66,710 research outputs found
Oscillator Variations of the Classical Theorem on Harmonic Polynomials
We study two-parameter oscillator variations of the classical theorem on
harmonic polynomials, associated with noncanonical oscillator representations
of sl(n) and o(n). We find the condition when the homogeneous solution spaces
of the variated Laplace equation are irreducible modules of the concerned
algebras and the homogeneous subspaces are direct sums of the images of these
solution subspaces under the powers of the dual differential operator. This
establishes a local (sl(2),sl(n)) and (sl(2),o(n)) Howe duality, respectively.
In generic case, the obtained irreducible o(n)-modules are infinite-dimensional
non-unitary modules without highest-weight vectors. As an application, we
determine the structure of noncanonical oscillator representations of sp(2n).
When both parameters are equal to the maximal allowed value, we obtain an
infinite family of explicit irreducible (G,K)-modules for o(n) and sp(2n).
Methodologically we have extensively used partial differential equations to
solve representation problems.Comment: 49pages; This paper is a two-parameter extension of the first
author's work "arXiv:0804.0305v2[math.RT]," which is equivalent to the
one-paratemter special case of this work. The approaches have changed. The
mistakes there have been correcte
Supersymmetyric Analogues of the Classical Theorem on Harmonic Polynomials
Classical harmonic analysis says that the spaces of homogeneous harmonic
polynomials (solutions of Laplace equation) are irreducible modules of the
corresponding orthogonal Lie group (algebra) and the whole polynomial algebra
is a free module over the invariant polynomials generated by harmonic
polynomials. In this paper, we first establish two-parameter \mbb{Z}^2-graded
supersymmetric oscillator generalizations of the above theorem for the Lie
superalgebra . Then we extend the result to two-parameter
\mbb{Z}-graded supersymmetric oscillator generalizations of the above theorem
for the Lie superalgebras and .Comment: 35pages. This an extension and replacement of the first author's
article arXiv:1001.3474v1[Math.RT
Volume Fluctuation and Autocorrelation Effects in the Moment Analysis of Net-proton Multiplicity Distributions in Heavy-Ion Collisions
Moments (Variance (), Skewness(), Kurtosis()) of
multiplicity distributions of conserved quantities, such as
net-baryon,net-charge and net-strangeness, are predicted to be sensitive to the
correlation length of the system and connected to the thermodynamic
susceptibilities computed in Lattice QCD and Hadron Resonance Gas (HRG) model.
In this paper, we present several measurement artifacts that could lead to
volume fluctuation and auto-correlation effects in the moment analysis of
net-proton multiplicity distributions in heavy-ion collisions using the UrQMD
model. We discuss methods to overcome these artifacts so that the extracted
moments could be used to obtain physical conclusions. In addition we present
methods to properly estimate the statistical errors in moment analysis.Comment: 8 pages, 12 figure
Tunable and switchable multi-wavelength erbium-doped fiber ring laser based on a modified dual-pass Mach-Zehnder interferometer
A tunable and switchable multi-wavelength erbium-doped fiber ring laser based
on a new type tunable comb filter is proposed and demonstrated. By adjusting
the polarization controllers, dual-function operation of the channel spacing
tunability and the wavelength switching (interleaving) can be readily achieved.
Up to 29 stable lasing lines with 0.4 nm spacing and 14 lasing wavelengths with
0.8 nm spacing in 3 dB bandwidth were obtained at room temperature. In
addition, the lasing output, including the number of the lasing lines, the
lasing evenness and the lasing locations, can also be flexibly adjusted through
the wavelength-dependent polarization rotation mechanism.Comment: 11 pages, 6 figure
Benefits from Superposed Hawkes Processes
The superposition of temporal point processes has been studied for many
years, although the usefulness of such models for practical applications has
not be fully developed. We investigate superposed Hawkes process as an
important class of such models, with properties studied in the framework of
least squares estimation. The superposition of Hawkes processes is demonstrated
to be beneficial for tightening the upper bound of excess risk under certain
conditions, and we show the feasibility of the benefit in typical situations.
