作者机构：
[Zhang, Xinan] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.;[Zhang, Xinan; Singh, Satish; Kumta, Prashant; Banerjee, Ipsita] Univ Pittsburgh, Dept Chem Engn, Pittsburgh, PA 15261 USA.;[Kumta, Prashant; Jaramillo, Maria; Banerjee, Ipsita] Univ Pittsburgh, Dept Bioengn, Pittsburgh, PA USA.;[Kumta, Prashant] Univ Pittsburgh, Dept Mech Engn & Mat Sci, Pittsburgh, PA USA.;[Kumta, Prashant] Univ Pittsburgh, Ctr Complex Engn Multifunct Mat, Pittsburgh, PA USA.
通讯机构：
[Zhang, Xinan] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.
摘要：
Embryonic stem cells are conventionally differentiated by modulating specific growth factors in the cell culture media. Recently the effect of cellular mechanical microenvironment in inducing phenotype specific differentiation has attracted considerable attention. We have shown the possibility of inducing endoderm differentiation by culturing the stem cells on fibrin substrates of specific stiffness [1]. Here, we analyze the regulatory network involved in such mechanically induced endoderm differentiation under two different experimental configurations of 2-dimensional and 3-dimensional culture, respectively. Mouse embryonic stem cells are differentiated on an array of substrates of varying mechanical properties and analyzed for relevant endoderm markers. The experimental data set is further analyzed for identification of co-regulated transcription factors across different substrate conditions using the technique of bi-clustering. Overlapped bi-clusters are identified following an optimization formulation, which is solved using an evolutionary algorithm. While typically such analysis is performed at the mean value of expression data across experimental repeats, the variability of stem cell systems reduces the confidence on such analysis of mean data. Bootstrapping technique is thus integrated with the bi-clustering algorithm to determine sets of robust bi-clusters, which is found to differ significantly from corresponding bi-clusters at the mean data value. Analysis of robust bi-clusters reveals an overall similar network interaction as has been reported for chemically induced endoderm or endodermal organs but with differences in patterning between 2-dimensional and 3-dimensional culture. Such analysis sheds light on the pathway of stem cell differentiation indicating the prospect of the two culture configurations for further maturation.
期刊：
Journal of Differential Equations,2014年257(2):566-600 ISSN：0022-0396
通讯作者：
Li, GB
作者机构：
[Li, Gongbao] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Li, Gongbao] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
关键词：
Kirchhoff equation;Ground state solutions;Pohoz̆aev type identity;Variational methods
摘要：
In this paper, we study the following nonlinear problem of Kirchhoff type with pure power nonlinearities: {-(a + b integral(R3) vertical bar Du vertical bar(2)) Delta u + V(x)u = vertical bar u vertical bar(p-1)u, x is an element of R-3, (0.1) u is an element of H-1 (R-3), u > 0, x is an element of R-3, where a, b > 0 are constants, 2 < p < 5 and V : R-3 -> R. Under certain assumptions on V. we prove that (0.1) has a positive ground state solution by using a monotonicity trick and a new version of global compactness lemma. Our main results especially solve problem (0.1) in the case where p is an element of (2, 3], which has been an open problem for Kirchhoff equations and can be viewed as a partial extension of a recent result of He and Zou in [14] concerning the existence of positive solutions to the nonlinear Kirchhoff problem {-(epsilon(2)a + epsilon b integral(R3) vertical bar Du vertical bar(2)) Delta u + V(x)u = f(u), x is an element of R-3, u is an element of H-1 (R-3), u > 0, x is an element of R-3, where epsilon > 0 is a parameter, V(x) is a positive continuous potential and f (u) similar to vertical bar u vertical bar(p-1)u with 3 < p < 5 and satisfies the Ambrosetti-Rabinowitz type condition. Our main results extend also the arguments used in [7,33], which deal with Schrodinger-Poisson system with pure power nonlinearities, to the Kirchhoff type problem. (C) 2014 Elsevier Inc. All rights reserved.
