On Density of State of Quantized Willmore Surface-A Way to Quantized Extrinsic String in R^3

Recently I quantized an elastica with Bernoulli-Euler functional in two-dimensional space using the modified KdV hierarchy. In this article, I will quantize a Willmore surface, or equivalently a surface with the Polyakov extrinsic curvature action, using the modified Novikov-Veselov (MNV) equation. In other words, I show that the density of state of the partition function for the quantized Willmore surface is expressed by volume of a subspace of the moduli of the MNV equation.Comment: AMS-Tex Us

The Coulomb phase shift revisited

We investigate the Coulomb phase shift, and derive and analyze new and more precise analytical formulae. We consider next to leading order terms to the Stirling approximation, and show that they are important at small values of the angular momentum $l$ and other regimes. We employ the uniform approximation. The use of our expressions in low energy scattering of charged particles is discussed and some comparisons are made with other approximation methods.Comment: 13 pages, 5 figures, 1 tabl

On the families of orthogonal polynomials associated to the Razavy potential

We show that there are two different families of (weakly) orthogonal polynomials associated to the quasi-exactly solvable Razavy potential V(x)=(\z \cosh 2x-M)^2 (\z>0, $M\in\mathbf N$). One of these families encompasses the four sets of orthogonal polynomials recently found by Khare and Mandal, while the other one is new. These results are extended to the related periodic potential U(x)=-(\z \cos 2x -M)^2, for which we also construct two different families of weakly orthogonal polynomials. We prove that either of these two families yields the ground state (when $M$ is odd) and the lowest lying gaps in the energy spectrum of the latter periodic potential up to and including the $(M-1)^{\rm th}$ gap and having the same parity as $M-1$. Moreover, we show that the algebraic eigenfunctions obtained in this way are the well-known finite solutions of the Whittaker--Hill (or Hill's three-term) periodic differential equation. Thus, the foregoing results provide a Lie-algebraic justification of the fact that the Whittaker--Hill equation (unlike, for instance, Mathieu's equation) admits finite solutions.Comment: Typeset in LaTeX2e using amsmath, amssymb, epic, epsfig, float (24 pages, 1 figure

Uniqueness of the potential function for the vectorial Sturm-Liouville equation on a finite interval

[[abstract]]In this paper, the vectorial Sturm-Liouville operator L Q =−d 2 dx 2 +Q(x) is considered, where Q(x) is an integrable m×m matrix-valued function defined on the interval [0,π] . The authors prove that m 2 +1 characteristic functions can determine the potential function of a vectorial Sturm-Liouville operator uniquely. In particular, if Q(x) is real symmetric, then m(m+1) 2 +1 characteristic functions can determine the potential function uniquely. Moreover, if only the spectral data of self-adjoint problems are considered, then m 2 +1 spectral data can determine Q(x) uniquely.[[notice]]補正完畢[[incitationindex]]SCI[[cooperationtype]]國外[[booktype]]電子

Crossâ Network Directory Service: Infrastructure to enable collaborations across distributed research networks

IntroductionExisting largeâ scale distributed health data networks are disconnected even as they address related questions of healthcare research and public policy. This paper describes the design and implementation of a fully functional prototype openâ source tool, the Crossâ Network Directory Service (CNDS), which addresses much of what keeps distributed networks disconnected from each other.MethodsThe set of services needed to implement a Crossâ Directory Service was identified through engagement with stakeholders and workgroup members. CNDS was implemented using PCORnet and Sentinel network instances and tested by participating data partners.ResultsWeb services that enable the four major functional features of the service (registration, discovery, communication, and governance) were developed and placed into an openâ source repository. The services include a robust metadata model that is extensible to accommodate a virtually unlimited inventory of metadata fields, without requiring any further software development. The user interfaces are programmatically generated based on the contents of the metadata model.ConclusionThe CNDS pilot project gathered functional requirements from stakeholders and collaborating partners to build a software application to enable crossâ network data and resource sharing. The two partnersâ one from Sentinel and one from PCORnetâ tested the software. They successfully entered metadata about their organizations and data sources and then used the Discovery and Communication functionality to find data sources of interest and send a crossâ network query. The CNDS software can help integrate disparate health data networks by providing a mechanism for data partners to participate in multiple networks, share resources, and seamlessly send queries across those networks.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/149237/1/lrh210187.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/149237/2/lrh210187_am.pd

Stateful Contracts for Affine Types

Abstract. Affine type systems manage resources by preventing some values from being used more than once. This offers expressiveness and performance benefits, but difficulty arises in interacting with components written in a conventional language whose type system provides no way to maintain the affine type system’s aliasing invariants. We propose and implement a technique that uses behavioral contracts to mediate between code written in an affine language and code in a conventional typed language. We formalize our approach via a typed calculus with both affine-typed and conventionally-typed modules. We show how to preserve the guarantees of both type systems despite both languages being able to call into each other and exchange higher-order values.

Tunneling of quantum rotobreathers

We analyze the quantum properties of a system consisting of two nonlinearly coupled pendula. This non-integrable system exhibits two different symmetries: a permutational symmetry (permutation of the pendula) and another one related to the reversal of the total momentum of the system. Each of these symmetries is responsible for the existence of two kinds of quasi-degenerated states. At sufficiently high energy, pairs of symmetry-related states glue together to form quadruplets. We show that, starting from the anti-continuous limit, particular quadruplets allow us to construct quantum states whose properties are very similar to those of classical rotobreathers. By diagonalizing numerically the quantum Hamiltonian, we investigate their properties and show that such states are able to store the main part of the total energy on one of the pendula. Contrary to the classical situation, the coupling between pendula necessarily introduces a periodic exchange of energy between them with a frequency which is proportional to the energy splitting between quasi-degenerated states related to the permutation symmetry. This splitting may remain very small as the coupling strength increases and is a decreasing function of the pair energy. The energy may be therefore stored in one pendulum during a time period very long as compared to the inverse of the internal rotobreather frequency.Comment: 20 pages, 11 figures, REVTeX4 styl

Inverse spectral problems for Sturm-Liouville operators with singular potentials

The inverse spectral problem is solved for the class of Sturm-Liouville operators with singular real-valued potentials from the space $W^{-1}_2(0,1)$. The potential is recovered via the eigenvalues and the corresponding norming constants. The reconstruction algorithm is presented and its stability proved. Also, the set of all possible spectral data is explicitly described and the isospectral sets are characterized.Comment: Submitted to Inverse Problem

Initial value problems in linear integral operator equations

For some general linear integral operator equations, we investigate consequent initial value problems by using the theory of reproducing kernels. A new method is proposed which -- in particular -- generates a new field among initial value problems, linear integral operators, eigenfunctions and values, integral transforms and reproducing kernels. In particular, examples are worked out for the integral equations of Lalesco-Picard, Dixon and Tricomi types