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Jun 29, 2018
06/18

by
Lun Zhang

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In this paper, we consider the Wright's generalized Bessel kernel $K^{(\alpha,\theta)}(x,y)$ defined by $$\theta x^{\alpha}\int_0^1J_{\frac{\alpha+1}{\theta},\frac{1}{\theta}}(ux)J_{\alpha+1,\theta}((uy)^{\theta})u^\alpha\,\mathrm{d} u, \qquad \alpha>-1, \qquad \theta>0,$$ where $$J_{a,b}(x)=\sum_{j=0}^\infty\frac{(-x)^j}{j!\Gamma(a+bj)},\qquad a\in\mathbb{C},\qquad b>-1,$$ is Wright's generalization of the Bessel function. This non-symmetric kernel, which generalizes the classical...

Topics: Exactly Solvable and Integrable Systems, Classical Analysis and ODEs, Mathematical Physics,...

Source: http://arxiv.org/abs/1608.02867

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60

Sep 23, 2013
09/13

by
Lun Zhang

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The product of M complex random Gaussian matrices of size N has recently been studied by Akemann, Kieburg and Wei. They showed that, for fixed M and N, the joint probability distribution for the squared singular values of the product matrix forms a determinantal point process with a correlation kernel determined by certain biorthogonal polynomials that can be explicitly constructed. We find that, in the case M=2, the relevant biorthogonal polynomials are actually special cases of multiple...

Source: http://arxiv.org/abs/1305.0726v2

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17

Jun 26, 2018
06/18

by
Lun Zhang

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We consider $n$ particles $0\leq x_1-1,~~ \theta>0, $$ where $Z_n$ is the normalization constant. This distribution arises in the context of modeling disordered conductors in the metallic regime, and can also be realized as the distribution for squared singular values of certain triangular random matrices. We give a double contour integral formula for the correlation kernel, which allows us to establish universality for the local statistics of the particles, namely, the bulk universality and...

Topics: Mathematics, Probability, Mathematical Physics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1502.03160

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4.0

Jun 29, 2018
06/18

by
Lun Zhang

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We consider mixed type multiple orthogonal polynomials associated with a system of weight functions consisting of two vectors. One vector is defined in terms of scaled modified Bessel function of the first kind $I_\mu$ and $I_{\mu+1}$, the other vector is defined in terms of scaled modified Bessel function of the second kind $K_\nu$ and $K_{\nu+1}$. We show that the corresponding mixed type multiple orthogonal polynomials exist. For the special case that each multi-index is on or close to the...

Topics: Classical Analysis and ODEs, Mathematical Physics, Mathematics

Source: http://arxiv.org/abs/1605.01899

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Sep 17, 2013
09/13

by
Lun Zhang; Pablo Román

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We study the asymptotic zero distribution of type II multiple orthogonal polynomials associated with two Macdonald functions (modified Bessel functions of the second kind). Based on the four-term recurrence relation, it is shown that, after proper scaling, the sequence of normalized zero counting measures converges weakly to the first component of a vector of two measures which satisfies a vector equilibrium problem with two external fields. We also give the explicit formula for the equilibrium...

Source: http://arxiv.org/abs/1003.4692v2

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4.0

Jun 30, 2018
06/18

by
Lun Zhang; Galina Filipuk

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We consider determinants of Wronskian type whose entries are multiple orthogonal polynomials associated with a path connecting two multi-indices. By assuming that the weight functions form an algebraic Chebyshev (AT) system, we show that the polynomials represented by the Wronskians keep a constant sign in some cases, while in some other cases oscillatory behavior appears, which generalizes classical results for orthogonal polynomials due to Karlin and Szeg\H{o}. There are two applications of...

Topics: Mathematics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1402.1569

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5.0

Jun 30, 2018
06/18

by
Haiyong Wang; Lun Zhang

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In this paper, we are concerned with Jacobi polynomials $P_n^{(\alpha,\beta)}(x)$ on the Bernstein ellipse with motivation mainly coming from recent studies of convergence rate of spectral interpolation. An explicit representation of $P_n^{(\alpha,\beta)}(x)$ is derived in the variable of parametrization. This formula further allows us to show that the maximum value of $\left|P_n^{(\alpha,\beta)}(z)\right|$ over the Bernstein ellipse is attained at one of the endpoints of the major axis if...