期刊：
IEEE Transactions on Industrial Electronics,2013年60(8):3218-3226 ISSN：0278-0046
通讯作者：
Jian, L.(ln.jian@siat.ac.cn)
作者机构：
[Zhao, Dongfang; Xue, Honghong; Zhu, Xinyu] School of Mathematics and Statistics, Huazhong Normal University, Wuhan 430079, China;[Jian, Linni] Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China;[Shao, Z.Y.] Department of Electrical and Electronic Engineering, University of Hong Kong, Hong Kong, Hong Kong;[Xu, Guoqing] RandD Centre for Electric Vehicle, Chinese Academy of Sciences, Shenzhen 518055, China;[Xu, Guoqing] Department of Electrical Engineering, Tongji University, Shanghai 200092, China
通讯机构：
[Jian, Linni] Chinese Acad Sci, Shenzhen Inst Adv Technol, Shenzhen 518055, Peoples R China.
关键词：
Coordinated charging;load variance;microgrid;plug-in hybrid electric vehicle (EV) (HEV) (PHEV);regulated charging;smart grid;vehicle to grid (V2G)
通讯机构：
[Xu, Ying] Univ Georgia, Dept Biochem & Mol Biol, Computat Syst Biol Lab, Athens, GA 30602 USA.
摘要：
We have recently developed a new version of the DOOR operon database, DOOR 2.0, which is available online at http://csbl.bmb.uga.edu/DOOR/ and will be updated on a regular basis. DOOR 2.0 contains genome-scale operons for 2072 prokaryotes with complete genomes, three times the number of genomes covered in the previous version published in 2009. DOOR 2.0 has a number of new features, compared with its previous version, including (i) more than 250 000 transcription units, experimentally validated or computationally predicted based on RNA-seq data, providing a dynamic functional view of the underlying operons; (ii) an integrated operon-centric data resource that provides not only operons for each covered genome but also their functional and regulatory information such as their cis-regulatory binding sites for transcription initiation and termination, gene expression levels estimated based on RNA-seq data and conservation information across multiple genomes; (iii) a high-performance web service for online operon prediction on user-provided genomic sequences; (iv) an intuitive genome browser to support visualization of user-selected data; and (v) a keyword-based Google-like search engine for finding the needed information intuitively and rapidly in this database.
摘要：
The expansion waves for the compressible Navier-Stokes equations have recently been shown to be nonlinear stable. The nonlinear stability results are called local stability or global stability depending on whether the H(1)-norm of the initial perturbation is small or not. Up to now, local stability results have been well established. However, for global stability, only partial results have been obtained. The main purpose of this paper is to study the global stability of rarefaction waves for the compressible Navier-Stokes equations. For this purpose, we introduce a positive parameter t(0) in the construction of smooth approximations of the rarefaction wave solutions for the compressible Euler equations so that the quantity l = t(0)/delta (delta denotes the strength of the rarefaction waves) is sufficiently large to control the growth induced by the nonlinearity of the system and the interaction of waves from different families. Then by using the energy method together with the continuation argument, we obtain some nonlinear stability results provided that the initial perturbation satisfies certain growth conditions as l -> +infinity. Notice that the assumption that the quantity l can be chosen to be sufficiently large implies that either the strength of the rarefaction waves is small or the rarefaction waves of different families are separated far enough initially.
摘要：
In this paper, we Study a free boundary value problem for two-phase liquid-gas model with mass-dependent viscosity coefficient when both the initial liquid and gas masses connect to Vacuum with a discontinuity. This is an extension of the paper [S. Evje, K.H. Karlsen, Global Weak Solutions for a Viscous liquid-gas model with singular pressure law, http://www.irisresearch.no/docsent/emp.nsf/wvAnsatte/SEV]. Just as in IS. Evje, K.H. Karlsen, Global weak solutions for a viscous liquid-gas model with singular pressure law. http://www.irisresearch.no/docsent/emp.nsf/wvAnsatte/SEV], the gas is assumed to be polytropic whereas the liquid is treated as an incompressible fluid. We give the proof of the global existence and uniqueness of weak solutions when beta is an element of (0, 1]. which have improved the previous result of Evje and Karlsen, and get the asymptotic behavior result, also we obtain the regularity of the Solutions by energy method. (C) 2009 Elsevier Inc. All rights reserved.
