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EXTENSIONS OF HIONG’S INEQUALITY MINGLIANG FANG AND DEGUI YANG
, 2002
"... ABSTRACT. In this paper, we treat the value distribution of φf n−1 f (k) , where f is a transcendental meromorphic function, φ is a meromorphic function satisfying T (r, φ) = S(r, f), n and k are positive integers. We generalize some results of Hiong and Yu. ..."
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ABSTRACT. In this paper, we treat the value distribution of φf n−1 f (k) , where f is a transcendental meromorphic function, φ is a meromorphic function satisfying T (r, φ) = S(r, f), n and k are positive integers. We generalize some results of Hiong and Yu.
A new invariant for σ models
 Commun. Math. Phys. Vol 209 No
, 2000
"... We introduce a new invariant for σ models (and foliations more generally) using the even pairing between Khomology and cyclic homology. We try to calculate it for the simplest case of foliations, namely principal bundles. We end up by discussing some possible physical applications including quantum ..."
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Cited by 11 (11 self)
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We introduce a new invariant for σ models (and foliations more generally) using the even pairing between Khomology and cyclic homology. We try to calculate it for the simplest case of foliations, namely principal bundles. We end up by discussing some possible physical applications including quantum gravity and MTheory. In particular for MTheory we propose an explicit topological Lagrangian and then using Sduality we conjecture on the existence of certain plane fields on S 11. PACS classification: 11.10.z; 11.15.q; 11.30.Ly
Normal Families of Meromorphic Functions whose Derivatives Omit a Function
, 2002
"... Abstract. Let F be a family of functions meromorphic on the plane domain D, and let h be a holomorphic function on D, h 6 ´ 0. Suppose that, for each f 2 F, f (m)(z) 6 = h(z) for z 2 D. Then F is normal on D (i) if all zeros of functions in F have multiplicity at least m+3, or (ii) if all zeros of ..."
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Cited by 3 (0 self)
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Abstract. Let F be a family of functions meromorphic on the plane domain D, and let h be a holomorphic function on D, h 6 ´ 0. Suppose that, for each f 2 F, f (m)(z) 6 = h(z) for z 2 D. Then F is normal on D (i) if all zeros of functions in F have multiplicity at least m+3, or (ii) if all zeros of functions in F have multiplicity at least m + 2 and h has only multiple zeros on D, or (iii) if all poles of functions in F are multiple and all zeros have multiplicity at least m + 2.
Computing approximate GCD of univariate polynomials by structured total least norm
 Institute of Systems Science, AMSS, Academia Sinica
, 2004
"... Abstract. The problem of approximating the greatest common divisor(GCD) for polynomials with inexact coefficients can be formulated as a low rank approximation problem with Sylvester matrix. This paper presents a method based on Structured Total Least Norm(STLN) for constructing the nearest Sylveste ..."
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Cited by 6 (0 self)
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Abstract. The problem of approximating the greatest common divisor(GCD) for polynomials with inexact coefficients can be formulated as a low rank approximation problem with Sylvester matrix. This paper presents a method based on Structured Total Least Norm(STLN) for constructing the nearest Sylvester matrix of given lower rank. We present algorithms for computing the nearest GCD and a certified ɛGCD for a given tolerance ɛ. The running time of our algorithm is polynomial in the degrees of polynomials. We also show the performance of the algorithms on a set of univariate polynomials.
Orbifold cohomology of hypertoric varieties
, 2007
"... Hypertoric varieties are hyperkähler analogues of toric varieties, and are constructed as abelian hyperkähler quotients T ∗ C n /T of a quaternionic affine space. Just as symplectic toric orbifolds are determined by labelled polytopes, orbifold hypertoric varieties are intimately related to the comb ..."
