• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.333-346
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• 2002

Let $F={F^v:S^1->S^1,v\in\; V$ and $g={G^v:S^1->S^1,v\in\; V$ be disjoint flows defined on the unit circle $S^1$, that is such flows that each their element either is the identity mapping or has no fixed point ((V, +) is a 2-divisible nontrivial abelian group). The aim of this paper is to give a necessary and sufficient codition for topological conjugacy of disjoint flows i.e., the existence of a homeomorphism $\Gamma:S^1->S^1$ satisfying $$\Gamma\circ\ F^v=G^v\circ\Gamma,\; v\in\; V$$ Moreover, under some further restrictions, we determine all such homeomorphisms.

• Bulletin of the Korean Mathematical Society
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• v.45 no.4
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• pp.729-737
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• 2008

In this paper we characterize multi-Jensen functions f : $V^n\;{\rightarrow}\;W$, where n is a positive integer, V, W are commutative groups and V is uniquely divisible by 2. Moreover, under the assumption that f : $\mathbb{R}\;{\rightarrow}\;\mathbb{R}$ is Borel measurable, we obtain representation of f (respectively, f, g, h : $\mathbb{R}\;{\rightarrow}\;\mathbb{R}$) such that the Jensen difference $$2f\;\(\frac{x\;+\;y}{2}\)\;-\;f(x)\;-\;f(y)$$ (respectively, the Pexider difference $$2f\;\(\frac{x\;+\;y}{2}\)\;-\;g(x)\;-\;h(y))$$ takes values in a countable subgroup of $\mathbb{R}$.

• Proceedings of the IEEK Conference
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• 2003.07e
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• pp.2471-2474
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• 2003

The modified discrete cosine transform (MDCT) and its inverse transform (IMDCT) are employed in subband/transform coding schemes as the analysis/synthesis filter bank based on time domain aliasing cancellation (TDAC). And they are the most computational intensive operations in layer III of the MPEG audio coding standard. In this paper, we propose a new efficient algorithm for the MDCT/IMDCT computation. It is based on the MDCT/IMDCT computation algorithm using the discrete cosine transforms (DCTs), and it employs two discrete cosine transform of type II(DCT-II) to compute the MDCT/IMDCT. In addition to, it takes advantage of ability in calculating the MDCT/IMDCT computation, where the length of a data block is divisible by 4. The proposed algorithm in this paper requires less calculation complexity than the existing methods. Also, it can be implemented by the parallel structure,, and its structure is particularly suitable for VLSI realization.

• Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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• 2001.11a
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• pp.177-180
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• 2001

선불방식의 화폐시스템에서 고객은 인출한 화폐를 은행으로부터 환불받을 수 있어야 한다. 그러나 분할된 화폐가 서로 연관될 수 있는 분할 가능한 화폐시스템에서는 고객이 사용한 화폐의 익명성을 유지하면서 남은 금액을 환불해주기가 어렵다. 이 논문에서 이런 문제를 해결한 새로운 방식의 환불 메커니즘을 제공한다. 제안된 새 방식에서 고객은 은행에 익명으로 접근하여 환불티켓을 인출하고, 나중에 인출된 티켓을 이용하여 기존 지불의 익명성을 유지하면서 환불을 받게 된다. 환불티켓을 사용하면 환불과정을 인출이나 지불과정과 독립적으로 제공할 수 있어 환불이 필요없는 경우에는 아무런 추가비용이 소요되지 않는 장점이 있다. 또한 같은 이유에서 여러 시스템에 쉽게 응용이 가능한 유연한 방식이다. 끝으로 환불액을 계속해서 하나의 티켓에 축적하는 방법을 사용하면 지불액과 환불액간에 직접적인 차액관계가 없어지므로 고객의 익명성이 증진되며, 은행에 접촉해야 하는 횟수를 줄여주는 효과가 있다.

