2nd Dalian University of Technology and Inha University Joint Workshop
on Mathematics and Software
Date: Oct 8—11, 2010
Hosted by: School of Mathematical Sciences and School of Software, Dalian University of Technology
Supported in part by:
International Office, Dalian University of Technology;
School of Mathematical Sciences, Dalian University of Technology;
School of Software, Dalian University of Technology
Invited Participants from Korea:
l Professor Hyundae Lee，Department of Mathematics, Inha University
l Professor Youngjin Lee，Department of Mathematics, Inha University
l Professor Yoonweon Lee, Department of Mathematics, Inha University
l Professor Hyeonbae Kang, Department of Mathematics, Inha University
l Professor Dohan Kim, Department of Mathematics, Seol National University, President of Korean Mathematical Society (大韩数学会理事长), invited guest
l Professor Do Wan Kim, Department of Mathematics, Inha University
l Professor Yongjin Song, Department of Mathematics, Inha University
l Professor Longhe Yan, Department of Mathematics, Inha University
Schedule
Oct 8, Friday
Arriving
Oct 9, Saturday, Place: Room 410 , Yan-Jiao Building （研教楼420）, Main Campus
l 9:00—9:15 AM Opening Cermony
l 9:15—9:30 AM Taking Photo (in front the east gate of the Chuangxinyuan Building)
l 9: 40—10:10 AM
Speaker: Dohan Kim (Chaired by Renhong Wang)
Title: Applications of heat kernel method in harmonic analysis
l 10:10—10:40 AM
Speaker: Junsheng Fang (Chaired by Renhong Wang)
Title: Mixing subalgebras of finite von Neumann algebras
l 10:40—11:00 AM, Coffee and Tea time
l 11:00—11:30 AM
Speaker:Yoonweon Lee (Chaired by Yongjin Song)
Title:The refined analytic torsion and the well-posed boundary condition for the odd signature operator
l 11:30—12:00
Speaker: Liwei Zhang (Chaired by Yongjin Song)
Title: Convergence Analysis of A Sequential Convex Approximation Approach to Joint Chance Constrained Programs
l 12:00—1:30 Lunch Time
l 1:30—2:00 PM
Speaker: Yi Wang (Chaired byYoungjin Lee)
Title: Log-concavity and LC-positivity
l 2:00—2:30 PM
Speaker: Hyundae Lee (Chaired byYoungjin Lee)
Title:Layer potential technique and narrow escape problem
l 2:30—2:50 PM, Coffee and Tea time
l 2:50—3:20 PM
Speaker: He Jiang (Chaired by Liwei Zhang)
Title：Approximate backbone based multilevel algorithm for next release problem
l 3:20—3:50 PM
Speaker: Bo Yu (Chaired by Liwei Zhang)
Title：Globally Convergent and Efficient Homotopy Methods for Nonconvex and Nonsmooth Programming
l 3:50—4:10 PM, Coffee and Tea time
l 4:10—4:40 PM
Speaker: Do Wan Kim (Chaired by Hyundae Lee)
Title: Discontinuous Meshfree Approximation and its Applications
l 4:40—5:10 PM
Speaker: Zhongxuan Luo (Chaired by Hyundae Lee)
Title： A P2-nonconforming quadrilateral finite element for elliptic problems
l 6:00—8:00 PM Banquet at Kejiyuan Hotel
Oct 10, Sunday Moring, Place: Lecture Hall, Software Campus
l 9:40—10:10 AM
Speaker: Mingchu LI (Chaired by Zhongxuan Luo)
Title: Indirect Reciprocity and Trust Models in Complicated Reputation Systems
l 10:10—10:40 AM
Speaker: Fengchun Lei (Chaired by Zhongxuan Luo)
Title: Tunnel number one knots, m-small knots and Morimoto-Moriah Conjecture
l 10:40—11:00 AM, Coffee and Tea time
l 11:00—11:30 AM
Speaker: Yongjin Song (Chaired by Zhongxuan Luo)
Title: Braid gourps, mapping class groups and loop spaces
l 11:30—1:00 Lunch time
l 1:00—5:00 PM Free time (Local sight seeing)
l 5:30—8:00 PM Dinner
Oct 11, Monday, Departure
Time Table
Oct 9, Saturday, Place: 研教楼 410, the Chuangxinyuan Building, Main Campus
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9:00—9:15 AM Opening Cermony
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9:15—9:30 AM Taking photo
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9: 40—10:10 AM
Dohan Kim
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10:10—10:40 AM Junsheng
Fang
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10:40—11:00 AM Coffee and Tea time
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11:00—11:30 AM
Yoonweon Lee
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11:30—12:00
Liwei Zhang
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12:00—1:30 Lunch Time
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1:30—2:00 PM Yi Wang
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2:00—2:30 PM Hyundae Lee
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2:30—2:50 PM, Coffee and Tea time
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2:50—3:20 PM
He Jiang
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3:20—3:50 PM
Bo Yu
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3:50—4:10 PM, Coffee and Tea time
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4:10—4:40 PM
Do Wan Kim
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4:40—5:10 PM
Zhongxuan Luo
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6:00—8:00 PM Banquet at Kejiyuan Hotel
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Oct 10, Sunrday Moring, Place: Lecture Hall, Software Campus
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9:40—10:10 AM
Mingchu LI
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10:10—10:40 AM
Fengchun Lei
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10:40—11:00 AM, Coffee and Tea time
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11:00—11:30 AM
Yongjin Song
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11:30—1:00
Lunch time
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Titles and Abstracts
l Dohan Kim
Title: Applications of heat kernel method in harmonic analysis
Abstract: We generalize random process and positive definiteness in hyperfunctions generalizing the results of Gelfand and Vilenkin in distributions in their treatise "Generalized functions, vol. 4". We also consider the Hyers-Ulam stability of functional equations including a generalized quadratic functional equation in the spaces of hyperfunctions and Gelfand-Shilov generalized functions modulo bounded distributions. To obtain these theorems on hyperfunctions we make use of the heat kernel method of Matsuzawa effectively which represents various generalized functions including hyperfunctions and distributions as initial values of smooth solutions of the heat equation satisfying suitable growth condition.
