國立臺南大學專任教師基本資料
姓名孫新民
系所應用數學系
職稱副教授
校內分機595
EMAILsunhm@mail.nutn.edu.tw
辦公室C209-5
網址 
專長/研究領域離散數學 (Discrete Mathematics), 代數 (Algebra)
學位畢業學校國別主修學門修業期間
學士中央大學中華民國數學系1983~1987
博士亞歷桑那大學美國數學系1991~1995
碩士亞歷桑那大學美國數學系1994/05
服務機關部門系所職稱服務期間
中央研究院資訊科學所研究助理1989/10~1991/06
嘉南藥學專科學校醫務管理學系副教授1995/08~1996/07
嘉南藥理學院醫務管理學系副教授1996/08~2000/07
嘉南藥理科技大學醫務管理學系副教授2000/08~2003/07
國立臺南師範學院應用數學系副教授2003/08/01-2004/07/31
國立臺南大學應用數學系副教授2004/08/01-
著作名稱:More Results on the Existence of Simple BIBDs with Number of Elements a Prime Power
年度:2016
類別:期刊論文
摘要:We study the existence of simple (q,k,λ) BIBDs when the number of elements is a prime power q and {c1,c2 }∩{1,2} is not empty, where c1gcd(k,q−1) and c2gcd(k−1,q−1). We show that in many situations the necessary conditions λ(q−1)≡0 mod (k−1), λq(q−1)≡0 mod k(k−1), and λ≤C(q−2,k−2) are also sufficient for the existence of a simple (q,k,λ) BIBD. These new results improve the valid range of simple BIBDs.
關鍵字:Balanced incomplete block design, Finite field, Generating block.
著作名稱:On the Existence of Simple BIBDs with Number of Elements a Prime Power
年度:2013
類別:期刊論文
摘要:We show that, when the number of elements is a prime power q, in many situations the necessary conditions (1) λ(q-1)≡0 mod(k-1), (2) λq(q-1)≡0 mod k(k-1), and (3) λC(q-1,k-1)  are also sufficient for the existence of a (q, k, λ) simple balanced incomplete block design.
關鍵字:Simple BIBDs
著作名稱:Correction to: “On the Existence of Simple BIBDs with Number of Elements a Prime Power”
年度:2013
類別:期刊論文
摘要:The author corrects some errors in Theorem 17 of the paper entitled “On the existence of simple BIBDs with number of elements a prime power”.
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著作名稱:From Planar Nearrings to Generating Blocks, Taiwanese Journal of Mathematics, Vol. 14, No. 5, 2010, 1713—1739.
年度:2010
類別:期刊論文
摘要:Planar nearrings, like most of the subjects in finite geometries, can be applied for the construction of block designs. In this article we introduce the ideas of constructing simple BIBDs (balanced incomplete block designs) from field-generated (or nearfield-generated) planar nearrings. Further investigation reveals that there are strong connections between these kinds of constructions and the action of a sharply $2$-transitive group on a set. We next explore the structures of the constructions. The theory is derived from finite fields directly. The main point is on finding a subset $S$ (called generating block) of the field $F$ with respect to the given stabilizer $Stab_{F^*}(S)$. A big portion of simple BIBDs with various parameters can be obtained in this way; many simple BIBDs with the same parameters appear. We classify the constructed BIBDs according to the types of the respective generating blocks.
關鍵字:finite field; balanced incomplete block design; difference family; planar nearring.
著作名稱:PBIB Designs and Association Schemes Obtained from Finite Rings, Discrete Mathematics, Vol. 252, 2002, 267—277.
