• Journal of the Korean Statistical Society
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• v.32 no.1
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• pp.21-24
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• 2003

In the recent papers by Harris and Park (1994) and by Hui and Park (2000), a family of lattice distributions derived from a sum of independent identically distributed random variables is examined. In this paper we generalize a result of Hui and Park (2000) on lattice distributions on the torus using the Poisson summation formula.

• East Asian mathematical journal
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• v.16 no.1
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• pp.71-79
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• 2000

We show that the intersection of two standard torus knots of type (${\lambda}_1$, ${\lambda}_2$) and (${\beta}_1$, ${\beta}_2$) induces an automorphism of the cyclic group ${\mathbb{Z}}_d$, where d is the intersection number of the two torus knots and give an elementary proof of the fact that all non-trivial torus knots are strongly invertiable knots. We also show that the intersection of two standard knots on the 3-torus $S^1{\times}S^1{\times}S^1$ induces an isomorphism of cyclic groups.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.23 no.3
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• pp.561-566
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• 2013

We propose an efficient exponentiation method which is resistant against some side channel attacks in $T_2(p)$, Torus-Based-Cryptosystem. It is more efficient than the general exponentiation method in $T_2(p)$ and is resistant against SPA by using that the difference of squaring and multiplication costs is negligible. Moreover, we can randomize a message in exponentiation step using the characteristic of quotient group which naturally protects against the first DPA.

• ETRI Journal
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• v.31 no.3
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• pp.327-329
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• 2009

In a network, broadcasting is the dissemination of a message from a source node holding a message to all the remaining nodes through a call. This letter proposes a one-to-all broadcasting algorithm in the Petersen-torus network PT(n, n) for the single-link-available and multiple-link-available models. A PT(n, n) is a regular network whose degree is 4 and number of nodes is $10n^2$, where the Petersen graph is set as a basic module, and the basic module is connected in the form of a torus. A broadcasting algorithm is developed using a divide-and-conquer technique, and the time complexity of the proposed algorithm approximates n+4, the diameter of PT(n, n), which is the lower bound of the time complexity of broadcasting.

• Journal of KIISE:Computer Systems and Theory
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• v.35 no.6
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• pp.263-272
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• 2008

We propose and analyze a new interconnection network, called petersen-torus(PT) network based on well-known petersen graph. PT network has a smaller diameter and a smaller network cost than honeycomb torus with same number of nodes. In this paper, we propose optimal routing algorithm and hamiltonian cycle algorithm. We derive diameter, network cost and bisection width.

• Korean Journal of Mathematics
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• v.16 no.4
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• pp.527-535
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• 2008

Let $I{\in}C^{1,1}$ be a strongly indefinite functional defined on a Hilbert space H. We investigate the number of the critical points of I when I satisfies one pair of Torus-Sphere variational linking inequality. We show that I has at least two critical points when I satisfies one pair of Torus-Sphere variational linking inequality with $(P.S.)^*_c$ condition. We prove this result by use of the limit relative category and critical point theory on the manifold with boundary.

• The KIPS Transactions:PartA
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• v.15A no.4
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• pp.189-198
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• 2008

In this paper, we prove mesh-like networks can be embedded into Petersen-Torus(PT) networks. Once interconnection network G is embedded in H, the parallel algorithm designed in Gcan be applied to interconnection network H. The torus is embedded into PT with dilation 5, link congestion 5 and expansion 1 using one-to-one embedding. The honeycomb mesh is embedded into PT with dilation 5, link congestion 2 and expansion 5/3 using one-to-one embedding. Additional, We derive average dilation. The embedding algorithm could be available in both wormhole routing system and store-and-forward routing system by embedding the generally known Torus and honeycomb mesh networks into PT at 5 or less of dilation and congestion, and the processor throughput could be minimized at simulation through one-to-one.

• Journal of the Korean Mathematical Society
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• v.46 no.3
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• pp.609-620
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• 2009

We establish some estimates on the hyper bilinear Hilbert transform on both Euclidean space and torus. We also use a transference method to obtain a Kenig-Stein's estimate on bilinear fractional integrals on the n-torus.

• Korean Journal of Mathematics
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• v.5 no.1
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• pp.17-27
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• 1997

In this paper we define a torsion function ${\log}\;T(M,{\varphi})(t)$) for $t{\gg}0$ and show that it has an asymptotic expansion $\frac{1}{2}{\chi}(M)t$ as $t{\rightarrow}{\infty}$.

• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.249-256
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• 2016

There are many concepts around classical theta functions, theta vectors and quantum theta functions. Manin clarified the relation among these concepts with the symmetry of functional equations. We extend his results to the super torus.