2014 AMMS
The International Mathematical Meeting and the Annual Meeting of the Taiwanese Mathematical Society
國際數學學術研討會暨中華民國數學年會
Dec67
大會手冊
主辦單位：中華民國數學會 承辦單位：國立成功大學數學系
2014 中華民國數學會年會暨數學學術研討會
日期：2014 年 12 月 6 日(星期六)至 12 月 7 日(星期日) 地點：國立成功大學成功校區數學系系館
主辦單位：中華民國數學會 承辦單位：國立成功大學數學系
贊助單位：科技部數學研究推動中心、國立成功大學「邁向頂尖 大學計畫」推動總中心、國立成功大學理學院、中華 民國數學會、國立成功大學數學系研發基金委員會 贊助廠商：Cambridge University Press、EBSCO、昊青股份有
限公司、思渤科技股份有限公司、科學文創有限公 司、滄海書局(鼎隆圖書)、高立出版集團、群翰資訊 有限公司、東華書局(新月圖書)、綠保股份有限公司、
知訊圖書、歐亞書局 學術委員會 Scientific Committee
陳榮凱 JungKai Chen 國立台灣大學 召集人 柯文峰 WenFong Ke 國立成功大學
李瑩英 YngIng Lee 國立台灣大學 陳建隆 JannLong Chern 國立中央大學 蔡東和 DongHo Tsai 國立清華大學 許元春 YuangChung Shen 國立交通大學 陳若淳 Roger Chen 國立成功大學 組織委員會 Organizing Committee
柯文峰 陳若淳 吳順益
林景隆 章源慶 黃世昌
黃柏嶧 方永富 王辰樹
史習偉 林育竹 連文璟
陳重弘 郭鴻文 舒宇宸
楊世偉 劉之中 劉育佑
劉珈銘 蕭仁傑 鄺國權
目錄
一、 大會議程 ··· ^{2}
二、 邀請講員 ··· ^{6}
三、 演講資訊 ··· ^{11}
四、 論壇資訊與摘要
數論與代數 Number Theory and Algebra··· ^{13}
分析與最佳化 Analysis and Optimization
··· ^{23}
幾何 Geometry
··· ^{33}
動態系統與生物數學 Dynamical Systems and Biomathematics
··· ^{41}
偏微分方程 Partial Differential Equations
··· ^{49}
離散數學 Discrete Mathematics
··· ^{59}
機率與統計 Probability & Statistics
··· ^{69}
計算數學 Computational Mathematics
··· ^{85}
數學教育 Mathematics Education
··· ^{95}
五、 附錄
數學系簡介··· ^{101}
大會會場示意圖
··· ^{103}
贊助
··· ^{106}
2014 年國際數學學術研討會暨中華民國數學會年會
2014.12.06 (六)
8:309:30 Registration 報到註冊
數學系館 1F9:3010:00 Opening Ceremony
Chair: Professor JungKai Chen
年會開幕式
主持人:
陳榮凱教授
經緯廳10:0010:50 Plenary Lecture by Professor Shigefumi Mori Chair: Professor JungKai Chen
大會演講 森 重文教授
主持人: 陳榮凱教授
經緯廳10:5011:10 Group Photo 團體照
成功大學圖書館 廣場11:1011:30 Coffee Break 茶會、討論
數學系館 1FSections
數論與代數 分析與
最佳化 幾何 動態系統
生物數學 偏微分方程 離散數學 機率 統計 計算數學
Number Theory and
Algebra
Analysis and
Optimization Geometry
Dynamical Systems and Biomathematics
Partial Differential
Equations
Discrete
Mathematics Probability & Statistics Computational Mathematics page pp.13~16 pp.23~26 pp.33~35 pp.41~44 pp.49~52 pp.59~62 pp.69~72 (機) pp.77~79 (統) pp.85~88
Room ^{數學系館 }
3174
數學系館 3172
測量教室 55180
測量教室 55150
數學系館 3173
測量教室 55170
數學系館 3176
數學系館 3177
測量教室 55160
 2 
11:3012:20
MingLun^{謝銘倫 }
HsiehWataru Takahashi
姚美琳
MeiLinYau
蔡志強
JeChiangTsai
陳子軒
ChiHinChan
游森棚
SenPengEu
陳冠宇
GuanYuChen
黃名鉞
MingYuehHuang
薛克民
KehMingShyue
12:2013:40 Lunch 午 餐
13:4014:05
彭勇寧
YungNingPeng
陳界山
JeinShanChen
吳進通
ChinTung Wu
梁育豪
YuHaoLiang
夏俊雄
ChunHsiungHsia
林延輯
YenChiLin
陳隆奇
LungChiChen
何弘棋
HungChiHo
黃聰明
TsungMingHuang
14:0514:30
ChengKai^{劉承楷 }
Liu吳金典
ChinTienWu
鄭文巧
WenChiaoCheng
林英杰
YingChiehLin
張惠蘭
HuiLanChang
Akira Sakai
王紹宣
ShaoHsuanWang
林得勝
TeShengLin
14:3015:00 Coffee Break 茶會、討論
數學系館 1F15:0015:25
FangTing^{凃芳婷 }
Tu黃楓南
FengNanHwang
趙玹珠
Hyunjoo Cho黃少遠
ShaoYuanHuang
江
金城 JinChengJiang
徐育鋒 YuFong
Hsu
張明淇
MingChiChang
施因澤
YinTzerShih
15:2515:50
楊策仲
TseChungYang
李育杰
YuhJyeLee
李國瑋
KuoWeiLee
林建仲
JianJhongLin
司靈得
Daniel Spector黃喻培 YuPei
Huang
謝希微
HsiWeiHsieh
胡偉帆 WeiFan
Hu 16:0016:50 Plenary Lecture by President Tony F. Chan
Chair: Professor ILiang Chern
大會演講 陳繁昌校長
主持人: 陳宜良教授
經緯廳16:5018:10 中華民國數學學會年度會議暨頒獎典禮
經緯廳 3 
2014 年國際數學學術研討會暨中華民國數學會年會
2014.12.07 (日)
8:309:00 Registration 報到註冊
數學系館 1FSections
數論與代數 分析與
最佳化 幾何 動態系統
生物數學 偏微分方程 離散數學 機率 統計 計算數學 數學教育
Number Theory and
Algebra
Analysis and
Optimization Geometry
Dynamical Systems and Biomathematics
Partial Differential
Equations
Discrete Mathematics
Probability &
Statistics
Computational Mathematics
Mathematics Education page pp.17~21 pp.27~31 pp.37~40 pp.45~48 pp.53~57 pp.63~67 pp.73~75 (機)
pp.81~83 (統) pp.89~93 pp.95~99
Room ^{數學系館 }
3174
數學系館 3172
測量教室 55180
測量教室 55150
數學系館 3173
測量教室 55170
數學系館 3176
測量教室 55160
數學系館 3177
9:009:50 ^{楊一帆 }
YiFan Yang徐洪坤
HongKunXu
蕭欽玉
ChinYuHsiao
陳兆年
ChaoNienChen
吳恭儉
KungChienWu
傅恆霖
HungLinFu
須上苑
ShangYuanShiu
洪子倫
TzyyLengHorng
李國偉
KoWeiLih
9:5010:10 Coffee Break 茶會、討論
數學系館 1F10:1011:00
Special Invited Lecture Professor Jongil Park
Chair: Roger Chen
特別邀請演講 Professor Jongil Park 主持人: 陳若淳
經緯廳
Interdisciplinary Lecture Professor Norden E.Huang
Chair: Professor Ming Chih Lai跨領域演講 黃鍔 院士 主持人: 賴明治
格致廳
 4 
11:1011:35
MingHsuan^{康明軒 }
Kang黃延安
YanAnHwang
張懷良
HuaiLiang Chang
張志鴻
ChihHungChang
Takayoshi Ogawa
