• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.385-397
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• 2022

Let (M, [ , ]) be a finite dimensional Malcev algebra over an algebraically closed field 𝔽 of characteristic 0. We first prove that, (M, [ , ]) (with [M, M] ≠ 0) is simple if and only if ind(M) = 1 (i.e., M admits a unique (up to a scalar multiple) invariant scalar product). Further, we characterize the form of skew-symmetric biderivations on simple Malcev algebras. In particular, we prove that the simple seven dimensional non-Lie Malcev algebra has no nontrivial skew-symmetric biderivation.

• Journal of Mechanical Science and Technology
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• v.18 no.9
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• pp.1559-1564
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• 2004

The process design of hot forging, asymmetric to symmetric rib-web shaped steel, which is used for the turnout of express rails has been studied. Owing to the great difference in shape between the initial billet and the final forged product, it is impossible to hot forge the rail in a single stage operation. The numerical simulation for hot forging of asymmetric shape to symmetric shape was carried out by using commercial FEM code, DEFORMTM-2D. For comparison with the simulation results, a experiment of flow analysis using plasticine was also carried out. The results of the flow experiment showed good agreement with those of the simulation.

• Communications for Statistical Applications and Methods
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• v.14 no.3
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• pp.583-592
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• 2007

Given the moments of a symmetric random variable, its density and distribution functions can be accurately approximated by making use of the algorithm proposed in this paper. This algorithm is specially designed for approximating symmetric distributions and comprises of four phases. This approach is essentially based on the transformation of variable technique and moment-based density approximants expressed in terms of the product of an appropriate initial approximant and a polynomial adjustment. Probabilistic quantities such as percentage points and percentiles can also be accurately determined from approximation of the corresponding distribution functions. This algorithm is not only conceptually simple but also easy to implement. As illustrated by the first two numerical examples, the density functions so obtained are in good agreement with the exact values. Moreover, the proposed approximation algorithm can provide the more accurate quantities than direct approximation as shown in the last example.

• Applied Chemistry for Engineering
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• v.9 no.6
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• pp.914-919
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• 1998

Optically pure $C_2-Symmetric$ pyrrolidine amides (8) were synthesized from readily available 1,2:5,6-di-O-isopropylidene-D-mannitol (1). Cyclization of dimesylated hexitol (4) with benzyl amine gave an inseparable mixture of $C_2-Symmetric$ pyrrolidine amine derivative (5) as a major product, concurring with its cis isomer (6) as a minor product. The pyrrolidine amines (5,6) were converted to separable pyrrolidine amides (8,9) via free amine (7). Optical purity of desired $C_2-Symmetric$ pyrrolidine amide (8a) was determined with its Mosher derivatives (13,14) by their $^1H$ and $^{19}F$ NMR spectra.

• Kyungpook Mathematical Journal
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• v.46 no.3
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• pp.367-376
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• 2006

We investigate semi-symmetry and pseudo-symmetry of some 3-dimensional Riemannian manifolds: the D'Atri spaces, the Thurston geometries as well as the ${\eta}$-Einstein manifolds. We prove that all these manifolds are pseudo-symmetric and that many of them are not semi-symmetric.

• Journal of the Korean Operations Research and Management Science Society
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• v.19 no.2
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• pp.45-56
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• 1994

This paper the profit maximizing order quantity model to the symmetric oligopoly consisting of sellers of a homogeneous product who compete with each other for the same potential buyers. Buyers are classified by type, each selecting an optimal purchase quantity in response to the nonlinear quantity discount pricing schedule given by the sellers. Symmetric equilibrium and the economic quantities that sellers must determine are analysed in a Cournot framework, which explicitly depend on the number of sellers. Economic implications are obtianed from the optimality conditions based on themarket share paraments which are used to characterize the competitior's marketing strategy.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.213-219
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• 2014

We prove that a semi-symmetric 3-dimensional gradient Ricci soliton is locally isometric to a space form $\mathbb{S}^3$, $\mathbb{H}^3$, $\mathbb{R}^3$ (Gaussian soliton); or a product space $\mathbb{R}{\times}\mathbb{S}^2$, $\mathbb{R}{\times}\mathbb{H}^2$, where the potential function depends only on the nullity.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.129-137
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• 2014

In this paper, a new proof of the following result is given: The product of the volumes of an origin-symmetric convex bodies K in $\mathbb{R}^2$ and of its polar body is minimal if and only if K is a parallelogram.

• Korean Journal of Mathematics
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• v.30 no.1
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• pp.61-66
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• 2022

A new type of Riemannian manifold called semirecurrent manifold has been defined and some of its geometric properties are studied. Among others we show that the scalar curvature of semirecurrent manifold is constant and hence semirecurrent manifold is also concircularly recurrent. In addition, we show that the associated 1-form (resp. the associated vector field) of semirecurrent manifold is closed (resp. an eigenvector of its Ricci tensor). Furthermore, we prove that if a Riemannian product manifold is semirecurrent, then either one decomposition manifold is locally symmetric or the other decomposition manifold is a space of constant curvature.

• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.561-570
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• 2005

Weak Crossed Product Algebras correspond to certain graphs called lower subtractive graphs. The properties of such algebras can be obtained by studying this kind of graphs ([4], [5]). In [1], the author showed that a weak crossed product is Frobenius and its restricted subalgebra is symmetric if and only if its associated graph has a unique maximal vertex. A special construction of these graphs came naturally and was known as standard lower subtractive graph. It was a deep question that when such a special graph possesses unique maximal vertex? This work is to answer the question partially and to give a particular characterization for such graphs at which the corresponding algebras are isomorphic. A graph that follows the mentioned characterization is called flexible. Flexibility is to some extend a generalization of the so-called Coxeter groups and its weak Bruhat ordering.