Topics: Classical Analysis and ODEs, Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1703.04243

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Sep 22, 2013
09/13

by
Dan Dai; Lun Zhang

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We study the Hankel determinant of the generalized Jacobi weight $(x-t)^{\gamma}x^\alpha(1-x)^\beta$ for $x\in[0,1]$ with $\alpha, \beta>0$, $t < 0 $ and $\gamma\in\mathbb{R}$. Based on the ladder operators for the corresponding monic orthogonal polynomials $P_n(x)$, it is shown that the logarithmic derivative of Hankel determinant is characterized by a $\tau$-function for the Painlev\'e VI system.

Source: http://arxiv.org/abs/0908.0558v2

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6.0

Jun 29, 2018
06/18

by
San-Dong Guo; Lun Zhang

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Strain engineering is a very effective method to tune electronic, optical, topological and thermoelectric properties of materials. In this work, we systematically study biaxial strain dependence of electronic structures and thermoelectric properties (both electron and phonon parts) of monolayer $\mathrm{PtSe_2}$ with generalized gradient approximation (GGA) plus spin-orbit coupling (SOC) for electron part and GGA for phonon part. Calculated results show that compressive or tensile strain can...

Topics: Materials Science, Condensed Matter

Source: http://arxiv.org/abs/1607.04979

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Sep 24, 2013
09/13

by
Haiyong Wang; Lun Zhang; Daan Huybrechs

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In this paper, we study the asymptotics and fast computation of the one-sided oscillatory Hilbert transforms of the form $$H^{+}(f(t)e^{i\omega t})(x)=-int_{0}^{\infty}e^{i\omega t}\frac{f(t)}{t-x}dt,\qquad \omega>0,\qquad x\geq 0,$$ where the bar indicates the Cauchy principal value and $f$ is a real-valued function with analytic continuation in the first quadrant, except possibly a branch point of algebraic type at the origin. When $x=0$, the integral is interpreted as a Hadamard...

Source: http://arxiv.org/abs/1112.2282v1

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Sep 18, 2013
09/13

by
Estelle Basor; Yang Chen; Lun Zhang

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In this paper we study, $\textsf{Prob}(n,a,b),$ the probability that all the eigenvalues of finite $n$ unitary ensembles lie in the interval $(a,b)$. This is identical to the probability that the largest eigenvalue is less than $b$ and the smallest eigenvalue is greater than $a$. It is shown that a quantity allied to $\textsf{Prob}(n,a,b)$, namely, $$ H_n(a,b):=\left[\frac{\partial}{\partial a}+\frac{\partial}{\partial b}\right]\ln\textsf{Prob}(n,a,b),$$ in the Gaussian Unitary Ensemble (GUE)...

Source: http://arxiv.org/abs/1102.0402v1

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Sep 23, 2013
09/13

by
Steven Delvaux; Dries Geudens; Lun Zhang

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We study the chiral two-matrix model with polynomial potential functions $V$ and $W$, which was introduced by Akemann, Damgaard, Osborn and Splittorff. We show that the squared singular values of each of the individual matrices in this model form a determinantal point process with correlation kernel determined by a matrix-valued Riemann-Hilbert problem. The size of the Riemann-Hilbert matrix depends on the degree of the potential function $W$ (or $V$ respectively). In this way we obtain the...

Source: http://arxiv.org/abs/1303.1130v1

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Jun 30, 2018
06/18

by
Dang-Zheng Liu; Dong Wang; Lun Zhang

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It has been shown by Akemann, Ipsen and Kieburg that the squared singular values of products of $M$ rectangular random matrices with independent complex Gaussian entries are distributed according to a determinantal point process with a correlation kernel that admits a representation in terms of Meijer G-functions. We prove the universality of the local statistics of the squared singular values, namely, the bulk universality given by the sine kernel and the edge universality given by the Airy...

Topics: Probability, Mathematics, Mathematical Physics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1412.6777

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Sep 21, 2013
09/13

by
Galina Filipuk; Walter Van Assche; Lun Zhang

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In this paper, we obtain the ladder operators and associated compatibility conditions for the type I and the type II multiple orthogonal polynomials. These ladder equations extend known results for orthogonal polynomials and can be used to derive the differential equations satisfied by multiple orthogonal polynomials. Our approach is based on Riemann-Hilbert problems and the Christoffel-Darboux formula for multiple orthogonal polynomials, and the nearest-neighbor recurrence relations. As an...

Source: http://arxiv.org/abs/1204.5058v1

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3.0

Jun 30, 2018
06/18

by
Min Huang; Shuai-Xia Xu; Lun Zhang

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We show that the well-known Hastings-McLeod solution to the second Painlev\'{e} equation is pole-free in the region $\arg x \in [-\frac{\pi}{3},\frac{\pi}{3}]\cup [\frac{2\pi}{3},\frac{ 4 \pi}{3}]$, which proves an important special case of a general conjecture concerning pole distributions of Painlev\'{e} transcedents proposed by Novokshenov. Our strategy is to construct explicit quasi-solutions approximating the Hastings-McLeod solution in different regions of the complex plane, and estimate...