l Hyundae Lee
Title: Layer potential technique and narrow escape problem
Abstract: The narrow escape problem consists of deriving the asymptotic expansion of the solution of a drift-diffusion equation with the Dirichlet boundary condition on a small absorbing part of the boundary and the Neumann boundary condition on the remaining reflecting boundaries. Using layer potential techniques, we rigorously find high-order asymptotic expansions of such solutions. The asymptotic formula explicitly exhibit the nonlinear interaction of many small absorbing targets. Based on the asymptotic theory for eigenvalue problems, we also construct highorder bation of eigenvalues of the Laplace and the drifted Laplace operators for mixed boundary conditions on large and small pieces of the boundary.
l Yoonweon Lee
Title: The refined analytic torsion and the well-posed boundary condition for the odd signature operator
Abstract: The refined analytic torsion was introduced by M. Braverman and T. Kappeler on an odd dimensional closed Riemannian manifold as an analytic analog of the refined combinatorial torsion developed by V. Turaev and M. Faber. Even though these two concepts are not exactly same, the are closely related. In case of an acyclic Hermitian connection, the refined analytic torsion is a complex number, whose modulus part is the Ray-Singer analytic torsion and the phase part is the eta invariant for the odd signature operator. In this talk we discuss the boundary value problem for the refined analytic torsion on a compact Riemannian manifold with boundary. For this purpose we introduce two well-posed boundary conditions for the odd signature operator which are complementary to each other and show that the refined analytic torsion is well defined.
l Do Wan Kim
Title: Discontinuous Meshfree Approximation and its Applications
Abstract: By the meshfree approximation, we usually mean that it is a kind of smooth approximation of functions using only unstructured points. Using this, methods to solve the numerical solutions of various partial differential equations have been extensively developed for the last two decades. The methods like EFG, RKPM, and MLSRK belong to such fields. However, if discontinuities happen to the solution inside the problem domain, then we need an effective method for approximating the discontinuity. In this talk, when the discontinuity takes place along an interface due to layer singularity, we propose efficient methods to approximate the layered discontinuity across the interface with the shape functions unchanged even if the interface is modified. Based on the developed approximations, we solve elliptic partial differential equations with layered discontinuous solutions and show the potential of the method.
l Hyeonbae Kang
Title: Generalized Polarization Tensors: Mathematics and Applications
Abstract: The generalized polarization tensors (GPT) are geometric and physical quantities associated with inclusions. They appear naturally in multipolar expansions of electric potentials near infinity in the presence of the inclusion. In this talk I will discuss about optimal bounds for GPTs, Kang-Milton's solution to the Polya-Szego conjecture, and connection to the Dirichlet-to-Neumann map. I then discuss their usage for reconstruction of fine details of the shape of the inclusion. I will also mention briefly on their connection to the cloaking (invisibility) which attracts much attention these years.
l Yongjin Song
Title: Braid gourps, mapping class groups and loop spaces
Abstract: The collection of braid groups easily forms a braided monoidal category. The collection of mapping class groups also forms a braided monoidal category. It has been known that a braided monoidal category gives rise to a double loop space through classifying space functor. A monoidal 2-category also gives rise to a double loop space. I will introduce a monoidal 2-category which is a conceptual extension of braid group. It plays a key role in the proof of Harer conjecture. I will also introduce various general forms of Harer conjecture.
l Liwei Zhang （张立卫）
Title：Convergence Analysis of A Sequential Convex Approximation Approach to Joint Chance Constrained Programs
Abstract：When there is parameter uncertainty in the constraints of a convex optimization problem, it is natural to formulate the problem as a joint chance constrained program (JCCP) which requires all constraints are satis¯ed simultaneously with a given large probability. We propose to solve the problem by a sequence of convex approximations. We show that the solutions of the sequence of approximations converge to a Karush-Kuhn-Tuck (KKT) point of the JCCP under a certain asymptotic regime. In this talk, we explain the issues about the convergence analysis for the proposed approach.
