• 대한수학회논문집
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• 제33권4호
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• pp.1217-1227
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• 2018

In the paper, we study the growth and fixed point of solutions of high order linear differential equations with entire coefficients of [p, q]-order in the complex plane. We improve and extend some results due to T. B. Cao, J. F. Xu, Z. X. Chen, and J. Liu, J. Tu, L. Z. Shi.

• Journal of the Korean Association of Oral and Maxillofacial Surgeons
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• 제32권4호
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• pp.287-294
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• 2006

The secondary correction of cleft lip nasal deformity (CLND) presents difficult surgical problems. Characteristically, nostrils are asymmetric. The present study was aimed to examine and compare the effect of Straith's alar web Z-plasty, Millard's alar web Z-plasty, alar web excision, and lateral V-Y advancement of the alar base for augmentation of the nostril with or without lengthening the columella in CLND. The subjects were 28 patients with unilateral cleft lip, who had secondary nostril correction. The nostril correction methods were Straith's alar web Z-plasty, Millard's alar web Z-plasty, alar web excision, and lateral V-Y advancement of the alar base. Facial photographs were taken before and 20 days after the operation. By using Adobe photoshop, the columella length and the nostril width were measured from the facial frontal photograph and Worm's eye view. The degree of improvement was calculated and statistically analyzed. The degree of improvement of the columella length using Straith's alar web Z-plasty was 70.20%. And then Millard's alar web Z-plasty was 55.01%, alar web excision was 39.93%, and lateral V-Y advancement of the alar base was 16.38% in order. The degree of improvement of the nostril size using lateral V-Y advancement of the alar base was 55.26%. And then alar web excision was 52.72%, Millard's alar web Z-plasty was 34.86%, and Straith's alar web Z-plasty was 16.06% in order. Straith's alar web Z-plasty and Millard's alar web Z-plasty resulted in elongation of the columella, equalization of asymmetrical nostril, and enlargement of small nostrils. Alar web excision enlarged nostrils and restored symmetry. Lateral VY advancement of the alar base increased nostril width and enlarged nostrils. These results indicate that the correction of nostrils improve the shape and the symmetry of the nostrils in CLND.

• 생약학회지
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• 제33권2호통권129호
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• pp.75-80
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• 2002

The Korean folk medicine 'Cho Pi Na Mu' has been used orally to tuberculosis, neuralgia, acute and chronic gastritis and arthritis. In order to clarify the botanical origin this crude drug, comparative anatomical studies were made on the branches of Zanthoxylum species growing wild in Korea, i.e. Z. coreanum, Z. piperitum, Z. piperitum var. pubescens, Z. planispinum, Z. schinifolium, Z. schinifolium var. inermis, Z. schinifolium var. microphyllum. As a result, it was clarified that 'Cho Pi Na Mu' was the branch of Z. piperitum.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제11권1호
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• pp.41-56
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• 2007

A 3-partite 2-digraph is an orientation of a 3-partite multi-graph that is without loops and contains at most two edges between any pair of vertices from distinct parts. Let D(X, Y, Z) be a 3-partite 2-digraph with ${\mid}X{\mid}=l,\;{\mid}Y{\mid}=m,\;{\mid}Z{\mid}=n$. For any vertex v in D(X, Y, Z), let $d^+_{\nu}\;and\;d^-_{\nu}$ denote the outdegree and indegree respectively of v. Define $p_x=2(m+n)+d^+_x-d^-_x,\;q_y=2(l+n)+d^+_y-d^-_y\;and\;r_z=2(l+m)+d^+_z-d^-_z$ as the marks (or 2-scores) of x in X, y in Y and z in Z respectively. In this paper, we characterize the marks of 3-partite 2-digraphs and give a constructive and existence criterion for sequences of non-negative integers in non-decreasing order to be the mark sequences of some 3-partite 2-digraph.

• 대한수학회논문집
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• 제32권4호
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• pp.959-970
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• 2017

In this paper, we investigate the transcendental meromorphic solutions with finite order of two different types of difference equations $${\sum\limits_{j=1}^{n}}a_jf(z+c_j)={\frac{P(z,f)}{Q(z,f)}}={\frac{{\sum_{k=0}^{p}}b_kf^k}{{\sum_{l=0}^{q}}d_lf^l}}$$ and $${\prod\limits_{j=1}^{n}}f(z+c_j)={\frac{P(z,f)}{Q(z,f)}={\frac{{\sum_{k=0}^{p}}b_kf^k}{{\sum_{l=0}^{q}}d_lf^l}}$$ that share three distinct values with another meromorphic function. Here $a_j$, $b_k$, $d_l$ are small functions of f and $a_j{\not{\equiv}}(j=1,2,{\ldots},n)$, $b_p{\not{\equiv}}0$, $d_q{\not{\equiv}}0$. $c_j{\neq}0$ are pairwise distinct constants. p, q, n are non-negative integers. P(z, f) and Q(z, f) are two mutually prime polynomials in f.

• 대한수학회보
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• 제61권2호
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• pp.317-333
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• 2024

For the classes of analytic functions f defined on the unit disk satisfying ${\frac{2zf'(z)}{f(z)-f(-z)}}{\prec}{\varphi}(z)$) and ${\frac{(2zf'(z))'}{(f(z)-f(-z))'}}{\prec}{\varphi}(z)$, denoted by S^*_s(𝜑) and C_s(𝜑), respectively, the sharp bound of the n^th Taylor coefficients are known for n = 2, 3 and 4. In this paper, we obtain the sharp bound of the fifth coefficient. Additionally, the sharp lower and upper estimates of the third order Hermitian Toeplitz determinant for the functions belonging to these classes are determined. The applications of our results lead to the establishment of certain new and previously known results.