孫新民
HsinMinSun
陳美如
MayRuChen
卓建宏
ChienHongCho
陳宜良
ILiangChern
11:3512:00 ^{魏福村 }
FuTsun Wei高華隆
HwaLongGau
胡文貴
WenGueiHu
Masaki Kurokiba
史青林
ChinLinShiue
孫立憲
LiHsienSun
林敏雄
MinHsiungLin
舒宇宸
YuChenShu
12:0013:30 Lunch (Research Fields Development Forum) 午 餐 (領域發展論壇) 13:3013:55
陳憲揚
HsianYangChen
陸行
HsingLuh
劉筱凡
HsiaoFanLiu
鄭凱仁
KaiRenZheng
Masashi Misawa
梁育菖
YuChangLiang
黃建豪
ChienHaoHuang
薛名成
MingChengShiue
曾正男
JengNanTzeng
14:0014:50 Plenary Lecture by Professor Ching Hung Lam Chair: Professor ShunJen Cheng
大會演講 林正洪教授
主持人: 程舜仁教授
經緯廳14:5015:20 Coffee Break 茶會、討論
數學系館 1F15:2015:45
XingJun^{林興君 }
Lin林來居
LaiJiuLin
張清皓
ChingHaoChang
黃志強
ChihChiangHuang
林立人
LiRenLin
羅元勳
YuanHsunLo
吳筱婷
HaiaoTingWu
陳麗貞
LiChenChen
張鎮華
Gerard J.Chang
15:4516:10
郭容妙
JungMiaoKuo
杜威仕
WeiShihDu
黃彥彰
YenChangHuang
魏秀娟
HsiuChuanWei
關汝琳
RuLinKuan
林凡軒
FanHsuanLin
李佳蓉
JiaRongLi
劉青松
ChingSungLiu
李源順
YuanShunLee
16:1016:35 Can Hatipoglu Yasunori
Kimura
周世偉
ShihWeiChou
學生發表
Student publication楊智雄
ZhiXiongYang
王辰樹
ChernShuhWang
吳昭容
ChaoJungWu
 5 
大會演講 Professor Shigefumi Mori
Extremal Rays and the Explicit Minimal Model Program in Dimension Three
Abstract
We will review the theory of extremal rays and the minimal model theory especially in dimension three with emphasis on explicit description of extremal contractions.
Professor Shigefumi Mori
現職
Professor, Research Institute of Mathematical Sciences (RIMS), Kyoto University, Japan
學歷
1973 B.A., Kyoto University, Japan 1975 M.A., Kyoto University, Japan 1978 Dr. Sci., Kyoto University, Japan
研究領域
Algebraic Geometry, especially birational classification and the birational geometry of algebraic varieties
學術榮譽
1990 Japanese Government Prize (Person of Cultural Merits) 1990 Fields Medal
1990 Japan Academy Prize (with S. Iitaka and Y. Kawamata) 1990 American Mathematical Society Cole Prize
1989 Inoue Science Prize
1988 Japan Mathematical Society Autumn Prize (with Y. Kawamata) 1984 Chunichi Culture Prize
1983 Japan Mathematical Society Iyanaga Prize
大會演講 President Tony F. Chan
Four Color Theorem for Image Segmentation
Abstract
Image segmentation is an essential problem in imaging science. One of the most successful segmentation models is the piecewise constant MumfordShah minimization model. This minimization problem is however difficult to carry out, mainly due to the nonconvexity of the energy. Recent advances based on convex relaxation methods are capable of estimating almost perfectly the geometry of the regions to be segmented when the mean intensity and the number of segmented regions are known a priori. The next important challenge is to provide a tight approximation of the optimal geometry, mean intensity and the number of regions simultaneously while keeping the computational time and memory usage reasonable.
In this work, we propose a new algorithm that combines convex relaxation methods with the four color theorem to deal with the unsupervised segmentation problem. The proposed algorithm can segment any a priori unknown number of regions with only four intensity functions and four indicator (labeling) functions. The number of regions in our segmentation model is decided by one parameter that controls the regularization strength of the geometry, i.e., the total length of the boundary of all the regions. The segmented image function can take as many constant values as needed. We will present the detail about the new model as well the numerical techniques used to solve it.
陳繁昌 校 長
現職
香港科技大學校長
學歷
史丹福大學博士 (1978)
跨領域演講 Professor Norden E. Huang
On the Degree of Nonlinearity
Abstract
The term ‘nonlinearity’ has been loosely used, in most cases, not to clarify the situation at hand, but rather as a fig leaf to hide our ignorance. As a result, any anomaly without obvious and ready explanations is labeled as being due to a
‘nonlinear effect.’ Such an approach is a hindrance to progress of our knowledge.
Unfortunately, under the present state of our understanding of nonlinearity, no better prescription is available. The central problem is that the present definition of
‘nonlinearity’ is only a qualitative one.
