• Journal of the Korean Mathematical Society
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• v.60 no.6
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• pp.1137-1169
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• 2023

Let C be a curve and V → C an orthogonal vector bundle of rank r. For r ≤ 6, the structure of V can be described using tensor, symmetric and exterior products of bundles of lower rank, essentially due to the existence of exceptional isomorphisms between Spin(r, ℂ) and other groups for these r. We analyze these structures in detail, and in particular use them to describe moduli spaces of orthogonal bundles. Furthermore, the locus of isotropic vectors in V defines a quadric subfibration Q_V ⊂ ℙV . Using familiar results on quadrics of low dimension, we exhibit isomorphisms between isotropic Quot schemes of V and certain ordinary Quot schemes of line subbundles. In particular, for r ≤ 6 this gives a method for enumerating the isotropic subbundles of maximal degree of a general V , when there are finitely many.

• Journal of the Korean Mathematical Society
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• v.59 no.1
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• pp.193-204
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• 2022

We present construction methods for free self-orthogonal (self-dual or Type II) codes over ℤ₄[v]/〈v² + 2v〉 which is one of the finite commutative local non-chain Frobenius rings of order 16. By considering their Gray images on ℤ₄, we give a construct method for a code over ℤ₄. We have some new and optimal codes over ℤ₄ with respect to the minimum Lee weight or minimum Euclidean weight.

• Honam Mathematical Journal
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• v.16 no.1
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• pp.47-54
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• 1994

We present a generating function and three semi-orthogonal relations for a class of hypergeometric functions. We employ semi-orthogonal relations to generate a theory concerning finite series expansions involving our hypergeometric functions.

• Journal of Korean Society for Quality Management
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• v.45 no.4
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• pp.889-902
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• 2017

Purpose: The orthogonality and trace optimal properties are desirable for constructing designs of experiments. This article focuses on the determination of the sizes of experiments for the balanced trace optimal resolution-V fractional factorial designs for 2-level factorial designs, which have near-orthogonal properties. Methods: In this paper, first we introduce the trace optimal $2^t$ fractional factorial designs for $4{\leq}t{\leq}7$, by exploiting the partially balanced array for various cases of experimental sizes. Moreover some orthogonality criteria are also suggested with which the degree of the orthogonality of the designs can be evaluated. And we appraise the orthogonal properties of the introduced designs from various aspects. Results: We evaluate the orthogonal properties for the various experimental sizes of the balanced trace optimal resolution-V fractional factorial designs of the 2-level factorials in which each factor has two levels. And the near-orthogonal 2-level balanced trace optimal resolution-V fractional factorial designs are suggested, which have adequate sizes of experiments. Conclusion: We can construct the trace optimal $2^t$ fractional factorial designs for $4{\leq}t{\leq}7$ by exploiting the results suggested in this paper, which have near-orthogonal property and appropriate experimental sizes. The suggested designs can be employed usefully especially when we intend to analyze both the main effects and two factor interactions of the 2-level factorial experiments.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.21 no.4
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• pp.80-87
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• 2007

This paper will suggest that the 1 cross orthogonal loop type sensor improves on the orthogonal loop form sensor-head, which is available a calibration of the linear birefringence, when a fiber optic current sensor was composed. An output characteristics of the 1 cross orthogonal loop form, a general closed loop form, the orthogonal loop form are compared by the IEC(International Electrotechnical Commission) 60044-8 standard, and the state of polarization is compared with three forms. As a result, when the closed loop form was changed to the orthogonal loop form, retardation decreased 15.3[%]. When the closed loop form was changed to the 1 cross orthogonal loop type, the retardation decreased 33.8[%]. As a result of the Faraday Effect measurement, the 1 cross orthogonal loop form has the highest output characteristic and the lowest error ratio. It met the 0.5 class of the IEC 60044-8 standard. Thus, in application of the 1cross orthogonal loop form, the possibility to develop high reliability fiber optic current sensors that have a high output and stable error ratio rises is increased.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.717-734
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• 1996

For a scalar rational function, the spectral data consisting of zeros and poles with their respective multiplicities uniquely determines the function up to a nonzero multiplicative factor. But due to the richness of the spectral structure of a rational matrix function, reconstruction of a rational matrix function from a given spectral data is not that simple.