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Cited by 6 (2 self)
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Hypertoric varieties are hyperkähler analogues of toric varieties, and are constructed as abelian hyperkähler quotients T ∗ C n /T of a quaternionic affine space. Just as symplectic toric orbifolds are determined by labelled polytopes, orbifold hypertoric varieties are intimately related to the combinatorics of hyperplane arrangements. By developing hyperkähler analogues of symplectic techniques developed by Goldin, Holm, and Knutson, we give an explicit combinatorial description of the ChenRuan orbifold cohomology of an orbifold hypertoric variety in terms of the combinatorial data of a rational cooriented weighted hyperplane arrangementH. We detail several explicit
Sudbery A. Quantum Supergroups of GL(nm) type: Differential Forms, Koszul Complex and Berezinians
, 1993
"... Abstract. We introduce and study the Koszul complex for a Hecke Rmatrix. Its cohomologies, called the Berezinian, are used to define quantum superdeterminant for a Hecke Rmatrix. Their behaviour with respect to Hecke sum of Rmatrices is studied. Given a Hecke Rmatrix in ndimensional vector spac ..."
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Cited by 6 (0 self)
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Abstract. We introduce and study the Koszul complex for a Hecke Rmatrix. Its cohomologies, called the Berezinian, are used to define quantum superdeterminant for a Hecke Rmatrix. Their behaviour with respect to Hecke sum of Rmatrices is studied. Given a Hecke Rmatrix in ndimensional vector space, we construct a Hecke Rmatrix in 2ndimensional vector space commuting with a differential. The notion of a quantum differential supergroup is derived. Its algebra of functions is a differential coquasitriangular Hopf algebra, having the usual algebra of differential forms as a quotient. Examples of superdeterminants related to these algebras are calculated. Several remarks about Woronowicz’s theory are made. 0.1. Short description of the paper. 0.1.1. We start with constructing differential Hopf algebras (Section 1). Data for such construction are morphisms in the category of graded differential complexes. 0.1.2. Given a Hecke Rmatrix for a vector space V, we construct in this paper another Hecke Rmatrix R for the space W = V ⊕ V equipped with the differential d = () 0 1 0 0 and the grading σ: W → W, σ = ()
DIRECTION FINDING FOR BISTATIC MIMO RADAR USING EM MAXIMUM LIKELIHOOD ALGORITHM
"... Abstract—In this paper, we investigate an expectationmaximization (EM) maximum likelihood (ML) algorithm of direction finding (DF) for bistatic multipleinput multipleoutput (MIMO) radar, where it is shown that the DF problem can be described as a special case of ML estimation with incomplete data ..."
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Abstract—In this paper, we investigate an expectationmaximization (EM) maximum likelihood (ML) algorithm of direction finding (DF) for bistatic multipleinput multipleoutput (MIMO) radar, where it is shown that the DF problem can be described as a special case of ML estimation with incomplete data. First, we introduce the signal and the noise models, and derive the ML estimations of the direction parameters. Considering the computational complexity, we make use of the EM algorithm to compute the ML algorithm, referred to EM ML algorithm, which can be applied to the arbitrary antenna geometry and realize the autopairing between directionofdepartures (DODs) and directionofarrivals (DOAs). Then the initialization is considered. In addition, both the convergence and the CramerRao bound (CRB) analysis are derived. Finally, simulation results demonstrate the potential and asymptotic efficiency of this approach for MIMO radar systems. 1.
Research Article Cerebral Activity Changes in Different Traditional Chinese Medicine Patterns of Psychogenic Erectile
"... Copyright © 2015 Qi Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Background. Pattern differentiation is the foundation ..."
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Copyright © 2015 Qi Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Background. Pattern differentiation is the foundation of traditional Chinese medicine (TCM) treatment for erectile dysfunction (ED). This study aims to investigate the differences in cerebral activity in ED patients with different TCM patterns. Methods. 27 psychogenic ED patients and 27 healthy subjects (HS) were enrolled in this study. Each participant underwent an fMRI scan in resting state. The fractional amplitude of lowfrequency fluctuation (fALFF) was used to detect the brain activity changes in ED patients with different patterns. Results.Compared to HS, ED patients showed an increased cerebral activity in bilateral cerebellum,
Results 1  10
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70