A Degree of Nonlinearity (DN) based primarily on intrawave frequency modulation is proposed here with the value always between 0 and 1. With this definition, the degree of nonlinearity measures the state rather than a system. The data needed for the definition is the state of the motion, or in effect, the complete suite of observational data. For a complicated state with more than one Intrinsic Mode Function (IMF) containing prominent energy density, the DN must also consider amplitude variations. The combination of both the intrawave frequency modulation and the amplitude variation then yields the Combined Degree of Nonlinearity (CDN). Extensive tests via the employment of well  known nonlinear systems indicate that the new definition is logical and the values of the CDN given are quite reasonable. With these definitions of the DN and the CDN, we can presumably mover forward and quantify the nonlinearity of any continuous system and the discussion of nonlinear effects can be conducted precisely. Applications of the DN and CDN for structural safety monitoring, biomedical applications and financial data, by way of example, will be presented and discussed.
黃 鍔 院 士
現職
中央大學數據分析方法研究中心
學歷
美國約翰霍普金斯大學博士 (1967) 國立台灣大學學士 (1960)
研究領域
流體力學、希爾伯特黃變換法
邀請演講 Professor Jongil Park
On Knot Surgery 4Manifolds
Abstract
Since the inception of gauge theory, in particular SeibergWitten theory, topologists and geometers working on 4manifolds have developed various techniques and they have obtained many fruitful and remarkable results on 4 manifolds in last 30 years. Among them, a knotsurgery technique introduced by R.
Fintushel and R. Stern turned out to be one of most effective techniques to modify smooth structures without changing the topological type of a given 4manifold.
Nevertheless, there are still fundamental problems on knot surgery 4manifolds to be settled down. For example, it is an intriguing question to know whether a knot surgery 4manifold determines a prime knot up to mirror, called FintushelStern conjecture on knot surgery 4manifold.
In this talk first I’d like to review a knotsurgery technique in some details. And then I’ll investigate some open problems such as FintushelStern conjecture.
Professor Jongil Park
現職
Professor, Seoul National University, South Korea
學歷
1996 Ph.D., Michigan State University East Lansing, Michigan, USA
1988 M.S., Seoul National University, Seoul, Korea 1986 B.S., Seoul National University, Seoul, Korea
研究領域
大會演講 Professor Ching Hung Lam
Moonshine Vertex Operator Algebra and Its Cousins
Abstract
The Moonshine vertex operator algebra
V^{}, whose full automorphism group is isomorphic to the Monster simple group, was first constructed by Frenkel LepowskyMeurman in 1983. Not only does it solve a conjecture of McKay Thompson that related the Monster simple group to certain modular functions but it also plays a fundamental role in shaping the theory of vertex operator algebra.
In this talk, I will first give few historical remarks about the Moonshine phenomenon and the development of the theory of vertex operator algebra (VOA). I will try to explain how the theory of vertex operator algebra could help us to understand some mysterious properties of the Monster simple group and the Moonshine phenomenon.
If time is permitted, I will also discuss some VOAs related to other sporadic simple groups and some relatively new moonshine phenomena.
林正洪 教 授
現職
中央研究院數學所研究員
學歷
俄亥俄州立大學博士 (1996) 香港大學學士 (1989)
研究領域
頂點算子代數、李代數、有限群論
學術榮譽
國立成功大學 特聘教授 2008
中華民國科技部 傑出研究獎 2009~2011
Plenary Speakers
Professor Shigefumi Mori Kyoto University
陳繁昌 校長 香港科技大學
林正洪 教授 中央研究院
Special Invited Speakers
跨領域專題 黃 鍔 院士 國立中央大學
韓國數學會 Professor Jongil Park Seoul National University
領域發展論壇
^{12}月 7 日 12:00~13:30，地點：各領域議場數論與代數 楊一帆 教授 國立交通大學
分析與最佳化 許瑞麟 教授 國立成功大學
幾何 蔡東和 教授 國立清華大學
動態系統與生物數學 陳兆年 教授 國立清華大學
偏微分方程 陳建隆 教授 國立中央大學
離散數學 翁志文 教授 國立交通大學
機率 黃啟瑞 教授 中央研究院
統計 陳玉英 教授 國立中央大學
計算數學 賴明治 教授 國立交通大學
雙邊會談
^{12}月 6 日 11:20~13:40，地點：數學系館三樓 會議室Korean Mathematical Society
Professor Jongil Park Seoul National University Professor Myung Hwan Kim Seoul National University Professor Yong Hoon Lee Pusan National University
Professor Dongsu Kim National Institute for Mathematical Sciences Professor Hyungju Park Postech for Mathematics
Professor Hyang Sook Lee Ewha Womans University
Taiwan Mathematical Society
陳榮凱 教授 台灣大學數學系
柯文峰 教授 成功大學數學系
王偉仲 教授 台灣大學數學系
于 靖 教授 台灣大學數學系
李瑩英 教授 台灣大學數學系
王振男 教授 台灣大學數學系
賴明治 教授 交通大學應用數學系
蔡東和 教授 清華大學數學系
程舜仁 教授 中央研究院數學研究所
陳宜良 教授 中央大學數學系
林文偉 教授 交通大學應用數學系
許世壁 教授 清華大學數學系
數論與代數
Organizers : ShihChang Huang 黃世昌 ChingHung Lam 林正洪
地點 : 數學系館 3174 時間 : ^{2014} 年 12 月 06 日 (六)
11：30~12：20 On the Derivatives of Anticyclotomic Padic Lfunctions
MingLun Hsieh 謝銘倫 (主持人：陳憲揚)13：40~14：05
Rectangular Finite superalgebras and the Super Yangian

YungNing Peng 彭勇寧 (主持人：楊一帆)
14：05~14：30 Engel Type Functional Identity in Semiprime Rings
ChengKai Liu 劉承楷 (主持人：楊一帆)
15：00~15：25 Generalized Legendre Curves and Quternion Multiplication
FangTing Tu 凃芳婷 (主持人：楊一帆)15：25~15：50 Monomial, Gorenstein and Bass Orders
TseChung Yang 楊策仲 (主持人：楊一帆)
On the Derivatives of Anticyclotomic p _{adic } _{L} functions
MingLun Hsieh ( 謝銘倫) National Taiwan University
mlhsieh@math.ntu.edu.tw
Abstract
I will report a recent work of PinChi Hung on the construction of anticyclotomic padic Lfunctions for Hilbert modular forms of finite slopes and a formula relating the first derivative of this padic L‐functions at the central point and Teieltbaum’s Linvariant defined by Chida, Mok and Park.
