• 천문학회지
• /
• 제29권spc1호
• /
• pp.285-286
• /
• 1996

A systematric method of exploring the 'geometrical' and 'non-geometrical' constants of the motion for an arbitrary spacetime is presented. This is done by introducing a series of coupled differential equation for the generators of the symmetry group of Vlasov's equation. The method is applied to the case of the maximaly symmetric spectime, and the geometrical and non-geometrical constants of motion are obtained.

• Nonlinear Functional Analysis and Applications
• /
• 제28권3호
• /
• pp.851-863
• /
• 2023

We study the appropriate conditions for the findings of uniqueness and existence for a group of boundary value problems for impulsive Ψ-Caputo fractional nonlinear Volterra-Fredholm integro-differential equations (V-FIDEs) with symmetric boundary non-instantaneous conditions in this paper. The findings are based on the fixed point theorem of Krasnoselskii and the Banach contraction principle. Finally, the application is provided to validate our primary findings.

• Bulletin of the Korean Chemical Society
• /
• 제34권12호
• /
• pp.3777-3781
• /
• 2013

A formal total synthesis of aliskiren was accomplished. A key in our synthesis was to use the symmetric ciscisoid-cis-bis-lactone 3' as a precursor, which was prepared from D-tartrate diester. Appending the end groups and functional group transformations completed the synthesis.

• Nuclear Engineering and Technology
• /
• 제53권2호
• /
• pp.357-367
• /
• 2021

In general, common cause failures (CCFs) have been modeled with the assumption that components within the same group are symmetric. This assumption reduces the number of parameters required for the CCF probability estimation and allows us to use a parametric model, such as the alpha factor model. Although there are various asymmetric conditions in nuclear power plants (NPPs) to be addressed, the traditional CCF models are limited to symmetric conditions. Therefore, this paper proposes the copulabased CCF model to deal with asymmetric as well as symmetric CCFs. Once a joint distribution between the components is constructed using copulas, the proposed model is able to provide the probability of common cause basic events (CCBEs) by formulating a system of equations without symmetry assumptions. In addition, Bayesian inferences for the parameters of the marginal and copula distributions are introduced and Markov Chain Monte Carlo (MCMC) algorithms are employed to sample from the posterior distribution. Three example cases using simulated data, including asymmetry conditions in total failure probabilities and/or dependencies, are illustrated. Consequently, the copula-based CCF model provides appropriate estimates of CCFs for asymmetric conditions. This paper also discusses the limitations and notes on the proposed method.

• 대한수학회보
• /
• 제61권1호
• /
• pp.13-27
• /
• 2024

A regular t-balanced Cayley map on a group Γ is an embedding of a Cayley graph on Γ into a surface with certain special symmetric properties. We completely classify regular t-balanced Cayley maps for a class of split metacyclic 2-groups.

• 대한수학회지
• /
• 제45권6호
• /
• pp.1705-1723
• /
• 2008

Let n be a 2-step nilpotent Lie algebra which has an inner product <, > and has an orthogonal decomposition $n\;=z\;{\oplus}v$ for its center z and the orthogonal complement v of z. Then Each element z of z defines a skew symmetric linear map $J_z\;:\;v\;{\longrightarrow}\;v$ given by <$J_zx$, y> = for all x, $y\;{\in}\;v$. In this paper we characterize Jacobi fields and calculate all conjugate points of a simply connected 2-step nilpotent Lie group N with its Lie algebra n satisfying $J^2_z$ = A for all $z\;{\in}\;z$, where S is a positive definite symmetric operator on z and A is a negative definite symmetric operator on v.

• 대한수학회지
• /
• 제43권3호
• /
• pp.507-528
• /
• 2006

In this paper we show that the Koecher's Jordan automorphic generators of one variable on an irreducible symmetric cone are enough to determine the elements of scalar multiple of the Jordan identity on the attached simple Euclidean Jordan algebra. Its various geometric, Jordan and Lie theoretic interpretations associated to the Cartan-Hadamard metric and Cartan decomposition of the linear automorphisms group of a symmetric cone are given with validity on infinite-dimensional spin factors

• 국제물리치료학회지
• /
• 제3권1호
• /
• pp.378-382
• /
• 2012

The purpose of this study effectiveness of core strengthening exercise programs on symmetric double limb support and balance ability for elderly. The subjects that 30 persons between the ages of 65~80 elderly participated were divided into two groups randomly for 8 weeks. Tetrax interactive balance system and Berg's balance scale were used to assess support and stability. Paired t-tests were used to evaluate the changes before and after intervention. The difference between the groups was compared using an independent t-test. The experimental group showed significantly increase weight support, stability, balance(p<.05). However, the control group not showed significantly increase weight support, stability, balance(p>.05). In a variation, experimental and control groups showed significantly increased rate of weight support, stability, balance(p<.05). Consequently, core strengthening exercise program should be considered as a therapeutic method for the elderly to improve the balance ability and effectiveness on falls.

• 대한수학회지
• /
• 제34권2호
• /
• pp.345-370
• /
• 1997

In this paper, we introduce the Fock representation $U^{F, M}$ of the Heisenberg group $H_R^(g, h)$ associated with a positive definite symmetric half-integral matrix $M$ of degree h and prove that $U^{F, M}$ is unitarily equivalent to the Schrodinger representation of index $M$.

• 대한수학회지
• /
• 제52권3호
• /
• pp.489-501
• /
• 2015

We study the structure of right duo ring property when it is restricted within the group of units, and introduce the concept of right unit-duo. This newly introduced property is first observed to be not left-right symmetric, and we examine several conditions to ensure the symmetry. Right unit-duo rings are next proved to be Abelian, by help of which the class of noncommutative right unit-duo rings of minimal order is completely determined up to isomorphism. We also investigate some properties of right unit-duo rings which are concerned with annihilating conditions.