• International Journal of Computer Science & Network Security
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• v.21 no.8
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• pp.17-27
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• 2021

Non-abelian group based cryptosystems are a latest research inspiration, since they offer better security due to their non-abelian properties. In this paper, we propose a novel approach to non-abelian group based public-key cryptographic protocols using semidirect products of finite groups. An intractable problem of determining automorphisms and generating elements of a group is introduced as the underlying mathematical problem for the suggested protocols. Then, we show that the difficult problem of determining paths and cycles of Cayley graphs including Hamiltonian paths and cycles could be reduced to this intractable problem. The applicability of Hamiltonian paths, and in fact any random path in Cayley graphs in the above cryptographic schemes and an application of the same concept to two previous cryptographic protocols based on a Generalized Discrete Logarithm Problem is discussed. Moreover, an alternative method of improving the security is also presented.

• Journal of Astronomy and Space Sciences
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• v.38 no.2
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• pp.93-103
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• 2021

In this work, the problem of resonance caused by some gravitational potentials due to Mercury and a third body, namely the Sun, together with some non-gravitational perturbations, specifically coronal mass ejections and solar wind in addition to radiation pressure, are investigated. Some simplifying assumptions without loss of accuracy are employed. The considered force model is constructed. Then the Delaunay canonical set is introduced. The Hamiltonian of the problem is obtained then it is expressed in terms of the Deluanay canonical set. The Hamiltonian is re-ordered to adopt it to the perturbation technique used to solve the problem. The Lie transform method is surveyed. The Hamiltonian is doubly averaged. The resonance capture is investigated. Finally, some numerical simulations are illustrated and are analyzed. Many resonant inclinations are revealed.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.741-754
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• 2023

In this paper, we study the existence and nonexistence of solutions for a class of Hamiltonian strongly degenerate elliptic system with subcritical growth $$\left{\array{-{\Delta}_{\lambda}u-{\mu}v={\mid}v{\mid}^{p-1}v&&\text{in }{\Omega},\\-{\Delta}_{\lambda}v-{\mu}u={\mid}u{\mid}^{q-1}u&&\text{in }{\Omega},\\u=v=0&&\text{ on }{\partial}{\Omega},}$$ where p, q > 1 and Ω is a smooth bounded domain in ℝ^N, N ≥ 3. Here Δ_λ is the strongly degenerate elliptic operator. The existence of at least a nontrivial solution is obtained by variational methods while the nonexistence of positive solutions are proven by a contradiction argument.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1137-1145
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• 1996

A Steinhaus graph is a labelled graph whose adjacency matrix $A = (a_{i,j})$ has the Steinhaus property : $a_{i,j} + a{i,j+1} \equiv a_{i+1,j+1} (mod 2)$. We consider random Steinhaus graphs with n labelled vertices in which edges are chosen independently and with probability $\frac{1}{2}$. We prove that almost all Steinhaus graphs are Hamiltonian like as in random graph theory.

• Proceedings of the Korean Information Science Society Conference
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• 2002.04a
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• pp.670-672
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• 2002

본 논문에서는 2개의 랩어라운드 에지를 갖는 m$\times$n(m 2, n$\geq$3, n 흘수) 그리드 그래프에서의 해밀톤 성질을 고려한다. 먼저 그리드 그래프가 해밀톤 연결된(hamiltonian-connected)그래프가 되기 위해 추가로 필요한 에지의 수가 2개 이상임을 보인다. 그리고 m$\times$n 그리드 그래프의 첫 행에 랩어라운드 에지를 추가한 그래프의 해밀톤 성질을 보인 후, m$\times$n 그리드 그래프의 첫 행과 마지막 행에 램어라운드 에지를 추가한 그래프가 해밀톤 연결된 그래프임을 보인다.

• Journal of the korean Society of Automotive Engineers
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• v.14 no.3
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• pp.43-56
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• 1992

This task is to derive the Hamiltonian equations of motion for BMW 323i vehicle. The kinematic relationships are defined. The cut constraint equations are derived. The cut constraint equations are stabilized. The stabilized constraint equations are used to derive the relationships between the independent and dependent coordinates. The Hamiltonian equations of motion are reduced only in terms of the independent generalized coordinates.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.23 no.3
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• pp.240-244
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• 2010

The surface segregation and surface order near the order-disorder phase transition of FeCo alloy was studied through Monte Carlo simulation of an Ising type model Hamiltonian. The results showed that the proper choice of Hamiltonian parameters could reproduce the recent observation of surface order above the transition temperature and that the field term played dominant role.

• Journal of The Korean Astronomical Society
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• v.40 no.2
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• pp.49-60
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• 2007

This paper deals with the theory for rotational motion of a two-layer Earth model (an inelastic mantle and liquid core) including the dissipation in the mantle-core boundary(CMB) along with tidal effects produced by Moon and Sun. An analytical solution being derived using Hori's perturbation technique at a second order Hamiltonian. Numerical nutation series will be deduced from the theory.

• Bulletin of the Korean Mathematical Society
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• v.54 no.5
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• pp.1803-1825
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• 2017

Let X be a smooth scheme with an action of an algebraic group G. We establish an equivalence of two categories related to the corresponding moment map ${\mu}:T^{\ast}X{\rightarrow}g^{\ast}$ - the derived category of G-equivariant coherent sheaves on the derived fiber ${\mu}^{-1}(0)$ and the derived category of G-equivariant matrix factorizations on $T^{\ast}X{\times}g$ with potential given by ${\mu}$.

• Nuclear Engineering and Technology
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• v.1 no.2
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• pp.103-106
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• 1969

A new representation for the Dirac equation, which may be appropriate to describe the interaction of the charged particle with the electric field, is derived by introducing a gauge-independent unitary transformation. It is shown that in this representation the effective Hamiltonian without potentials has a new feature in the non-relativistic limit.