His results extend previous works of Bertolini, Darmon, Iovita and Speiss to Hilbert modular forms.
Rectangular Finite superalgebras and the Super Yangian
_{}YungNing Peng (彭勇寧) National Central University
ynp@math.ncu.edu.tw
Abstract
Finite algebra _{,} are certain associative algebras determined by a nilpotent element and a semisimple element satisfying certain relations in a finite dimensional semisimple or reductive Lie algebra g. In general, they are very complicated and difficult to study. In 2006, Brundan and Kleshchev found a concrete description of _{,} when g gl in terms of Yangian algebra and obtained a powerful tool for the study of finite algebras.
In this talk, we will generalize the technique of Brundan and Kleshchev to the case of general linear Lie superalgebra gl _{} , where the given and are “ ”, and hence a concrete description of the corresponding finite superalgebra in terms of super Yangian _{} is obtained. It gives a new proof of the earlier result observed by Briot and Ragoucy in 2003.
Engel Type Functional Identity in Semiprime Rings ChengKai Liu (劉承楷)
National Chang Hua University of Education ckliu@cc.ncue.edu.tw
Abstract
Let R be a semiprime ring with center Z R( ), extended centroid C and Q the maximal right ring of quotients of R . A map f :RQ is called k commuting on R if [ ( ), ]f x xk for all 0 xR, where [ , ]y x1[ , ]y x yxxy and [ , ]y x n [[ , ]y x n1, ]x , , , for n1. It is proved that if f is a
kcommuting additive map on R, then there exists an idempotent eC such that ef x( )x( )x for all xR, where C and : RC is an additive map. Moreover, (1e Q) is a n!torsion noncommutative reduced ring satisfying the standard identity of degree 2n. As a consequence of the theorem, it is proved that every k commuting Z R( )module homomorphism on R is 1commuting. In the case of prime rings, our theorem gives a partial answer to the unsolved problem of such functional identities initiated in 1995 by Brešar.
Generalized Legendre Curves and Quternion Multiplication FangTing Tu (凃芳婷)
National Center for Theoretical Sciences (North) ft12@math.cts.nthu.edu.tw
Abstract
In this talk, we will discuss some results on the Jacobian varieties of the generalized Legendre curves 1 1 , λ ∈ ; , , , ∈ and their primitive subvarieties with Quternion Multiplication, which are based on explicit computations on the corresponding Galois representations and periods.
Monomial, Gorenstein and Bass Orders TseChung Yang ( 楊策仲)
Academia Sinica jmkuo@amath.nchu.edu.tw
Abstract
In the integral theory for central simple algebras over nonArchimedean local fields, we have the following important classes of orders: maximal orders, hereditary orders, Bass orders and Gorenstein orders. Many theories and relations are investigated by many authors for understanding these classes of orders, as well as their module structures.
It is wellknown that they form the following proper inclusions :
(maximal orders)(hereditary orders)(Bass orders)(Gorenstein orders)
In this talk, we study a class of orders called monomial orders in a central simple algebra over a nonArchimedean local field. Monomial orders are easily represented and they may be also viewed as a direct generalization of Eichler orders in quaternion algebras. A criterion for monomial orders to be Gorenstein or to be Bass is given. It is shown that a monomial order is Bass if and only if it is either a hereditary or an Eichler order of period two.
數論與代數
Organizers : ShihChang Huang 黃世昌 ChingHung Lam 林正洪
地點 : 數學系館 3174 時間 : ^{2014} 年 12 月 07 日 (日)
09：00~09：50 Quaternionic Loci in Siegel’s Modular Threefold
YiFan Yang 楊一帆 (主持人：郭容妙)11：10~11：35 BassIhara Zeta Functions for Nonuniform Tree Lattices
MingHsuan Kang 康明軒 (主持人：郭容妙)11：35~12：00 Kronecker Limit Formula over Function Fields Revisited
FuTsun Wei 魏福村 (主持人：郭容妙)13：30~13：55 Fusion Rules of the VOA
HsianYang Chen 陳憲揚 (主持人：彭勇寧)^{ൈ}15：20~15：45 Unitary Vertex Operator Algebras
XingJun Lin 林興君 (主持人：彭勇寧)15：45~16：10 On Three Dimensional Representations of the Clifford Algebra of a Ternary Cubic Form
JungMiao Kuo 郭容妙 (主持人：彭勇寧)
16：10~16：35
Injective Hulls of Simple Modules over Some Noetherian
Rings
Quaternionic Loci in Siegel’s Modular Threefold YiFan Yang ( 楊一帆)
National Chiao Tung University yfyang@math.nctu.edu.tw
Abstract
An abelian surface over is said to have quaternionic multiplication if its endomorphism algebra contains a quaternion algebra over _{}. Let be the moduli space of isomorphism classes of principally polarized abelian surfaces over . In this talk, we will discuss the loci of principally polarized abelian surfaces with QM is .
BassIhara Zeta Functions for Nonuniform Tree Lattices MingHsuan Kang (康明軒)
National Chiao Tung University mhkang@math.nctu.edu.tw
Abstract
We will discuss zeta functions on noncompact arithmetic quotient graph. Despite the in finitedimensional setting, it turns out to be a rational function, generally with zeros and poles, in contrast to the compact case. The determinant formulas of Bass and Ihara hold true if one denes the determinant as limit of all finite principal minors.
Kronecker Limit Formula over Function Fields Revisited FuTsun Wei ( 魏福村)
Academia Sinica ftwei@math.sinica.edu.tw
Abstract
In this talk, I will discuss an analogue of Kronecker limit formula in the function field context. This formula is applied to the study of “noncentral” values of the Rankin product Lfunctions associated with two Drinfeld type new forms. Moreover, we relate the “Taguchi height” of rank 2 Drinfeld modules with "complex multiplication" to logarithmic derivatives of zeta functions.
Fusion Rules of the VOA HsianYang Chen (陳憲揚)
Academia Sinica hychen@math.sinica.edu.tw
Abstract
In this talk, we determine quantum dimensions and fusion rules for the orbifold code VOA . As an application, we construct certain 3local subgroups inside the automorphism group of the VOA ^{#}, where ^{#} is a holomorphic VOA obtained by the orbifold construction on the Leech lattice VOA.