The usefulness of superposed Hawkes processes is verified on synthetic data,
and its potential to solve the cold-start problem of recommendation systems is
demonstrated on real-world data
Baseline for the cumulants of net-proton distributions at STAR
We present a systematic comparison between the recently measured cumulants of
the net-proton distributions by STAR for 0-5% central Au+Au collisions at
=7.7-200 GeV and two kinds of possible baseline measures, the
Poisson and Binomial baselines. These baseline measures are assuming that the
proton and anti-proton distributions independently follow Poisson statistics or
Binomial statistics. The higher order cumulant net-proton data are observed to
deviate from all the baseline measures studied at 19.6 and 27 GeV. We also
compare the net-proton with net-baryon fluctuations in UrQMD and AMPT model,
and convert the net-proton fluctuations to net-baryon fluctuations in AMPT
model by using a set of formula.Comment: 4 pages, 5 figures, Proceedings of XXIV International Conference on
Ultrarelativistic Nucleus-Nucleus Collisions (Quark Matter 2014), May 19-24,
2014, Darmstadt, German
Completely Positive Tensors and Multi-Hypergraphs
Completely positive graphs have been employed to associate with completely
positive matrices for characterizing the intrinsic zero patterns. As tensors
have been widely recognized as a higher-order extension of matrices, the
multi-hypergraph, regarded as a generalization of graphs, is then introduced to
associate with tensors for the study of complete positivity. To describe the
dependence of the corresponding zero pattern for a special type of completely
positive tensors--the completely positive tensors, the completely
positive multi-hypergraph is defined. By characterizing properties of the
associated multi-hypergraph, we provide necessary and sufficient conditions for
any associated tensor to be completely positive. Furthermore,
a necessary and sufficient condition for a uniform multi-hypergraph to be
completely positive multi-hypergraph is proposed as well
Numerical meshless solution of high-dimensional sine-Gordon equations via Fourier HDMR-HC approximation
In this paper, an implicit time stepping meshless scheme is proposed to find
the numerical solution of high-dimensional sine-Gordon equations (SGEs) by
combining the high dimensional model representation (HDMR) and the Fourier
hyperbolic cross (HC) approximation. To ensure the sparseness of the relevant
coefficient matrices of the implicit time stepping scheme, the whole domain is
first divided into a set of subdomains, and the relevant derivatives in
high-dimension can be separately approximated by the Fourier HDMR-HC
approximation in each subdomain. The proposed method allows for stable large
time-steps and a relatively small number of nodes with satisfactory accuracy.
The numerical examples show that the proposed method is very attractive for
simulating the high-dimensional SGEs
Sequential Analysis of Cox Model under Response Dependent Allocation
Sellke and Siegmund (1983) developed the Brownian approximation to the Cox
partial likelihood score as a process of calendar time, laying the foundation
for group sequential analysis of survival studies. We extend their results to
cover situations in which treatment allocations may depend on observed
outcomes. The new development makes use of the entry time and calendar time
along with the corresponding -filtrations to handle the natural
information accumulation. Large sample properties are established under
suitable regularity conditions
Some new properties of Confluent Hypergeometric Functions
The confluent hypergeometric functions (the Kummer functions) defined by
${}_{1}F_{1}(\alpha;\gamma;z):=\sum_{n=0}^{\infty}\frac{(\alpha)_{n}}{n!(\gamma)_{n}}z^{n}\
(\gamma\neq 0,-1,-2,\cdots){}_{1}F_{1}(\alpha;\gamma;z)\alpha\in
\mathbb{Z}_{\leq 0}\alpha\not\in \mathbb{Z}_{\leq 0}{}_{1}F_{1}(\alpha;\gamma;z)T(r,{}_{1}F_{1}(\alpha;\gamma;z))m\left(r,
\frac{{}_{1}F_{1}'(\alpha;\gamma;z)}{{}_{1}F_{1}(\alpha;\gamma;z)}\right)c$-values.Comment: 20 pages. Submitted to Journal of Mathematical Analysis and
Application
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