30,976 research outputs found
The K-Z Equation and the Quantum-Group Difference Equation in Quantum Self-dual Yang-Mills Theory
From the time-independent current \tcj(\bar y,\bar k) in the quantum
self-dual Yang-Mills (SDYM) theory, we construct new group-valued quantum
fields and which satisfy
a set of exchange algebras such that fields of \tcj(\bar y,\bar k)\sim\tilde
U(\bar y,\bar k)~\partial\bar y~\tilde U^{-1}(\bar y,\bar k) satisfy the
original time-independent current algebras. For the correlation functions of
the products of the and fields defined in the invariant state constructed through the current
\tcj(\bar y,\bar k) we can derive the Knizhnik-Zamolodchikov (K-Z) equations
with an additional spatial dependence on . From the and fields we construct the
quantum-group generators --- local, global, and semi-local --- and their
algebraic relations. For the correlation functions of the products of the
and fields defined in the invariant state
constructed through the semi-local quantum-group generators we obtain the
quantum-group difference equations. We give the explicit solution to the two
point function.Comment: 15 pages, uses phyzz
Fitting an error distribution in some heteroscedastic time series models
This paper addresses the problem of fitting a known distribution to the
innovation distribution in a class of stationary and ergodic time series
models. The asymptotic null distribution of the usual Kolmogorov--Smirnov test
based on the residuals generally depends on the underlying model parameters and
the error distribution. To overcome the dependence on the underlying model
parameters, we propose that tests be based on a vector of certain weighted
residual empirical processes. Under the null hypothesis and under minimal
moment conditions, this vector of processes is shown to converge weakly to a
vector of independent copies of a Gaussian process whose covariance function
depends only on the fitted distribution and not on the model. Under certain
local alternatives, the proposed test is shown to have nontrivial asymptotic
power. The Monte Carlo critical values of this test are tabulated when fitting
standard normal and double exponential distributions. The results obtained are
shown to be applicable to GARCH and ARMA--GARCH models, the often used models
in econometrics and finance. A simulation study shows that the test has
satisfactory size and power for finite samples at these models. The paper also
contains an asymptotic uniform expansion result for a general weighted residual
empirical process useful in heteroscedastic models under minimal moment
conditions, a result of independent interest.Comment: Published at http://dx.doi.org/10.1214/009053606000000191 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Fire extinguishant materials
Fire extinguishant composition comprising a mixture of a finely divided aluminum compound and alkali metal, stannous or plumbous halide is provided. Aluminum compound may be aluminum hydroxide, alumina or boehmite but preferably it is an alkali metal dawsonite. The metal halide may be an alkali metal, e.g. potassium iodide, bromide or chloride or stannous or plumbous iodide, bromide or chloride. Potassium iodide is preferred
Convolutional compressed sensing using deterministic sequences
This is the author's accepted manuscript (with working title "Semi-universal convolutional compressed sensing using (nearly) perfect sequences"). The final published article is available from the link below. Copyright @ 2012 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.In this paper, a new class of orthogonal circulant matrices built from deterministic sequences is proposed for convolution-based compressed sensing (CS). In contrast to random convolution, the coefficients of the underlying filter are given by the discrete Fourier transform of a deterministic sequence with good autocorrelation. Both uniform recovery and non-uniform recovery of sparse signals are investigated, based on the coherence parameter of the proposed sensing matrices. Many examples of the sequences are investigated, particularly the Frank-Zadoff-Chu (FZC) sequence, the m-sequence and the Golay sequence. A salient feature of the proposed sensing matrices is that they can not only handle sparse signals in the time domain, but also those in the frequency and/or or discrete-cosine transform (DCT) domain
Dual-lattice ordering and partial lattice reduction for SIC-based MIMO detection
This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2009 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.In this paper, we propose low-complexity lattice detection algorithms for successive interference cancelation (SIC) in multi-input multi-output (MIMO) communications. First, we present a dual-lattice view of the vertical Bell Labs Layered Space-Time (V-BLAST) detection. We show that V-BLAST ordering is equivalent to applying sorted QR decomposition to the dual basis, or equivalently, applying sorted Cholesky decomposition to the associated Gram matrix. This new view results in lower detection complexity and allows simultaneous ordering and detection. Second, we propose a partial reduction algorithm that only performs lattice reduction for the last several, weak substreams, whose implementation is also facilitated by the dual-lattice view. By tuning the block size of the partial reduction (hence the complexity), it can achieve a variable diversity order, hence offering a graceful tradeoff between performance and complexity for SIC-based MIMO detection. Numerical results are presented to compare the computational costs and to verify the achieved diversity order
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