Unitary Vertex Operator Algebras XingJun Lin ( 林興君)
Academia Sinica
linxingjun@math.sinica.edu.tw
Abstract
Unitary vertex operator algebras are introduced. Most wellknown rational vertex operator algebras are shown to be unitary. The classification of unitary vertex operator algebras with central charge 1 is also discussed.
On Three Dimensional Representations of the Clifford Algebra of a Ternary Cubic Form
JungMiao Kuo (郭容妙) National Chung Hsing University
jmkuo@amath.nchu.edu.tw
Abstract
Let be a ternary cubic form over an algebraically closed field and let denote its Clifford algebra. It was shown recently that has exactly 72 inequivalent three dimensional representations. In this talk, we will give an explicit classification of these representations.
Injective Hulls of Simple Modules over Some Noetherian Rings Can Hatipoglu
National Center for Theoretical Sciences (South) hatipoglucan@gmail.com
Abstract
I will talk about Noetherian rings over which injective hulls of simple right modules are locally Artinian.
Specifically, I will talk about enveloping algebras of finite dimensional solvable Lie superalgebras with this property, as well as the Ore extensions of the polynomial rings k[x].
分析與最佳化
Organizer : SoonYi Wu 吳順益
地點 : 數學系館 3172 時間 : ^{2014} 年 12 月 06 日 (六)
11：30~12：20 Iterative Methods for Split Common Fixed Point Problems
Wataru Takahashi (主持人：吳順益)13：40~14：05
What is the Generalization of Natural Residual Function for NCP
JeinShan Chen 陳界山 (主持人：徐洪坤)
14：05~14：30
Optimization in Path Planning, Image Registration and Optical Design Using Particle Swarm Method
ChinTien Wu 吳金典 (主持人：徐洪坤)
15：00~15：25
Nonlinear Preconditioner for Fullspace
LagrangeNewtonKrylov Algorithms with Applications in Largescale PDEconstrained Optimization Problems
FengNan Hwang 黃楓南 (主持人：陳界山)
15：25~15：50
Online Nonlinear Support Vector Machine for LargeScale Classification
YuhJye Lee 李育杰 (主持人：陳界山)
Iterative Methods for Split Common Fixed Point Problems Wataru Takahashi
Keio University, Japan wtaka@osakaue.ac.jp
Abstract
In this talk, motivated by the iterative methods for the split feasibility problem and the split common null point problem in Hilbert spaces, we consider split common fixed point problems. Then, using nonlinear analysis, we establish weak and strong convergence theorems for split common fixed point problems.
As applications, we get wellknown and new weak and strong convergence theorems which are connected with fixed point problems, split feasibility problems, split common null point problems and equilibrium problems.
What is the Generalization of Natural Residual Function for NCP JeinShan Chen (陳界山)
National Taiwan Normal University jschen@math.ntnu.edu.tw
Abstract
It is well known that the generalized FischerBurmeister is a natural extension of the popular FischerBurmeister function NCPfunction, in which the 2 norm is replaced by general p norm. As for another popular natural residual NCPfunction, its generalization was unknown during the past three decades. In this short communication, we answer this longstanding open question. In particular, we propose the generalization of natural residual function for NCP, which possesses twice differentiability. This feature enables.
Optimization in Path Planning, Image Registration and Optical Design Using Particle Swarm Method
ChinTien Wu ( 吳金典) National Chiao Tung University
ctw@math.nctu.edu.tw
Abstract
Particle swarm optimization (PSO) is a populationbased stochastic approach for solving continuous and discrete optimization problems. Just like the other heuristic approaches such as differential evolution and genetic algorithm, various PSO methods are employed to solve complex optimization problems in which proper search direction and contraction trust region are difficult to find. The basic ingredients in various PSO methods include randomly generated swarm particle and velocity filed that is employed to update the particle positions. One of the recent developed PSO method is the QPSO (quantum particle swarm optimization) where quantum laws of mechanics is used to govern the movement of swarm particles. Successes of the QPSO have been found in many areas including neural networks, machine learning, antenna design and data mining. In this talk, we will present some of our recent works in path planning of unmanned aerial vehicle (UVA), nonrigid registrations of magnetic resonance (MR) images and optical free form design where PSO and QPSO play crucial roles.
Nonlinear Preconditioner for Fullspace LagrangeNewtonKrylov Algorithms with Applications in Largescale PDEconstrained Optimization Problems
FengNan Hwang (黃楓南) National Central University hwangf@math.ncu.edu.tw
Abstract
PDEconstrained optimization problems are a class of important and computationally challenging problems. The fullspace LagrangeNewton algorithms is one of the most popular numerical algorithms for solving the problems, since Newtontype method enjoys fast convergence when the nonlinearities in the system are well balanced. However, in many practical problems such as flow control, if some of the equations are much more nonlinear than the others in the system, the method become slow convergent or at worse case it diverges. The radius of convergence is often constrained by a small number of the variables of equations in the system with the strong nonlinearities. In the talk, we introduce and study a parallel nonlinear elimination preconditioned inexact Newton algorithm for the boundary control of thermally convective flows. In this approach, in the standard manner, once the objective function and the PDE constrained problem discretized by some numerical schemes, we convert the constrained optimization problem into unconstrained optimization problem by introducing the augmented Lagrange function, then find the candidate optimal solution by solving the first order necessary condition using an inexact Newton method with backtracking techniques.
The key point of new proposed algorithm is that before performing the global Newton update, we first identify the tobeeliminated components that cause Newton method's into a slow convergence, and then remove the high nonlinearity by using a subspace correction, which can be interpretated the application of nonlinear elimination based preconditioner to the nonlinear system. As a result, the new approach shows a significantly improved performance when compared to a standard LagrangeNewton type method or its gridsequencing version. Some numerical results are presented to demonstrate the robustness and efficiency of the proposed algorithm.
Online Nonlinear Support Vector Machine for LargeScale Classification YuhJye Lee ( 李育杰)
National Taiwan University of Science and Technology yuhjye@mail.ntust.edu.tw
Abstract
Online learning is an important technique for handling largescale problems. In general, most of realworld classification problems are not linearly separable but most online learning algorithms give a linear model. Support vector machine (SVM) is one of the most popular nonlinear learning methods by taking the advantage of the kernel trick. Unfortunately, the computational overhead prohibits it for dealing with large scale problems. We propose an online nonlinear SVM algorithm with the reduced kernel trick. Similar to other online learning algorithms such as the passive and aggressive algorithm, we also have a closed form updating rule. Thus, it will be extremely fast for each updating. Moreover, we introduce a proximal model that “memorizes” the statistical information of the instances shown in the learning process. Combining the nonlinear SVM model and the proximal model, our proposed method is insensitive to the input order and is able to quickly achieve a reasonable good solution in a single pass.
