• Korean Journal of Mathematics
• /
• 제28권4호
• /
• pp.791-802
• /
• 2020

We obtain a two variable generating function for the number of triangular partitions. Using this generating function, we study arithmetic properties of a certain weighted count of triangular partitions. Finally, we introduce a rank-type function for triangular partitions, which gives a combinatorial explanation for a triangular partition congruence.

• 대한수학회논문집
• /
• 제32권3호
• /
• pp.745-763
• /
• 2017

The Borel-Serre partial compactification gives cofinite models for the proper classifying space for arithmetic lattices. Non-arithmetic lattices arise only in semisimple Lie groups of ${\mathbb{R}}$-rank one. The author generalizes the Borel-Serre partial compactification to construct cofinite models for the proper classifying space for lattices in semisimple Lie groups of ${\mathbb{R}}$-rank one by using the reduction theory of Garland and Raghunathan.

• 대한수학회지
• /
• 제56권5호
• /
• pp.1355-1370
• /
• 2019

A curve $X{\subset}\mathbb{P}^r$ has maximal rank if for each $t{\in}\mathbb{N}$ the restriction map $H^0(\mathcal{O}_{\mathbb{P}r}(t)){\rightarrow}H^0(\mathcal{O}_X(t))$ is either injective or surjective. We show that for all integers $d{\geq}r+1$ there are maximal rank, but not arithmetically Cohen-Macaulay, smooth curves $X{\subset}\mathbb{P}^r$ with degree d and genus roughly $d^2/2r$, contrary to the case r = 3, where it was proved that their genus growths at most like $d^{3/2}$ (A. Dolcetti). Nevertheless there is a sector of large genera g, roughly between $d^2/(2r+2)$ and $d^2/2r$, where we prove the existence of smooth curves (even aCM ones) with degree d and genus g, but the only integral and non-degenerate maximal rank curves with degree d and arithmetic genus g are the aCM ones. For some (d, g, r) with high g we prove the existence of reducible non-degenerate maximal rank and non aCM curves $X{\subset}\mathbb{P}^r$ with degree d and arithmetic genus g, while (d, g, r) is not realized by non-degenerate maximal rank and non aCM integral curves.

• 대한전기학회논문지:시스템및제어부문D
• /
• 제54권8호
• /
• pp.501-503
• /
• 2005

In this paper, using ranks of co-occurrence frequency about indices in pairs of neighboring pixels, we introduce a new re-indexing algorithm for efficiency of index color image lossless compression. The proposed algorithm is suitable for arithmetic coding because it has concentrated distributions of small variance. Experimental results proved that the proposed algorithm reduces the bit rates than other coding schemes, more specifically $15\%$, $54\%$ and $12\%$ for LZW algorithm of GIF, the plain arithmetic coding method and Zeng's scheme, respectively.

• Korean Journal of Mathematics
• /
• 제10권1호
• /
• pp.67-74
• /
• 2002

Suppose linear forms whose coefficients are arithmetic progressions are given. In this paper, we will find the upper and lower bounds of the minimal ranks of subforms of these forms which left the Frobenius numbers invariant. This is an improvement of Ritter's bounds.

• Communications for Statistical Applications and Methods
• /
• 제19권3호
• /
• pp.367-379
• /
• 2012

야구경기에서 순위를 예측하는 것은 야구팬들에게 관심의 대상이 된다. 이러한 순위를 예측하기 위해서 2011년 한국프로야구 기록 자료를 바탕으로 산술평균방법, 가중평균방법, 주성분분석방법, 주성분회귀분석 방법을 제시한다. 표준화를 통한 산술평균, 상관계수를 이용한 가중평균과 주성분 분석을 이용해서 순위를 예측하고, 최종모형으로 주성분회귀분석 모형이 선택되었다. 주성분 분석으로 축약된 변수를 이용해서 회귀분석을 실시하여, 투수부분, 타자부분, 투수와 타자부분의 순위예측 모형을 제안한다. 예측된 회귀모형을 통해서 2012년도 순위 예측이 가능하다.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 2005년도 심포지엄 논문집 정보 및 제어부문
• /
• pp.164-166
• /
• 2005

In this paper, using ranks of co-occurrence frequency about indices in neighboring pixels, we introduce a new re-indexing scheme for efficiency of index color image lossless compression. The proposed method is suitable for arithmetic coding because it has skewed distributions of small variance. Experimental results proved that the proposed method reduces the bit rates than other coding schemes, more specifically 15%, 54% and 12% for LZW algorithm of GIF, the plain arithmetic coding method and Zeng's scheme.

• 대한수학회보
• /
• 제56권5호
• /
• pp.1219-1233
• /
• 2019

Let $E{\rightarrow}M$ be an arbitrary vector bundle of rank k over a Riemannian manifold M equipped with a fiber metric and a compatible connection $D^E$. R. Albuquerque constructed a general class of (two-weights) spherically symmetric metrics on E. In this paper, we give a characterization of locally symmetric spherically symmetric metrics on E in the case when $D^E$ is flat. We study also the Einstein property on E proving, among other results, that if $k{\geq}2$ and the base manifold is Einstein with positive constant scalar curvature, then there is a 1-parameter family of Einstein spherically symmetric metrics on E, which are not Ricci-flat.

• 대한수학회보
• /
• 제32권2호
• /
• pp.337-342
• /
• 1995

A semiring is a binary system $(S, +, \times)$ such that (S, +) is an Abelian monoid (identity 0), (S,x) is a monoid (identity 1), $\times$ distributes over +, 0 $\times s s \times 0 = 0$ for all s in S, and $1 \neq 0$. Usually S denotes the system and $\times$ is denoted by juxtaposition. If $(S,\times)$ is Abelian, then S is commutative. Thus all rings are semirings. Some examples of semirings which occur in combinatorics are Boolean algebra of subsets of a finite set (with addition being union and multiplication being intersection) and the nonnegative integers (with usual arithmetic). The concepts of matrix theory are defined over a semiring as over a field. Recently a number of authors have studied various problems of semiring matrix theory. In particular, Minc [4] has written an encyclopedic work on nonnegative matrices.

• East Asian mathematical journal
• /
• 제35권1호
• /
• pp.9-15
• /
• 2019

Kaavya introduce an involution on the set of partitions with crank 0 and studied the number of partitions of n which are invariant under Kaavya's involution. If a partition ${\lambda}$ with crank 0 is invariant under her involution, we say ${\lambda}$ is a self-conjugate partition with crank 0. We prove that the number of such partitions of n is equal to the number of partitions with rank 0 which are invariant under the usual partition conjugation. We also study arithmetic properties of such partitions and their q-theoretic implication.