• 한국환경과학회지
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• 제20권12호
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• pp.1607-1615
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• 2011

The adsorption performance of cupper and zinc ions($Cu^{2+}$ and $Zn^{2+}$) in aqueous solution was investigated by an adsorption process on reagent grade Na-A zeolite(Z-WK) and Na-A zeolite (Z-C1) prepared from coal fly ash. Z-C1 was synthesized by a fusion method with coal fly ash from a thermal power plant. Batch adsorption experiment with Z-C1 was employed to study the kinetics and equilibrium parameters such as initial metal ions concentration and adsorption time of the solution on the adsorption process. Adsorption rate of metal ions occurred rapidly and adsorption equilibrium reached at less than 120 minutes. The kinetics data of $Cu^{2+}$ and $Zn^{2+}$ ions were well fitted by a pseudo-second-order kinetics model more than a pseudo-first-order kinetics model. The equilibrium data were well fitted by a Langmuir model and this result showed $Cu^{2+}$ and $Zn^{2+}$ adsorption on Z-C1 would be occupied by a monolayer adsorption. The maximum adsorption capacity($q_{max}$) by the Langmuir model was determined as $Cu^{2+}$ 99.8 mg/g and $Zn^{2+}$ 108.3 mg/g, respectively. It appeared that the synthetic zeolite, Z-C1, has potential application as absorbents in metal ion recovery and mining wastewater.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2007년도 정기 학술대회 논문집
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• pp.481-486
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• 2007

The Zienkiewicz-Zhu(Z/Z) error estimate is slightly modified for the hierarchical p-refinement, and is then applied to L-shaped plates subjected to bending to demonstrate its effectiveness. An adaptive procedure in finite element analysis is presented by p-refinement of meshes in conjunction with a posteriori error estimator that is based on the superconvergent patch recovery(SPR) technique. The modified Z/Z error estimate p-refinement is different from the conventional approach because the high order shape functions based on integrals of Legendre polynomials are used to interpolate displacements within an element, on the other hand, the same order of basis function based on Pascal's triangle tree is also used to interpolate recovered stresses. The least-square method is used to fit a polynomial to the stresses computed at the sampling points. The strategy of finding a nearly optimal distribution of polynomial degrees on a fixed finite element mesh is discussed such that a particular element has to be refined automatically to obtain an acceptable level of accuracy by increasing p-levels non-uniformly or selectively. It is noted that the error decreases rapidly with an increase in the number of degrees of freedom and the sequences of p-distributions obtained by the proposed error indicator closely follow the optimal trajectory.

• 대한수학회보
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• 제60권6호
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• pp.1651-1672
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• 2023

In 2010, Li-Ye [13, Theorem 0.1] proved that P(ζ(z), ζ'(z), . . . , ζ^(m)(z), Γ(z), Γ'(z), Γ"(z)) ≢ 0 in ℂ, where m is a non-negative integer, and P(u₀, u₁, . . . , u_m, v₀, v₁, v₂) is any non-trivial polynomial in its arguments with coefficients in the field ℂ. Later on, Li-Ye [15, Theorem 1] proved that P(z, Γ(z), Γ'(z), . . . , Γ⁽ⁿ⁾(z), ζ(z)) ≢ 0 in z ∈ ℂ for any non-trivial distinguished polynomial P(z, u₀, u₁, . . ., u_n, v) with coefficients in a set L_δ of the zero function and a class of nonzero functions f from ℂ to ℂ ∪ {∞} (cf. [15, Definition 1]). In this paper, we prove that P(z, ζ(z), ζ'(z), . . . , ζ^(m)(z), Γ(z), Γ'(z), . . . , Γ⁽ⁿ⁾(z)) ≢ 0 in z ∈ ℂ, where m and n are two non-negative integers, and P(z, u₀, u₁, . . . , u_m, v₀, v₁, . . . , v_n) is any non-trivial polynomial in the m + n + 2 variables u₀, u₁, . . . , u_m, v₀, v₁, . . . , v_n with coefficients being meromorphic functions of order less than one, and the polynomial P(z, u₀, u₁, . . . , u_m, v₀, v₁, . . . , v_n) is a distinguished polynomial in the n + 1 variables v₀, v₁, . . . , v_n. The question studied in this paper is concerning the conjecture of Markus from [16]. The main results obtained in this paper also extend the corresponding results from Li-Ye [12] and improve the corresponding results from Chen-Wang [5] and Wang-Li-Liu-Li [23], respectively.

• Fibers and Polymers
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• 제4권4호
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• pp.199-203
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• 2003

In order to investigate the effects of cross-sectional shapes on the sound characteristics of polyester fibers, 10 specimens were woven into a twill structure made of round, hollow, triangular, u-shape, cruciform, and composite cross-sectional (▲/▲ ,()/▲, Y/Y) fibers. Their rustling sounds were recorded, and their sound spectra were obtained from FFT analysis. Physical sound parameters (LPT, ΔL, Δf) and Zwicker's psychoacoustic parameters of the loudness(Z), sharpness(Z), roughness(Z), and fluctuation strength(Z) were calculated from the sound spectra. According to noncircular cross-section fibers, the hollow shaped fiber had the highest value of LPT, ΔL, loudness(Z), and fluctuation strength(Z). The triangular shaped fiber had a lower value of LPT, ΔL, loudness(Z), and roughness(Z) than those of the round shaped fiber. Among composite cross-section fibers, C1(▲/▲) and C3 (Y/Y) had higher values of LPT, ΔL, Δf and loudness(Z) but C2(()/▲) had lower values. Also the LPT, ΔL, sharpness(Z), and roughness(Z) values of different denier were similar to each other, but the Δf and loudness(Z) values increased as the denier increased.