• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.22 no.3
• /
• pp.417-425
• /
• 2012

In 2010, Sebe et al. proposed an efficient and lightweight mixnet scheme for remote voting systems. The scheme based on a cryptographic secure hash function, does not require complex and costly zero-knowledge proofs of their correct mixing operations, thus they claimed that their scheme is simple and efficient. In this paper, we propose more efficient and fast mixnet scheme than Sebe et al.'s scheme under the same assumption.

• Communications of the Korean Mathematical Society
• /
• v.37 no.2
• /
• pp.551-566
• /
• 2022

We apply Fourier-Legendre-based integration methods that had been given by Campbell in 2021, to evaluate new rational double hypergeometric sums involving ${\frac{{1}}{\pi}}$. Closed-form evaluations for dilogarithmic expressions are key to our proofs of these results. The single sums obtained from our double series are either inevaluable $_2F_1({\frac{4}{5}})$- or $_2F_1({\frac{1}{2}})$-series, or Ramanujan's ₃F₂(1)-series for the moments of the complete elliptic integral K. Furthermore, we make use of Ramanujan's finite sum identity for the aforementioned ₃F₂(1)-family to construct creative new proofs of Landau's asymptotic formula for the Landau constants.

• Proceedings of the Korea Society of Design Studies Conference
• /
• 2003.05a
• /
• pp.136-137
• /
• 2003

• Communications of the Korean Mathematical Society
• /
• v.10 no.3
• /
• pp.751-758
• /
• 1995

We prove the existence of solution for a Dirichlet singular boundary value problem. The proofs are based on the method of upper and lower solutions.

• Bulletin of the Korean Mathematical Society
• /
• v.41 no.3
• /
• pp.427-434
• /
• 2004

The purpose of the paper is to correct erroneous proofs of two theorems of Walters ([1]) about the pressure of continuous transformations.

• Bulletin of the Korean Mathematical Society
• /
• v.46 no.4
• /
• pp.701-712
• /
• 2009

In this paper, we study the simultaneous approximation to functions in $C^m$[0, 1] by neural networks with a squashing function and the complexity related to the simultaneous approximation using a Bernstein polynomial and the modulus of continuity. Our proofs are constructive.

• Journal of the Korean Mathematical Society
• /
• v.36 no.6
• /
• pp.1169-1180
• /
• 1999

Two-point comparison theorems between hyperbolic and euclidean geometry for convex regions in the complex plane are known([5], [6]). We give new geometric proofs of sharp two-point comparison theorems for convex regions.

• East Asian mathematical journal
• /
• v.22 no.1
• /
• pp.53-59
• /
• 2006

We introduce the resistant length and examine its properties. And consider the applications of resistant length to the boundary behavior of conformal mappings. We obtain the theorems in the connection with the resistant length zero and the fundamental sequences. The method of resistant length leads a simple proofs of theorems.

• Journal of applied mathematics & informatics
• /
• v.20 no.1_2
• /
• pp.647-655
• /
• 2006

We consider the applications of modulus to the boundary behavior of meromorphic functions in connection with the singularities. The proofs are based on the method of modulus. The relations between the moduli and the logarithmic capacities shall be introduced and we have shown that the conformal capacity is related to the modulus.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.6
• /
• pp.1855-1899
• /
• 2015

We discuss some additivity properties of the simplicial volume for manifolds with boundary: we give proofs of additivity for glueing amenable boundary components and of superadditivity for glueing amenable submanifolds of the boundary, and we discuss doubling of 3-manifolds.