年度:2002
類別:期刊論文
摘要:We assume $(R,+,\cdot)$ is a ring with unit. Let $\cu (R)$ denote the set of invertible elements and suppose $\Phi$ is a subgroup of $\cu (R)$ with $-1\in\Phi$. Define an equivalence relation $\sim$ on $R^* R \setminus \{0\}$ by $s_1 \sim s_2$ if there is $b \in \Phi$ such that $bs_1 s_2$. Let $s_1, s_2, \dots ,s_{m}$ be representatives of the distinct equivalence classes. Define $A_i\{\{x,y\}\mid (y-x)\sim s_i\}$ for $i1,2,\dots,m$. We prove that $(R, \ca)$ is an association scheme, where $\ca \{A_i\mid i 1, 2,\dots, m\}$. Next suppose $R$ is finite and let $S$ be a proper subset of $R$ with $|S|\geq 2$. Define $\cb \{bS+a\mid b\in\Phi,\,a\in R\}$. Then $(R,\cb,\ca)$ is a PBIBD\,(partially balanced incomplete block design). Moreover, if $S$ satisfies $S\ne -S+a$ for any $a$, then the above PBIBD can be partitioned into two isomorphic PBIBDs. The application of PBIBDs to constant weight codes is introduced.
關鍵字:association scheme; partially balanced incomplete block design; PBIBD; ring; constant weight code.
著作名稱:Segments in a Planar Nearring, Discrete Mathematics, Vol. 240, 2001, 205—217.
年度:2001
類別:期刊論文
摘要:We prove that under many circumstances we have \[ \overline{a,b}\overline{c,d}\Longleftrightarrow \{a,b\}\{c,d\}, \] which is the same phenomenon as in the Euclidean plane.
關鍵字:ring; field; nearfield; planar nearring; segment.
著作名稱:A Note on Breaking and Repairing a Secure Broadcasting in Large Networks, Computer Communications, Vol. 22, No. 2, 1999, 193—194.
年度:1999
類別:期刊論文
摘要:In this note, we show that a proposed secure broadcasting scheme is insecure. We also present a modified scheme to overcome this weakness. The modified scheme has the extra advantage that each participant can derive his group keys from group identities without the need of knowing other information.
關鍵字:Secure system; Broadcasting; Network security; Cryptography; Computer network.
著作名稱:醫院及衛生機構對醫務管理人才專業能力需求之初探, 醫護科技學刊, Vol. 2, No. 1, 2000, 56—64.
年度:2000
類別:期刊論文
摘要:社會進步加上醫療環境的巨變,對於醫院的經營管理產生極大的衝擊,因此醫管專業也越來越受重視,而我國醫管人才的培育管道從專科到研究所都有,尤其在近幾年面臨教育制度的改革,許多原本以培育醫管人力的專科學校,紛紛升格為技術學院,從人力素質層面而言,可使專科畢業生多了一個選擇進修的機會,對整體素質的提升有其正面的意義,但從人力應用層面而言,專科學生畢業後多數選擇繼續升學的傾向,也影響到學校的課程內容與設計,甚至扭曲了醫管專科以培養醫院中基層實務專業人員的教育目標。此外,就技專校院設立的宗旨,在於培養專業技術及管理人才以符合產業及工作所需的目的來看,設有醫管科系所的學校其所開設的醫管相關專業課程,是否能滿足醫療相關工作的需要,便是本研究主要探討的目的。本研究主要針對衛生署在84至86年評鑑合格的區域級以上醫院及各級衛生機關(包括衛生署、衛生局、中央健康保險局總局及各分局)首長,進行郵寄問卷調查,研究結果顯示有高達93.5%的醫院內有進用醫管人力,而衛生機關則僅有50%有進用醫管人力,對於未來醫管人力的培育方式而言,多數醫院院長建議以大學(含二技及四技)以上最適當,而衛生機關首長則建議以研究所方式為宜。此外,醫院院長也建議醫管人力應加強醫療行銷管理、醫療品質管理、醫療財務管理、醫療資訊管理及保險申報實務等學科的訓練,而衛生機關首長則建議應加強其衛生行政與醫療政策、流行病學、醫療保險制度、醫療相關法規及醫療品質管理等學科的訓練。
關鍵字:醫務管理;醫管人力;醫管教育。
著作名稱:Simple Balanced Incomplete Block Designs with Parameters (q,k,k(k-1)), Chia Nan Annual Bulletin, Vol. 25, 1999, 90—94.