Topics: Mathematics, Mathematical Physics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1410.3338

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Sep 23, 2013
09/13

by
Galina Filipuk; Walter Van Assche; Lun Zhang

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We show that the coefficients of the three-term recurrence relation for orthogonal polynomials with respect to a semi-classical extension of the Laguerre weight satisfy the fourth Painlev\'e equation when viewed as functions of one of the parameters in the weight. We compare different approaches to derive this result, namely, the ladder operators approach, the isomonodromy deformations approach and combining the Toda system for the recurrence coefficients with a discrete equation. We also...

Source: http://arxiv.org/abs/1105.5229v1

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Sep 19, 2013
09/13

by
Steven Delvaux; Arno B. J. Kuijlaars; Lun Zhang

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We study a model of $n$ one-dimensional non-intersecting Brownian motions with two prescribed starting points at time $t=0$ and two prescribed ending points at time $t=1$ in a critical regime where the paths fill two tangent ellipses in the time-space plane as $n \to \infty$. The limiting mean density for the positions of the Brownian paths at the time of tangency consists of two touching semicircles, possibly of different sizes. We show that in an appropriate double scaling limit, there is a...

Source: http://arxiv.org/abs/1009.2457v1

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Sep 23, 2013
09/13

by
Steven Delvaux; Arno B. J. Kuijlaars; Pablo Román; Lun Zhang

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We consider a model of $n$ non-intersecting squared Bessel processes with one starting point $a>0$ at time t=0 and one ending point $b>0$ at time $t=T$. After proper scaling, the paths fill out a region in the $tx$-plane. Depending on the value of the product $ab$ the region may come to the hard edge at 0, or not. We formulate a vector equilibrium problem for this model, which is defined for three measures, with upper constraints on the first and third measures and an external field on...

Source: http://arxiv.org/abs/1105.2481v2

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5.0

Jun 29, 2018
06/18

by
Bo Li; Tianfu Wu; Shuai Shao; Lun Zhang; Rufeng Chu

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Jointly integrating aspect ratio and context has been extensively studied and shown performance improvement in traditional object detection systems such as the DPMs. It, however, has been largely ignored in deep neural network based detection systems. This paper presents a method of integrating a mixture of object models and region-based convolutional networks for accurate object detection. Each mixture component accounts for both object aspect ratio and multi-scale contextual information...

Topics: Computer Vision and Pattern Recognition, Computing Research Repository

Source: http://arxiv.org/abs/1612.00534

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58

Sep 21, 2013
09/13

by
Lies Boelen; Galina Filipuk; Christophe Smet; Walter Van Assche; Lun Zhang

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We study the recurrence coefficients of the orthogonal polynomials with respect to a semi-classical extension of the Krawtchouk weight. We derive a coupled discrete system for these coefficients and show that they satisfy the fifth Painlev\'e equation when viewed as functions of one of the parameters in the weight.

Source: http://arxiv.org/abs/1204.5070v2

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Oct 25, 2014
10/14

by
Su-Que, Lan; Ya-Ning, Meng; Xing-Pu, Li; Ye-Lun, Zhang; Guang-Yao, Song; Hui-Juan, Ma

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This article is from Nutrition Journal , volume 12 . Abstract Background: Steamed wheat bread have previously been shown to induce comparatively high postprandial plasma glucose responses, on the contrary, buckwheat products induced lower postprandial plasma glucose. The present study was to assess the effects of micronutrient enriched bread wheat variety Jizi439 and buckwheat on postprandial plasma glucose in healthy and diabetic subjects comparing with buckwheat and other bread wheat...

Source: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3679746

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Oct 27, 2014
10/14

by
Tsai, Cheng-Kun; Wang, Tzung-Dau; Lin, Jong-Wei; Hsu, Ron-Bin; Guo, Lun-Zhang; Chen, San-Tai; Liu, Tzu-Ming

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This article is from Biomedical Optics Express , volume 4 . Abstract Using the sectioning capability of third harmonic generation (THG) microscopy, we assessed the morphologic features of human adipocytes directly without fixation and labeling. At the plane of the largest cross-sectional area, both area-equivalent circular diameters (AECD) and perimeters of adipocytes were measured, and their statistical distributions were examined. We found, in patients with no cardiovascular risk factors, the...

Source: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3539194