作者机构：
[Yanqin Feng; Xia Hu] School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;[Shuchao Li] Faculty of Mathematics and Statistics, Hubei Key Laboratory of Mathematical Science, Central China Normal University, Wuhan 430079, China
通讯机构：
[Li, Shuchao] Cent China Normal Univ, Fac Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
关键词：
Adjacent vertices - Clique - Connected graph - Connectivity indices - Cut edge - First Zagreb indices - Second zagreb indices - Zagreb index
作者：
Dougherty, Steven T.;Kim, Jon-Lark;Kulosman, Hamid;Liu, Hongwei
期刊：
Finite Fields and their Applications,2010年16(1):14-26 ISSN：1071-5797
通讯作者：
Kulosman, H
作者机构：
[Liu, Hongwei] Department of Mathematics, Huazhong Normal University, Wuhan, Hubei 430079, China;[Kulosman, Hamid; Kim, Jon-Lark] Department of Mathematics, University of Louisville, Louisville, KY 40292, United States;[Dougherty, Steven T.] Department of Mathematics, University of Scranton, Scranton, PA 18510, United States
通讯机构：
[Kulosman, Hamid] Univ Louisville, Dept Math, Louisville, KY 40292 USA.
期刊：
ARCHIV DER MATHEMATIK,2008年90(2):150-157 ISSN：0003-889X
通讯作者：
Deng, GT
作者机构：
[Deng, Guo-Tai; He, Xing-Gang] Cent China Normal Univ, Dept Math, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Deng, Guo-Tai] Cent China Normal Univ, Dept Math, Wuhan 430079, Hubei, Peoples R China.
关键词：
iterated function systems;refinement equations;self-affine sets;quasi product-form digit sets
摘要：
A self-affine region is an integral self-affine set with positive Lebesgue measure. In this note we give two criteria for integral self-affine sets being self-affine regions. As their applications we study the L 1-solutions of refinement equations, which play an important role in constructing wavelets, and we give several interesting examples.
作者机构：
[李工宝; 张国] College of Mathematics and Statistics, Central China Normal University
通讯机构：
[Li Gongbao] Cent China Normal Univ, Coll Math & Stat, Wuhan 430079, Peoples R China.
关键词：
p&q-Laplacian;multiplicity of solutions;critical exponent;35J60;35B33
摘要：
In this paper, we study the existence of multiple solutions for the following nonlinear elliptic problem of p&q-Laplacian type involving the critical Sobolev exponent: [GRAPHICS] where Omega subset of R(N) is a bounded domain, N > p, p* = Np/N-p is the critical Sobolev exponent and mu > 0. We prove that if 1 < r < q < p < N, then there is a mu(0) > 0, such that for any mu epsilon (0,mu(0)), the above mentioned problem possesses infinitely many weak solutions. Our result generalizes a similar result in [8] for p-Laplacian type problem.
期刊：
Journal of Differential Equations,2015年259(4):1256-1274 ISSN：0022-0396
通讯作者：
Shuai, W
作者机构：
[Shuai, Wei; Shuai, W] Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
通讯机构：
[Shuai, Wei] Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
关键词：
Kirchhoff-type equations;Sign-changing solutions;Nonlocal term
摘要：
We are interested in the existence of least energy sign-changing solutions for a class of Kirchhoff-type problem in bounded domains. Because the so-called nonlocal term b(integral(Omega)vertical bar del u vertical bar(2)dx)Delta u is involving in the equation, the variational functional of the equation has totally different properties from the case of b = 0. Combining constraint variational method and quantitative deformation lemma, we prove that the problem possesses one least energy sign-changing solution u(b). Moreover, we show that the energy of u(b) is strictly larger than the ground state energy. Finally, we regard b as a parameter and give a convergence property of ub as b SE arrow 0. (C) 2015 Elsevier Inc. All rights reserved.