分析與最佳化
Organizer : SoonYi Wu 吳順益
地點 : 數學系館 3172 時間 : ^{2014} 年 12 月 07 日 (日)
09：00~09：50 Optimization Techniques for Nonlinear Compressed Sensing
HongKun Xu 徐洪坤 (主持人：Wataru Takahashi)11：10~11：35 ComplementAssociated Games
YanAn Hwang 黃延安 (主持人：許瑞麟)11：35~12：00 Numerical Radii for Tensor Products of Matrices
HwaLong Gau 高華隆 (主持人：許瑞麟)13：30~13：55 A Queueing Model for the Congestion Problem in Taipei Maokong Gondola System
Hsing Luh 陸行 (主持人：許瑞麟)
15：20~15：45 Split Mathematical Programs with Semiinfinite
Equilibrium Constraints
LaiJiu Lin 林來居 (主持人：林來居)
15：45~16：10 On New Generalizations of Smarzewski's Fixed Point
Theorem
WeiShih Du 杜威仕 (主持人：林來居)
16：10~16：35 Common Fixed Points of a Family of Mappings Defined on a
Complete Geodesic Space
Yasunori Kimura (主持人：林來居)
16：35~17：00
Hybrid Moreau’s Proximal Algorithms and Convergence Theorems for Minimization Problem in Hilbert Spaces with Related Problem
ChihSheng Chuang 莊智升 (主持人：林來居)
Optimization Techniques for Nonlinear Compressed Sensing HongKun Xu ( 徐洪坤)
National Sun Yatsen University xuhk@math.nsysu.edu.tw
Abstract
The compressed sensing (CS) addresses the problem of recovering a (nearly) sparse signal through much fewer measurements than the traditional Nyquist rate. One of the restrictions of CS is that the measurements are taken in the linear way. This however would not fit certain practical cases (such as phase retrievals where only the magnitudes of the measurements are given). A consequence of nonlinear measurements lies in nonlinear constraints attached to the CS optimization.
ComplementAssociated Games YanAn Hwang (黃延安)
National Dong Hwa University yahwang@mail.ndhu.edu.tw
Abstract
In this work, an alternative definition of the associated game is constructed, we name the Ecomplementassociated game. We define a sequence of games; the term of order m , in this sequence, is the Ecomplementassociated game of the term of order (m1). We show that the sequence converges and that the limit game is the sum of an inessential game and a constant game. Based on the Ecomplementassociated game, the equal allocation of nonseparable costs (EANSC) is characterized by associated consistency (AC) and other four axioms, Pareto optimality (PO), translation covariance (TC), symmetry (SYM), continuity(CONT). Additionally, we also introduce a corresponding complementassociated game of the Shapley value, we name the Shcomplementassociated game. Based on the Shcomplementassociated game, the corresponding sequence also converges but its limit game is a constantsum game.
Numerical Radii for Tensor Products of Matrices HwaLong Gau ( 高華隆)
National Central University hlgau@math.ncu.edu.tw
Abstract
For nbyn and mbym complex matrices A and B, it is known that the inequality (A⊗B) ≤ A (B) holds, where (˙) and ˙ denote, respectively, the numerical radius and the operator norm of a matrix. In this talk, we consider when this becomes an equality. We give necessary and su_cient conditions for (A⊗B) = A (B) to hold.
In this case, we show that the numerical range. (A⊗B) must be a circular disc centered at the origin. Among other things, for some classes of matrices A, we also show that (A⊗A) is a circular disc centered at the origin if and only if (A) is a circular disc centered at the origin.
A Queueing Model for the Congestion Problem in Taipei Maokong Gondola System
Hsing Luh (陸行) National Chengchi University
slu@nccu.edu.tw
Abstract
The Taipei Maokong Gondola system was opened on July 4, 2007 and has been in operation with two types of cabins since April 2010. There are about 140 cabins with 30 crystal cabins (about 110 regular cabins). The service interval is about 3 min. Two separate queues form to the two types of cabins. There are six stations around the transportation area with the Maokong Gondola system.
The maximum capacity for regular cabin is 8 people while the maximum capacity for the crystal cabin is 5. The service interval for regular cabin is about 15 seconds (based on the ratio of the numbers of cabins of two types).
Customers arrive in batches to take the Maokong gondola. During the rush hours like holidays or weekends, the long lineups occur and congestion or overcrowding becomes a problem from the customer service's point of view. In this presentation, we introduce a queueing model that describes a system of dependent queues and solve for the optimal services time for both regular and crystal cabins.
Split Mathematical Programs with Semiinfinite Equilibrium Constraints LaiJiu Lin ( 林來居)
National Changhua University of Education maljlin@cc.ncue.edu.tw
Abstract
In this paper we study split mathematical programs with semiinfinite equilibrium constraints, mathematical programs with semiinfinite constraints. We give algorithms and prove strong convergence theorems of these problems.
As simple consequence, we obtain some results on common solutions for a countable family of split feasibility problems. Our results contain many original results on optimization theory. Our results also improve and generalized results on fixed point theory and optimization theory.
On New Generalizations of Smarzewski's Fixed Point Theorem WeiShih Du (杜威仕)
National Kaohsiung Normal University wsdu@nkucc.nknu.edu.tw
Abstract
In this work, we prove some slightly more general versions of the Smarzewski's fixed point theorem and some new fixed point theorems which are original and quite different from the well known results in the literature.
Common Fixed Points of a Family of Mappings Defined on a Complete Geodesic Space
Yasunori Kimura Toho University, Japan yasunori@is.sci.tohou.ac.jp
Abstract
The problem of approximation of a common fixed point for a family of mappings is one of the most crucial problems in nonlinear analysis. It has been applied to a various types of problems such as convex minimization problems, variational inequality problems, equilibrium problems, minimax problems, and others. In this talk, we propose several types of iterative methods to approximate a common fixed point of mappings defined on a complete geodesic space. We also show some recent development related to this topic.