• Journal of the Korean Mathematical Society
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• v.57 no.1
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• pp.131-144
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• 2020

Characterizations of almost perfect domains by certain covers and envelopes, due to Bazzoni-Salce [7] and Bazzoni [4], are generalized to almost perfect commutative rings (with zero-divisors). These rings were introduced recently by Fuchs-Salce [14], showing that the new rings share numerous properties of the domain case. In this note, it is proved that admitting strongly flat covers characterizes the almost perfect rings within the class of commutative rings (Theorem 3.7). Also, the existence of projective dimension 1 covers characterizes the same class of rings within the class of commutative rings admitting the cotorsion pair (𝒫₁, 𝒟) (Theorem 4.1). Similar characterization is proved concerning the existence of divisible envelopes for h-local rings in the same class (Theorem 5.3). In addition, Bazzoni's characterization via direct sums of weak-injective modules [4] is extended to all commutative rings (Theorem 6.4). Several ideas of the proofs known for integral domains are adapted to rings with zero-divisors.

• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.961-973
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• 1994

A stochastics process $X = {X(t) : t \in T}$, with an index set T, is said to be infinitely divisible (ID) if its finite dimensional distributions are all ID. An ID process X is said to be a stochastic integral process if $X = {X(t) : t \in T} =^D {\int f_td\Lambda : t \in T}$ where $f : T \times S \to R$ is a deterministic function and $\Lambda$ is an ID random measure on a $\delta$-ring S of subsets of an arbitrary non-empty set S with the property; there exists an increasing sequence ${S_n}$ of sets in S with $U_n S_n = S$. Here $=^D$ denotes equality in all finite dimensional distributions.

• The Korean Journal of Applied Statistics
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• v.3 no.2
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• pp.55-77
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• 1990

In this paper we descuss some E-optimal block designs having unequal block sizes, and give a table of E-optimal designs with 2 different block sizes which can be constructed using the method described in Theorem 3. 2, Theorem 3. 4 and Theorem 3. 5 proved by Lee and Jacroux (1987). All of source designs used are Group Divisible designs which can be found in Clathworthy(1973) or Balanced Incomplete block designs in Raghavarar(1971).

• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1513-1528
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• 2021

Let R be a commutative ring with prime nilradical Nil(R) and M an R-module. Define the map 𝜙 : R → R_Nil(R) by ${\phi}(r)=\frac{r}{1}$ for r ∈ R and 𝜓 : M → M_Nil(R) by ${\psi}(x)=\frac{x}{1}$ for x ∈ M. Then 𝜓(M) is a 𝜙(R)-module. An R-module P is said to be 𝜙-projective if 𝜓(P) is projective as a 𝜙(R)-module. In this paper, 𝜙-exact sequences and 𝜙-projective R-modules are introduced and the rings over which all R-modules are 𝜙-projective are investigated.

• Korean Journal of Mathematics
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• v.29 no.4
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• pp.733-740
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• 2021

Let (F_n)_n≥0 be the Fibonacci sequence and p be a prime number. For 1≤k≤m, the Fibonomial coefficient is defined as $$\[\array{m\\k}\]_F=\frac{F_{m-k+1}{\ldots}{F_{m-1}F_m}}{{F_1}{\ldots}{F_k}}$$ and $\[\array{m\\k}\]_F=0$ whan k>m. Let a and n be positive integers. In this paper, we find the conditions of prime number p which divides Fibonomial coefficient $\[\array{P^{a+n}\\{p^a}}\]_F$. Furthermore, we also find the conditions of p when $\[\array{P^{a+n}\\{p^a}}\]_F$ is not divisible by p.

• Journal of the Korean Mathematical Society
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• v.60 no.5
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• pp.1087-1107
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• 2023

Let E be an elliptic curve defined over ℚ of conductor N, c the Manin constant of E, and m the product of Tamagawa numbers of E at prime divisors of N. Let K be an imaginary quadratic field where all prime divisors of N split in K, P_K the Heegner point in E(K), and III(E/K) the Shafarevich-Tate group of E over K. Let 2u_K be the number of roots of unity contained in K. Gross and Zagier conjectured that if P_K has infinite order in E(K), then the integer c · m · u_K · |III(E/K)| $\frac{1}{2}$ is divisible by |E(ℚ)_tor|. In this paper, we prove that this conjecture is true if E(ℚ)_tor ≅ ℤ/2ℤ or ℤ/4ℤ except for two explicit families of curves. Further, we show these exceptions can be removed under Stein-Watkins conjecture.