期刊：
JOURNAL OF FUNCTIONAL ANALYSIS,2015年269(11):3500-3527 ISSN：0022-1236
通讯作者：
Peng, SJ
作者机构：
[Peng, Shuangjie; Deng, Yinbin; Shuai, Wei] Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
通讯机构：
[Peng, Shuangjie] Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
关键词：
Kirchhoff-type equations;Nodal solutions;Non local term
摘要：
In this paper, we study the existence and asymptotic behavior of nodal solutions to the following Kirchhoff problem -(a+b integral(3)(R)vertical bar del u vertical bar(2)dx)Delta u + v(vertical bar x vertical bar)u = f(vertical bar x vertical bar, u), in R-3 , u is an element of H-1(R-3), where V(x) is a smooth function, a, b are positive constants. Because the so-called nonlocal term (integral(3)(R)vertical bar del u vertical bar(2)dx)Delta u)Au is involved in the equation, the variational functional of the equation has totally different properties from the case of b = 0. Under suitable construction conditions, we prove that, for any positive integer k, the problem has a sign-changing solution u(k)(b), which changes signs exactly k times. Moreover, the energy of u(k)(b) is strictly increasing in k, and for any sequence {b(n)}-> 0(+) (n -> + infinity), there is a subsequence {b(ns)}, such that u(k)(bs) converges in H-1 (R-3) to wk as s -> infinity, where wk also changes signs exactly k times and solves the following equation -a Delta u +V (|x|), u) = f(|x|, u), in R-3, u is an element of H-1 (R-3). (C) 2015 Elsevier Inc. All rights reserved.
期刊：
ADVANCES IN MATHEMATICS,2010年225(5):2741-2785 ISSN：0001-8708
通讯作者：
Cao, Daomin
作者机构：
[Shuangjie Peng] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.;[Shusen Yan] Univ New England, Sch Math Stat & Comp Sci, Armidale, NSW 2351, Australia.;[Daomin Cao] Chinese Acad Sci, Inst Appl Math, Beijing 100190, Peoples R China.
通讯机构：
[Cao, Daomin] Chinese Acad Sci, Inst Appl Math, Beijing 100190, Peoples R China.
摘要：
Let Omega be a bounded domain in R(2), u(+) = u if u >= 0, u(+) = 0 if u < 0, u(-) = u(+) - u. In this paper we study the existence of solutions to the following problem arising in the study of a simple model of a confined plasma (P(lambda)) {Delta u - lambda u(-) = o, in Omega, u = c, on partial derivative Omega, integral partial derivative u/partial derivative nu ds = I, partial derivative Omega where nu is the outward unit normal of partial derivative Omega at x, c is a constant which is unprescribed, and I is a given positive constant. The set Omega(p) = {x is an element of Omega, u(x) < 0} is called plasma set. Existence of solutions whose plasma set consisting of one component and asymptotic behavior of plasma set were studied by Caffarelli and Friedman (1980) [3] for large lambda. Under the condition that the homology of Omega is nontrivial we obtain in this paper by a constructive way that for any given integer k >= 1, there is lambda(k) > 0 such that for lambda > lambda(k), (P(lambda)) has a solution with plasma set consisting of k components. (C) 2010 Elsevier Inc. All rights reserved.
摘要：
In this paper, the compressible non-isentropic Navier-Stokes-Poisson (NSP) system is considered in R-3 and the influences of internal electric field on the qualitative behaviors of solutions are analyzed. We observe that the electric field leads to the rotating phenomena in charge transport and reduces the speed of fluid motion, but it does not influence the transport of charge density and the heat diffusion. Indeed, we show that both density and temperature of the NSP system converge to their equilibrium state at the same rate (1 + t)(-3/4) as the non-isentropic compressible Navier-Stokes system, but the momentum decays at the rate (1 + t)(-1/4) A. which is slower than the rate (1 + t)(-3/4) for the pure compressible Navier-Stokes system. These convergence rates are also shown to be optimal for the non-isentropic compressible NSP system. (C) 2010 Elsevier Inc. All rights reserved.
期刊：
SIAM Journal on Mathematical Analysis,2010年42(4):1874-1897 ISSN：0036-1410
通讯作者：
Zhu, C.(cjzhu@mail.ccnu.cn)
作者机构：
[Zhang, Ting] Department of Mathematics, Zhejiang University, Hangzhou 310027, China;[Zhu, Changjiang] Department of Mathematics, Huazhong Normal University, Wuhan 430079, China;[Yao, Lei] Department of Mathematics, Central China Normal University, Wuhan 430079, China
通讯机构：
[Zhu, Changjiang] Huazhong Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
关键词：
A-priori estimates - Asymptotic behaviors - Global existence - Global weak solution - One dimension - Two-dimension - Viscous liquids - Weak solution
作者机构：
[Guo Jun; Zhao Huijiang] School of Mathematics and Statistics, Wuhan University;[Xiao Jixiong; Zhu Changjiang] Laboratory of Nonlinear Analysis, School of Mathematics and Statistics,Central China Normal University
通讯机构：
[Zhu Changjiang] Cent China Normal Univ, Sch Math & Stat, Lab Nonlinear Anal, Wuhan 430079, Peoples R China.
