• Honam Mathematical Journal
• /
• v.43 no.3
• /
• pp.453-463
• /
• 2021

In this study, tubular surfaces that play an important role in technological designs in various branches are examined for the case of the base curve is not satisfying the fundamental theorem of the differential geometry. In order to give an alternative perspective to the researches on tubular surfaces, the modified orthogonal frame is used in this study. Firstly, the relationships between the Serret-Frenet frame and the modified orthogonal frame are summarized. Then the definitions of the tubular surfaces, some theorems, and results are given. Moreover, the fundamental forms, the mean curvature, and the Gaussian curvature of the tubular surface are calculated according to the modified orthogonal frame. Finally, the properties of parameter curves of the tubular surface with modified orthogonal frame are expressed and the tubular surface is drawn according to the Frenet frame and the modified orthogonal frame.

• Bulletin of the Korean Mathematical Society
• /
• v.36 no.4
• /
• pp.779-797
• /
• 1999

We find necessary and sufficient conditions for an orthogonal polynomial system to be compatible with another orthogonal polynomial system. As applications, we find new characterizations of semi-classical and clasical orthorgonal polynomials.

• The Pure and Applied Mathematics
• /
• v.13 no.4 s.34
• /
• pp.303-310
• /
• 2006

M. $Bre\v{s}ar$ and J. Vukman obtained some results concerning orthogonal derivations in semiprime rings which are related to the result that is well-known to a theorem of Posner for the product of two derivations in prime rings. In this paper, we present orthogonal generalized derivations in semiprime near-rings.

• Journal of Korean Society for Quality Management
• /
• v.36 no.3
• /
• pp.13-21
• /
• 2008

The orthogonality is an important property in the experimental designs. When we use nearly orthogonal arrays(for example, supersaturated designs), we need evaluate the degree of the orthogonality of given nearly orthogonal arrays. We can use the mutual information as a new criterion for evaluating and testing the degree of the orthogonality of given nearly orthogonal arrays.

• Bulletin of the Korean Mathematical Society
• /
• v.42 no.1
• /
• pp.179-188
• /
• 2005

We give a method to derive partial differential equations for the product of any two classical orthogonal polynomials in one variable and thus find several new differential equations. We also explain with an example that our method can be extended to a more general case such as product of two sets of orthogonal functions.

• Journal of the Korean Mathematical Society
• /
• v.36 no.2
• /
• pp.333-344
• /
• 1999

In [4], it was shown that an n by n orthogonal matrix which has a row of nonzeros has at least ( log2n + 3)n - log2n +1 nonzero entries. In this paper, the matrices achieving these bounds are constructed. The analogous sparsity problem for m by n row-orthogonal matrices which have a row of nonzeros in conjectured.

• Journal of the Korean Statistical Society
• /
• v.35 no.1
• /
• pp.49-61
• /
• 2006

Wu et al. (1992) constructed some general classes of tight asymmetric orthogonal arrays of strength 2 using the method of grouping. Rains et al. (2002) obtained asymmetric orthogonal arrays of strength 2 using the concept of mixed spread in finite projective geometry. In this paper, we obtain some new tight asymmetric orthogonal arrays of strength 2 using the concept of mixed partition in finite projective geometry.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2008.04a
• /
• pp.156-159
• /
• 2008

Proper orthogonal decomposition is a statistical pattern analysis technique for finding the dominant components, called the proper orthogonal modes, in ensembles of spatially distributed data. We present recent ideas based on proper orthogonal decomposition (POD) and detailed experiments that yield new perspectives into the microscale structures. The linearized modeling technique based on POD is very useful to show the principal characteristics of the complex dynamic responses.

• Communications of the Korean Mathematical Society
• /
• v.15 no.4
• /
• pp.587-595
• /
• 2000

We contain a simple construction for the sparse n x n connected orthogonal matrices which have a row of p nonzero entries with 2$\leq$p$\leq$n. Moreover, we study the analogous sparsity problem for an m x n connected row-orthogonal matrices.

• The Korean Journal of Applied Statistics
• /
• v.15 no.1
• /
• pp.179-186
• /
• 2002

We usually execute the blocking under heterogeneity of experimental condition in response surface methodology. We can suggest the measure for evaluating nearly orthogonal blocking under second order models.