年度:1999
類別:期刊論文
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著作名稱:On the Existence of Simple BIBDs
年度:2015
類別:研討會
摘要:We introduce more results showing that, when the number of elements is a prime power, in many situations the necessary conditions \begin{enumerate} \item $\lambda (q-1)\equiv 0 \mod (k-1)$, \item $\lambda q(q-1)\equiv 0 \mod k(k-1)$, and \item $\lambda\leq \binom{q-2}{k-2}$ \end{enumerate} are also sufficient for the existence of a $(q,k,\lambda)$ simple BIBD. Some series of cyclic simple BIBDs are also obtained.
關鍵字:balanced incomplete block design; finite field; generating block.
著作名稱:On the Existence of Simple BIBDs
年度:2014
類別:研討會
摘要:We show that, when the number of elements is a prime power, in many situations the necessary conditions are also sufficient for the existence of a simple BIBD.
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著作名稱:Some Results on Segments and Lines of a Planar Nearring, 20th International Conference on Nearrings and Nearfields, 2007
年度:2007
類別:研討會
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著作名稱:From Planar Nearrings to Block Designs, 19th International Conference on Nearrings and Nearfields, 2005.
年度:2005
類別:研討會
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著作名稱:New Series of Optimal Constant Weight Codes, 2002 International Mathematics Conference and Annual Meeting of Mathematical Society of R.O.C., Dec. 6-8, 2002.
年度:2002
類別:研討會
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著作名稱:Maximizing the Elementary Symmetric Functions Subject to Constant Sum and Simple Bounds, International Conference on Optimization and Optimal Control, June 1-4, 2001.
年度:2001
類別:研討會
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著作名稱:Recursive Constructions of Simple Balanced Incomplete Block Designs, Second Pacific Rim Conference on Mathematics, Jan. 4-8, 2001.
年度:2001
類別:研討會
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著作名稱:BIBDs and Constant Weight Codes, 2000年夏季組合數學研討會, June 30/July 1, 2000.
年度:2000
類別:研討會
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著作名稱:Interval Sequence, 理論中心第二屆組合數學暨演算法研討會, May 12-14, 2000.
年度:2000
類別:研討會
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著作名稱:BIB Designs, 理論中心第二屆組合數學暨演算法研討會, May 12-14, 2000.
年度:2000
類別:研討會
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著作名稱:Constructions of Resolvable BIB Designs, 第十七屆組合數學與計算理論研討會, April 29, 2000.
年度:2000
類別:研討會
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著作名稱:Constructions of Regular Simple Graphs and Factorizations of the Complete Graphs by Association Schemes, 2000年組合數學研討會, Jan. 28-29, 2000.
年度:2000
類別:研討會
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著作名稱:Cryptanalysis of the Wu-Dawson Public-Key Cryptosystem Based on Generalized Inverses of Matrices, Proceedings of Ninth National Conference on Information Security, 1999, 218—220.
年度:1999
類別:研討會
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著作名稱:A Secure Broadcasting Cryptosystem in Large Computer Networks, Proceedings of Eighth National Conference on Information Security, May 15-16, 1998, 369—378.
年度:1998
類別:研討會
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著作名稱:On-line Multiple Secret Sharing Based on a One-Way Function, Proceedings of Eighth National Conference on Information Security, May 15-16, 1998, 331—336.
年度:1998
類別:研討會
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著作名稱:On the Existence of Simple BIBDs and Cyclic Simple BIBDs
年度:2015
類別:研討會
摘要:We show that in many situations necessary conditions λ(v−1)≡0 (mod k−1), λv(v−1)≡0 (mod k (k−1)), λ≤(v−2k−2)λmax are also sufficient for the existence of a (v,k,λ) simple BIBD, some series of cyclic simple BIBDs are obtained.
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著作名稱:On the Decomposition of $\lambda K_q$ into Distinct k-cliques
年度:2015
類別:研討會
摘要:In this talk I will introduce the decomposition of the multigraph $\lambda K_q$ into distinct $k$-cliques.
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