Hybrid Moreau’s Proximal Algorithms and Convergence Theorems for Minimization Problem in Hilbert Spaces with Related Problem
ChihSheng Chuang (莊智升) National Sun Yatsen University
cschuang@math.nsysu.edu.tw
Abstract
In this paper, motivated by Moreau's proximal algorithm, we give several algorithms and related weak and strong convergence theorems for minimization problems under suitable conditions. These algorithms and convergence theorems are different from the results in the literatures. In the final, we also study algorithms and convergence theorems for the split feasibility problem in real Hilbert spaces.
幾何
Organizer : WanKeng Cheong 章源慶
地點 : 測量系教室 55180 時間 : ^{2014} 年 12 月 06 日 (六)
11：30~12：20 Isotopy and Invariants of Legendrian Surfaces
MeiLin Yau 姚美琳 (主持人：章源慶)
13：40~14：30 The CR Almost Schur Lemma
ChinTung Wu 吳進通 (主持人：蕭仁傑)
15：00~15：25 Manifolds with G _{2} Holonomy and Contact Structures
Hyunjoo Cho 趙玹珠 (主持人：劉珈銘)15：25~15：50
Constant Mean Curvature Foliations and CMC Time Functions in Spacetimes
KuoWei Lee 李國瑋 (主持人：劉珈銘)
Isotopy and Invariants of Legendrian Surfaces MeiLin Yau ( 姚美琳)
National Central University yau@math.ncu.edu.tw
Abstract
In this talk we will review the Lagrangian Gauss map associated to a Lagrangian surface, and explore a rigidity property of this map under Hamiltonian deformations. We then apply this rigidity to study the isotopy problem of Legendrian surfaces. This is a work in progress.
The CR almost Schur Lemma ChinTung Wu (吳進通) National Pingtung University
ctwu@mail.nptu.edu.tw
Abstract
I will talk about a general almost Schur Lemma on pseudoHermitian (2n1)manifolds. When the equality of almost Schur inequality holds, we derive the contact form is pseudoEinstein and the pseudoHermitian scalar curvature is constant.
Manifolds with
_{}Holonomy and Contact Structures Hyunjoo Cho ( 趙玹珠)
National Center for Theoretical Sciences (Taipei Office) hyunjoocho19@gmail.com
Abstract
A 7 dimensional Riemannian manifold M is called a _{} manifold if its holonomy group of its metric g is contained in the group _{}. In this talk, I first give brief introduction of _{} manifolds, and then discuss the _{} and contact structures. This is a joint work with Firat Arikan and Sema Salur.
Constant Mean Curvature Foliations and CMC Time Functions in Spacetimes KuoWei Lee (李國瑋)
National Taiwan University d93221007@gmail.com
Abstract
In this talk, we first give a brief introduction to the time functions in spacetimes and the relation between CMC foliations and time functions. Then we summarize some CMC foliations results in cosmological spacetimes, and discuss CMC foliations in the Schwarzschild spacetime, which is conjectured by Malec and O Murchadha in [1,2]. We will give more explanation in latter case and show some partial results in this conjecture. This is the joint work with YngIng Lee.
References：
[1] Malec, E.; O Murchadha, N.: Constant mean curvature slices in the extended Schwarz schild solution and the collapse of the lapse, Phys. Rev. D (3) 68 (2003), no. 12, 124019, 16 pp.
幾何
Organizer : WanKeng Cheong 章源慶
地點 : 測量系教室 55180 時間 : ^{2014} 年 12 月 07 日 (日)
09：00~09：50
Bergman Kernel Asymptotics for Big and Semipositive Line Bundles
ChinYu Hsiao 蕭欽玉 (主持人：鄺國權)
11：10~12：00 Landau Ginzburg Type Theories from Algebraic Geometry
HuaiLiang Chang 張懷良 (主持人：章源慶)13：30~13：55 Geometric Airy Curve Flows
HsiaoFan Liu 劉筱凡 (主持人：章源慶)
15：20~15：45
The Isotopy Problems of Symplectic Submanifolds and Jholomorphic Curves
ChingHao Chang 張清皓 (主持人：章源慶)
15：45~16：10
The Crofton Formula in the ThreeDimensional Heisenberg Group
YenChang Huang 黃彥彰 (主持人：章源慶)
Bergman Kernel Asymptotics for Big and Semipositive Line Bundles ChinYu Hsiao (蕭欽玉)
Academia Sinica chsiao@math.sinica.edu.tw
Abstract
Let L be a holomorphic line bundle over a complex manifold M and let be the k th power of L. If L is semipositive and positive at some point, we show that the Bergman kernel of admits a full asymptotic expansion on the set where L is positive, with the possible exception of a proper analytic variety Σ ⊂ M . We also prove the asymptotics for big line bundles endowed with singular Hermitian metrics with strictly positive curvature current. In this case the full asymptotics holds outside the singular locus of the metric. As a corollary, we could reprove the Shiffman conjecture, asserting that Moishezon manifolds can be characterized in terms of integral Kähler currents.
Landau Ginzburg Type Theories from Algebraic Geometry HuaiLiang Chang (張懷良)
Hong Kong University of Science and Technology mahlchang@ust.hk
Abstract
The Landau Ginzburg model unifies different moduli spaces and their counting in A side of mirror symmetry.
Algebrageometric approach to define it via pfields and cosection localization unifies these different theories, as like GromovWitten theory, FJRW theory, and also others. We will brief on their constructions, comparisons, and also relations which is work under progress.
Geometric Airy Curve Flows HsiaoFan Liu ( 劉筱凡)
Academia Sinica hfliu@math.sinica.edu.tw
Abstract
In this talk, I will explain geometric curves flows whose invariants flow according to some soliton equations. One of the most famous curve flows is the vortex filament equation in which corresponds to the nonlinear Schrödinger(NLS) equation. I will discuss the geometric airy curve flows on space forms whose invariants satisfy the vector modified KdV(vmKdV) type equations. The existence of solutions of such curve flows follows from the correspondence.
