• Bulletin of the Korean Chemical Society
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• 제25권5호
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• pp.673-675
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• 2004

The tetranuclear copper(II) cluster compound $[Cu_4OCl_6(C_{14}H_{12}N_2)_4]$ has been synthesized by hydrothermal reaction and studied by X-ray diffraction. The four copper(II) atoms locate four capsheaves of a tetrahedral skeletal structure and a oxygen atom as interstitial atom occupies the center position of the same tetrahedron, and each edge of the Cu-Cu tetrahedron is bridged by one ${\mu}_2$-Cl anion. The copper atom possesses slightly distorted trigonal bipyramidal geometry with three ${\mu}_2$-Cl atoms in equatorial position and the interstitial O atom and one N atom from 3-benzyl-benzimidazole ligand occupying axial position. The Cu-Cu distances are in the range of 3.0986-3.1162 ${\AA}$. The EPR spectrum suggested that the copper(II) ground state $d_{x2-y2}$ and the coordination geometry was trigonal bipyramidal.

• 수산해양기술연구
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• 제19권2호
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• pp.125-129
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• 1983

이상의 연구로부터 결론은 아래와 같다. 1. 점성저항과 조파저항 성분의 상호작용에 대한 어떤 측정 근거를 산출하였다. 2. Froude의 가정 ∂C sub(t)/∂R-dC sub(f)/∂R은 부정확하다는 것을 밝혀둔다. 3. 거친 표면을 가지는 모형선에 대한, 상응하는 결과는, 완전히 다른 결론을 산출할 것이라고 기대한다. 4. 다른 기하학적 동일선의 결과에 기본 마찰곡선을 적용하여 이와 같은 연구를 반복하는 것이 가능하다는 것을 남겨둔다.

• Kyungpook Mathematical Journal
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• 제52권3호
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• pp.265-269
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• 2012

In this paper, we prove the following theorem which gives a characterization of $M_1$-spaces by g-function.

• 대한수학회보
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• 제59권2호
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• pp.431-452
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• 2022

For any positive integer 𝜇, we compute the mean value of the 𝜇-th derivative of quadratic Dirichlet L-functions over the rational function field 𝔽_q(t), where q is a power of 2.

• Korean Journal of Mathematics
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• 제28권2호
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• pp.361-378
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• 2020

The most apparent aspect of the present study is to introduce a new sequence space 𝚽^⋆(𝓛_p) derived by double Euler-Totient matrix operator. We examine its topological and algebraic properties and give an inclusion relation. In addition to those, the α-, β(bp)- and γ-duals of the space 𝚽^⋆(𝓛_p) are determined and finally, some 4-dimensional matrix mapping classes related to this space are characterized.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제22권3호
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• pp.263-273
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• 2015

In this paper, a boundary version of Schwarz lemma is investigated. For the function holomorphic f(z) = a + c_pz^p + c_p+₁z^p+1 + ... defined in the unit disc satisfying |f(z) − 1| < 1, where 0 < a < 2, we estimate a module of angular derivative at the boundary point b, f(b) = 2, by taking into account their first nonzero two Maclaurin coefficients. The sharpness of these estimates is also proved.

• 센서학회지
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• 제29권6호
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• pp.412-419
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• 2020

In this study, a PID control method for sweeping automatic linearization of a wavelength swept laser is proposed. First, the closedloop transfer function embodying the PID control is derived. Through the simulation of the function, K_p = 0.022, K_i = 0.008, K_d = 0.002 were obtained as the best PID coefficients for fast linear sweeping. The performance test using the PID coefficients showed that linear sweeping was held up well with a 98.7% decrement in nonlinearity after the 10th feedback, and 45 nm sweeping range, 1 kHz sweeping frequency, and 8.8 mW average optical power were obtained. The equipment consists of a fiber Bragg grating array, an optical-electronic conversion circuit, and a LabVIEW FPGA program. Every 5s, automatic feedback and PID control generate a new compensated waveform and produce a better linear sweeping than before. Compared with nonlinear sweeping, linear sweeping can reduce the cumbersome and time-consuming recalibration processes and produce more accurate measurement results.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제24권3호
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• pp.293-303
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• 2020

The present work aims to analyzed the transient thermoelastic stress analysis of a thin circular plate with uniform internal heat generation. Initially, the plate is characterized by a parabolic temperature distribution along the z-direction given by T = T₀(r, z) and perfectly insulated at the ends z = 0 and z = h. For times t > 0, the surface r = a is subjected to convection heat transfer with convection coefficient h_c and fluid temperature T_∞. The integral transform method used to obtain the analytical solution for temperature, displacement, and thermal stresses. The associated thermoelastic field is analyzed by making use of the temperature and thermoelastic displacement potential function. Numerical results are carried out with the help of computational software PTC Mathcad Prime-3.1 and shown in figures.

• 대한수학회지
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• 제58권5호
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• pp.1109-1129
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• 2021

This paper considers an anisotropic polytropic infiltration equation with a source term $$u_t={\sum\limits_{i=1}^{N}}{\frac{{\partial}}{{\partial}x_i}}\(a_1(x){\mid}u{\mid}^{{\alpha}_i}{\mid}u_{x_i}{\mid}^{p_i-2}u_{x_i}\)+f(x,t,u)$$, where p_i > 1, α_i > 0, a_i(x) ≥ 0. The existence of weak solution is proved by parabolically regularized method. Based on local integrability $u_{x_i}{\in}W_{loc}^{1,p_i}(\Omega)$, the stability of weak solutions is proved without boundary value condition by the weak characteristic function method. One of the essential characteristics of an anisotropic equation different from an isotropic equation is found originally.

• 대한수학회지
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• 제59권2호
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• pp.299-309
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• 2022

Let k ⩾ 2 be an integer, S^k = {1^k, 2^k, 3^k, …} and B = {b₁, b₂, b₃, …} be an additive complement of S^k, which means all sufficiently large integers can be written as the sum of an element of S^k and an element of B. In this paper we prove that $${{\lim}\;{\sup}}\limits_{n{\rightarrow}{\infty}}\;{\frac{{\Gamma}(2-{\frac{1}{k}})^{\frac{k}{k-1}}{\Gamma}(1+{\frac{1}{k}})^{\frac{k}{k-1}}n^{\frac{k}{k-1}}-b_n}{n}}\;{\geqslant}\;{\frac{k}{2(k-1)}}\;{\frac{{\Gamma}(2-{\frac{1}{k}})^2}{{\Gamma}(2-{\frac{2}{k}})}},$$ where 𝚪(·) is Euler's Gamma function.