• The Pure and Applied Mathematics
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• v.13 no.4 s.34
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• pp.303-310
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• 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 the Korean Mathematical Society
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• v.45 no.6
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• pp.1613-1622
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• 2008

Let G be a graph with vertex set V(G) and edge set E(G), and let g, f be two nonnegative integer-valued functions defined on V(G) such that $g(x)\;{\leq}\;f(x)$ for every vertex x of V(G). We use $d_G(x)$ to denote the degree of a vertex x of G. A (g, f)-factor of G is a spanning subgraph F of G such that $g(x)\;{\leq}\;d_F(x)\;{\leq}\;f(x)$ for every vertex x of V(F). In particular, G is called a (g, f)-graph if G itself is a (g, f)-factor. A (g, f)-factorization of G is a partition of E(G) into edge-disjoint (g, f)-factors. Let F = {$F_1$, $F_2$, ..., $F_m$} be a factorization of G and H be a subgraph of G with mr edges. If $F_i$, $1\;{\leq}\;i\;{\leq}\;m$, has exactly r edges in common with H, we say that F is r-orthogonal to H. If for any partition {$A_1$, $A_2$, ..., $A_m$} of E(H) with $|A_i|=r$ there is a (g, f)-factorization F = {$F_1$, $F_2$, ..., $F_m$} of G such that $A_i\;{\subseteq}E(F_i)$, $1\;{\leq}\;i\;{\leq}\;m$, then we say that G has (g, f)-factorizations randomly r-orthogonal to H. In this paper it is proved that every (0, mf - (m - 1)r)-graph has (0, f)-factorizations randomly r-orthogonal to any given subgraph with mr edges if $f(x)\;{\geq}\;3r\;-\;1$ for any $x\;{\in}\;V(G)$.

• Communications for Statistical Applications and Methods
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• v.15 no.2
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• pp.235-244
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• 2008

Balanced arrays which are generalized orthogonal arrays, introduced by Chakravarti (1956) can be used to construct the fractional factorial designs. Especially for 2-level factorials, balanced arrays with strength 4 are identical to the resolution-V fractional designs. In this paper criteria for evaluation the degree of the orthogonality of balanced arrays of 2-levels with strength 4 are developed and some application methods of the suggested criteria are discussed. As a result, in this paper, we introduce the constructing methods of near orthogonal saturated balanced resolution-V fractional 2-level factorial designs.

• Wind and Structures
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• v.38 no.1
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• pp.1-13
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• 2024

In order to effectively simulate nonstationary stochastic turbulent wind fields, four separation hybrid (SEP-H) models are proposed in the present study. Based on the assumption that the lateral turbulence component at one single-point is uncorrelated with the longitudinal and vertical turbulence components, the fluctuating wind is separated into 2nV-1D and nV1D nonstationary stochastic vector processes. The first process can be expressed as double proper orthogonal decomposition (DPOD) or proper orthogonal decomposition and spectral representation method (POD-SRM), and the second process can be expressed as POD or SRM. On this basis, four SEP-H models of nonstationary stochastic turbulent wind fields are developed. In addition, the orthogonal random variables in the SEP-H models are presented as random orthogonal functions of elementary random variables. Meanwhile, the number theoretical method (NTM) is conveniently adopted to select representative points set of the elementary random variables. The POD-FFT (Fast Fourier transform) technique is introduced in frequency to give full play to the computational efficiency of the SEP-H models. Finally, taking a long-span bridge as the engineering background, the SEP-H models are compared with the dimension-reduction DPOD (DR-DPOD) model to verify the effectiveness and superiority of the proposed models.