197 research outputs found
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 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, ). 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 is odd) and the lowest lying gaps in
the energy spectrum of the latter periodic potential up to and including the
gap and having the same parity as . 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 .
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
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