l Junsheng Fang (房军生)
Title：Mixing subalgebras of finite von Neumann algebras
Abstract: Jolissaint and Stalder introduced the defintion of weak mixing and mixing for subalgebras of finite von Neumann algebras. They proved that a measure prserving action of a countable group on a finite measure space is (weakly) mixing if and only if the von Neumann subalgebra induced by the group is (weakly) mixing in the cross-product finite von Neumann algebra. In this talk, I will give a characterization of weak mixing subalgebras in terms of "normalizers" of the subalgebras. I will also talk about some interesting properties of mixing subalgebras. This is joint work with Jan Cameron and Kunal Mukherjee.
l Bo Yu（于波）
Title：Globally Convergent and Efficient Homotopy Methods for Nonconvex and Nonsmooth Programming
Abstract: In this talk, I will give a brief survey of some homotopy methods for nonconvex programming. They are globally convergent under fairly weak conditions: normal cone condition, quasi-normal-cone condition or pseudo-cone condition. Some smoothing homotopy methods for min-max-min programming, a typical class of nonsmooth programming, as well as some new results on their efficient numerical implementation will also be introduced.
l Yi Wang（王毅）
Title：Log-concavity and LC-positivity
Abstract：A triangle $\{a(n,k)\}_{0\leq k\leq n}$ of nonnegative numbers is LC-positive if for each $r$, the sequence of polynomials $\sum_{k=r}^{n}a(n,k)q^k$ is $q$-log-concave. It is double LC-positive if both triangles $\{a(n,k)\}$ and $\{a(n,n-k)\}$ are LC-positive. We show that if $\{a(n,k)\}$ is LC-positive then the log-concavity of the sequence $\{x_k\}$ implies that of the sequence $\{z_n\}$ defined by $z_n=\sum_{k=0}^{n}a(n,k)x_k$, and if $\{a(n,k)\}$ is double LC-positive then the log-concavity of sequences $\{x_k\}$ and $\{y_k\}$ implies that of the sequence $\{z_n\}$ defined by $z_n=\sum_{k=0}^{n}a(n,k)x_ky_{n-k}$. Examples of double LC-positive triangles include the constant triangle and the Pascal triangle. We also give a generalization of a result of Liggett that is used to prove a conjecture of Pemantle on characteristics of negative dependence. (joint work with Y.-N. Yeh)
l Mingchu LI （李明础）
Title: Indirect Reciprocity and Trust Models in Complicated Reputation Systems
Abstract：TBA
l Zhongxuan Luo（罗钟铉）
Title：A P2-nonconforming quadrilateral finite element for elliptic problems
Abstract：In this talk, we propose a new innovative P2-nonconforming quadrilateral element for a second-order elliptic problems. The nonconforming element consists of P2 ⊕ Span12{(l13)+,(l24)+}' type="#_x0000_t75"> , which is an enrichment of P2.12l13,l24' type="#_x0000_t75"> are a piecewise linear algebraic curves on an arbitrary quadrilaterals. Our element is essentially of seven degrees of freedom since the degree of freedom associated with the integration on quadrilateral is essentially of bubble-function nature. Global basis functions are constructed for both Dirichlet and Neumann type of problems; accordingly the corresponding dimensions are counted. The local and global interpolation operators are defined. Error estimates of optimal order are derived in both broken energy and 12L2惟' type="#_x0000_t75"> norms for second-order of elliptic problems. Brief numerical results are also shown to confirm the optimality of the presented quadratic nonconforming element on quadrilaterals.
l He Jiang （江贺）
Title：Approximate backbone based multilevel algorithm for next release problem
Abstract：The next release problem (NRP) aims to effectively select software requirements in order to acquire maximum customer profits. As an combinatorial optimization problem in software requirement engineering, NRP lacks efficient approximate algorithms for large scale instances. The backbone is a new tool for tackling large scale NP-hard problems in recent years. In this talk, we employ the backbone to design high performance approximate algorithms for large scale NRP instances. Firstly we show that it is NP-hard to obtain the backbone of NRP. Then, we illustrate by fitness landscape analysis that the backbone can be well approximated by the shared common parts of local optimal solutions. Therefore, we propose an approximate backbone based multilevel algorithm (ABMA) to solve large scale NRP instances. This algorithm iteratively explores the search spaces by multilevel reductions and refinements. Experimental results demonstrate that ABMA outperforms existing algorithms on large instances in terms of solution quality and running time.
l Fengchun Lei (雷逢春)
Title: Tunnel numbers of knots under connected sum
Abstract：In the talk, we will review some progress on the behavior of the tunnel numbers of knots under connected sum, including our two recent results, one gives a sufficient condition in terms of some kinds of m-essential surfaces for the super additivity to hold, another gives an positive answer to Morimoto-Moriah Conjecture on the super additivity of the tunnel numbers of knots in the 3-sphereunder connected sum in the situation that each Ki is either tunnel number 1 or m-small, i = 1; 2, which extends two known results by Morimoto.
Local Organizers：
Fengchun Lei （雷逢春），portable phone number: 13889675612
Zhengguo Jin（金正国），portable phone number: 13704093209
Zhongxuan Luo （罗钟铉），portable phone number: 13940907580
Huadong Yu （于化东），portable phone number: 1399863496