The Isotopy Problems of Symplectic Submanifolds and J holomorphic Curves ChingHao Chang (張清皓)
Academia Sinica chinghao@math.sinica.edu.tw
Abstract
The isotopy problem for symplectic submanifolds in a symplectic manifold is always a very interesting topic in symplectic topology. There are many researches about the isotopy problems for different categories of symplectic submanifolds in different symplectic manifolds using various techniques. For the compact symplectic 4manifold case, one of the approaches to attack the isotopy problem for the symplectic surfaces in a compact symplectic 4manifold ( , )M w is to study the isotopies for J holomorphic curves in ( , )M w where J is an
w
tame almost complex structure on M. In this talk, we will briefly introduce the idea and take a walk in the moduli space of Jholomorphic curves.The Crofton Formula in the ThreeDimensional Heisenberg Group YenChang Huang ( 黃彥彰)
National Central University yenchang.huang1@gmail.com
Abstract
In Euclidean space, the Crofton formula is a classic result of integral geometry. It states that the length of a given curve is equal to an integral over all straight lines. The formula has had many applications, for example Buffon’s needle and noodle problem, minimumtotalcurvature results, and a special case of Hilbert’s Fourth Problem; it has also been generated to the higher dimension. We derive the Croftonlike formula in the threedimensional Heisenberg group which can be realized as an example of the subRiemannian manifold. By using the method of the moving frames, we show that the parea of the regular surface is equal to the integral over all geodesics in the Heisenberg group.
動態系統與生物數學
Organizer : JungChao Ban 班榮超
地點 : 測量系教室 55150 時間 : ^{2014} 年 12 月 06 日 (六)
11：30~12：20
Mathematical Modeling of Bimodal Epigenetic Control in Ovarian Cancer Stem Cells
JeChiang Tsai 蔡志強 (主持人：許正雄)
13：40~14：05 Cluster Synchronization in Neural Networks
YuHao Liang 梁育豪 (主持人：蔡志強)
14：05~14：30 Zero Entropy Systems
WenChiao Cheng 鄭文巧 (主持人：蔡志強)
15：00~15：25
Proof of a Conjecture for the Onedimensional Perturbed Gelfand Problem from Combustion Theory
ShaoYuan Huang 黃少遠 (主持人：鄭文巧)
15：25~15：50
Traveling Wave Solutions for KolmogorovType Delayed Lattice ReactionDiffusion Systems
JianJhong Lin 林建仲 (主持人：鄭文巧)
Mathematical Modeling of Bimodal Epigenetic Control in Ovarian Cancer Stem Cells
JeChiang Tsai ( 蔡志強) National Chung Cheng University
tsaijc@math.ccu.edu.tw
Abstract
In ovarian and other cancers, emerging data indicate that cancer stem cells contribute to chemoresistance and that their persistence alters clinical outcome.
Previous study has shown that ovarian cancer may be initiated by ovarian cancer initiating cells characterized by surface antigen CD44 and cKIT.
Based on experimental evidence observation, we develop a mathematical mode to explore how the interaction between cKIT, tumor suppressor microRNA, and estrogenmediated RNA leads to overexpression of cKIT, and thus promotes ovarian carcinogenesis. This is a joint work with the human epigenomics group in CCU.
Cluster Synchronization in Neural Networks YuHao Liang (梁育豪)
National Chiao Tung University yhliang@mx.nthu.edu.tw
Abstract
In many chemical, biochemical, biological and neural systems, oscillatory cluster patterns have been observed frequently. Such cluster patterns facilitate some important chemical reactions easily to occur. In this talk, we consider the cluster synchronization in neural network consisting of coupled excitatory or inhibitory neurons. Moreover, in addition to the standard coupling between neurons, we also address a type of coupling for which one fast variable (activator) receives feedback from the slow variable (inhibitor). Examples of networks of identical/nonindentical FitzHughNagumo and HindmarshRose neurons are also taken into consideration.This is joint work with Jonq Juang.
Zero Entropy Systems WenChiao Cheng ( 鄭文巧) Chinese Culture University zwq2@faculty.pccu.edu.tw
Abstract
During this talk, for the zero entropy systems, entropy dimension, pressure dimension and local entropy dimension will be defined and some properties will be derived. In particular, analogue of variational principle and mass distribution principle will be shown.
Proof of a Conjecture for the Onedimensional Perturbed Gelfand Problem from Combustion Theory
ShaoYuan Huang (黃少遠) National Tsing Hua University
syhuang@math.nthu.edu.tw
Abstract
We study the global bifurcation curves and exact multiplicity of postive solutions for the onedimensional perturbed Gelfand problem
( ) exp 0, 1 x 1,
( 1) (1) 0, u x au
a u
u u
where is the FrankKamenetskii parameter and 0
a 0
is the activation energy parameter. We prove that there exists a critical bifurcation value a_{0}( 4.069) 4 such that, on the ( ,  ) u _{} plane, the bifurcation curve is Sshaped for aa_{0} and is monotone increasing for 0 a a _{0}.Traveling Wave Solutions for KolmogorovType Delayed Lattice Reaction Diffusion Systems
JianJhong Lin ( 林建仲) Feng Chia University jjlin@mx.math.ncu.edu.tw
Abstract
In this talk, we will focus on the existence of traveling wave solutions for Kolmogorovtype delayed lattice reaction diffusion systems. Employing the cross iterative technique coupled with the explicit construction of upper and lower solutions in the theory of quasimonotone dynamical systems, we can prove the existence of such solutions connecting two different equilibria. Moreover, our results can be applied to several ecological examples including onespecies, two species and threespecies models with various functional responses and time delays.
動態系統與生物數學
Organizer : JungChao Ban 班榮超
地點 : 測量系教室 55150 時間 : ^{2014} 年 12 月 07 日 (日)
09：00~09：50 Localized Waves in FitzHughNagumo Equations
ChaoNien Chen 陳兆年 (主持人：班榮超)
11：10~11：35
Conjugacy on the Symbolic Spaces of SFTs under (j,m) decimation
ChihHung Chang 張志鴻 (主持人：陳兆年)
11：35~12：00
Pattern Generation Problems Arising in Multiplicative Integer Systems
WenGuei Hu 胡文貴 (主持人：陳兆年)
13：30~13：55 Chaos in a Model for Masting
KaiRen Zheng 鄭凱仁 (主持人：胡文貴)
15：20~15：45
Traveling Wave Solutions for Two Species LotkaVolterra System with Spatial Segregations
ChihChiang Huang 黃志強 (主持人：張志鴻)
15：45~16：10
A Numerical Method for Bifurcations of Fixed Points of ODE Systems with Periodically Pulsed Inputs
HsiuChuan Wei 魏秀娟 (主持人：張志鴻)