摘要：
This paper is concerned with the existence of global solutions to the Cauchy problem of a hyperbolic-parabolic coupled system with large initial data.To this end, we first construct its local solutions by the standard iteration technique, then we deduce the basic energy estimate by constructing a convex entropy-entropy flux pair to this system.Moreover, the L~∞-estimates and H~2-estimates of solutions are obtained through some delicate estimates.In our results, we do not ask the far fields of the initial data to be equal and the initial data can be arbitrarily large which generalize the result obtained in [7].
期刊：
Communications in Statistics - Theory and Methods,2009年38(9):1383-1392 ISSN：0361-0926
通讯作者：
Qin, H.(qinhong@mail.ccnu.edu.cn)
作者机构：
[Qin, Hong] Department of Statistics, Central China Normal University, Wuhan 430079, China;[Chatterjee, Kashinath] Department of Statistics, Visva-Bharati University, Santiniketan, India
通讯机构：
[Qin, Hong] Cent China Normal Univ, Dept Stat, Wuhan 430079, Peoples R China.;Department of Statistics , Central China Normal University , Wuhan, China
摘要：
The objective of this article is to study the issue of the projection discrepancy (Fang and Qin, 2005 Fang , K. T. , Qin , H. ( 2005 ). Uniformity pattern and related criteria for two-level factorials . Sci. China Ser. A 48 : 1 – 11 .[Crossref] , [Google Scholar]; Ma et al. 2003 Ma , C. X. , Fang , K. T. , Lin , D. K. J. ( 2003 ). A note on uniformity and orthogonality . J. Statist. Plann. Infer. 113 : 323 – 334 . [Google Scholar]), which has wide application to the field of fractional factorials. Fang and Qin (2005 Fang , K. T. , Qin , H. ( 2005 ). Uniformity pattern and related criteria for two-level factorials . Sci. China Ser. A 48 : 1 – 11 .[Crossref] , [Google Scholar]) and Zhang and Qin (2006 Zhang , S. L. , Qin , H. ( 2006 ). Minimum projection uniformity criterion and its application . Statist. Probab. Lett. 76 : 634 – 640 .[Crossref], [Web of Science ®] , [Google Scholar]) derived some properties of the projection properties of two-level factorials. Here we extend their results to asymmetric factorials. Some lower bounds of projection discrepancy of asymmetrical factorials are also obtained.
期刊：
Nonlinear Analysis, Theory, Methods and Applications,2010年73(10):3456-3461 ISSN：0362-546X
通讯作者：
Xiao, T.-J.(tjxiao@fudan.edu.cn)
作者机构：
[Liang, Jin] Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China;[Xiao, Ti-Jun] Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences, Fudan University, Shanghai 200433, China;[Zhang, Jun] Department of Mathematics, Central China Normal University, Wuhan 430079, China
通讯机构：
[Xiao, Ti-Jun] Fudan Univ, Sch Math Sci, Shanghai Key Lab Contemporary Appl Math, Shanghai 200433, Peoples R China.
关键词：
Weighted pseudo-almost periodic function;Decomposition;Translation invariant;Mean value
作者机构：
[Li, Gongbao] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Li, Gongbao] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
摘要：
We study the concentration and multiplicity of weak solutions to the Kirchhoff type equation with critical Sobolev growth, -(epsilon(2)a + epsilon b integral(R3) vertical bar del u vertical bar(2))del u + V(z)u = f(u) + u(5) in R-3, u is an element of H-1(R-3), u > 0 in R-3, where e is a small positive parameter and a, b > 0 are constants, f is an element of C-1(R+, R) is subcritical, V : R-3 -> R is a locally Holder continuous function. We first prove that for epsilon(0) > 0 sufficiently small, the above problem has a weak solution u(epsilon) with exponential decay at infinity. Moreover, u(epsilon) concentrates around a local minimum point of V in Lambda as epsilon -> 0. With minimax theorems and Ljusternik-Schnirelmann theory, we also obtain multiple solutions by employing the topological construction of the set where the potential V(z) attains its minimum.