姓名 孫新民 系所 應用數學系 校內分機 595 EMAIL sunhm@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)

 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 Taiwanese Journal of Mathematics 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 Journal of Combinatorial Designs 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 Journal of Combinatorial Designs 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”. 關鍵字： 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 Taiwanese Journal of Mathematics 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： Minimum variance allocation among constrained intervals 年度： 2019 類別： 期刊論文 Journal of Global Optimization 摘要： We propose a weighted minimum variance allocation model, denoted by WMVA, which distributes an amount of a divisible resource as fairly as possible while satisfying all demand intervals. We show that the problem WMVA has a unique optimal solution and it can be characterized by the uniform distribution property (UDP in short). Based on the UDP property, we develop an efficient algorithm. Theoretically, our algorithm has a worst-case O(n^2) complexity, but we prove that, subject to slight conditions, the worst case cannot happen on a 64-bit computer when the problem dimension is greater than 129. We provide extensive simulation results to support the argument and it explains why, in practice, our algorithm runs significantly faster than most existing algorithms, including many O(n) algorithms. 關鍵字： Singly constrained quadratic program, Separable convex programming, Quadratic knapsack problem, Resource distribution 著作名稱： Existence of simple BIBDs from a prime power difference family with minimum index 年度： 2018 類別： 期刊論文 Journal of Algebra and Its Applications 摘要： We show that under certain technical conditions that simple (q,k,iλ_min) balanced incomplete block designs (BIBDs) exist for all allowable values of i, where q is an odd prime power. Our primary technique is to argue for the existence of difference families in finite fields, in the flavor of Wilson [J. Number Theory 4 (1972) 17–47]. We provide an extensive analysis in the cases, where q≡1 (modk(k−1)) and also for k 9,16. 關鍵字： balanced incomplete block design, finite field 著作名稱： Some sequences of optimal constant weight codes 年度： 2017 類別： 期刊論文 Journal of Algebra and Its Applications 摘要： We introduce some sequences of binary constant weight codes which are constructed from the affine constructions of balanced incomplete block designs. They give the values for the function A(n,d,w) of constant weight codes, and they are optimal since those values reach the Johnson Bound. We focus on the values obtained by this method. 關鍵字： A(n,d,w); BIBD; finite field. 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 摘要： 關鍵字： 著作名稱： On the Existence of Simple BIBDs 年度： 2015 類別： 會議論文 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： 會議論文 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. 關鍵字： 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： 會議論文 摘要： 關鍵字： 著作名稱： From Planar Nearrings to Block Designs, 19th International Conference on Nearrings and Nearfields, 2005. 年度： 2005 類別： 會議論文 摘要： 關鍵字： 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： 會議論文 摘要： 關鍵字： 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： 會議論文 摘要： 關鍵字： 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： 會議論文 摘要： 關鍵字： 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： 會議論文 摘要： 關鍵字： 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： 會議論文 摘要： 關鍵字： 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： 會議論文 摘要： 關鍵字： 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： 會議論文 摘要： 關鍵字： 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： 會議論文 摘要： 關鍵字： 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： 會議論文 摘要： 關鍵字： 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： 會議論文 摘要： 關鍵字： 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： 會議論文 摘要： 關鍵字： 著作名稱： On the Existence of Simple BIBDs and Cyclic Simple BIBDs 年度： 2015 類別： 會議論文 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. 關鍵字： 著作名稱： On the Decomposition of $\lambda K_q$ into Distinct k-cliques 年度： 2015 類別： 會議論文 摘要： In this talk I will introduce the decomposition of the multigraph $\lambda K_q$ into distinct $k$-cliques. 關鍵字：