadratic function on the tangent hyperplane. Finally, we derive a computational algorithm for checking the algebraic hypotheses, and we compare this algorithm with the classical Volterra-Liapunov stability theorem for Lotka-Volterra systems.
Sign Under the Domino Robinson-Schensted Maps
Date: 2014-01-01
Creator: Thomas Pietraho
Access: Open access
- We generalize a formula obtained independently by Reifegerste and Sjöstrand for the sign of a permutation under the classical Robinson-Schensted map to a family of domino Robinson-Schensted algorithms. © 2014 Springer Basel.
BEING CAYLEY AUTOMATIC IS CLOSED under TAKING WREATH PRODUCT with VIRTUALLY CYCLIC GROUPS
Date: 2021-12-13
Creator: Dmitry Berdinsky, Murray Elder, Jennifer Taback
Access: Open access
- We extend work of Berdinsky and Khoussainov ['Cayley automatic representations of wreath products', International Journal of Foundations of Computer Science 27(2) (2016), 147-159] to show that being Cayley automatic is closed under taking the restricted wreath product with a virtually infinite cyclic group. This adds to the list of known examples of Cayley automatic groups.
A note on convexity properties of Thompson's group F
Date: 2012-01-01
Creator: Matthew Horak, Melanie Stein, Jennifer Taback
Access: Open access
- We prove that Thompson's group F is not minimally almost convex with respect to any generating set which is a subset of the standard infinite generating set for F and which contains x1. We use this to show that F is not almost convex with respect to any generating set which is a subset of the standard infinite generating set, generalizing results in [4]. © Gruyter 2012.