• Communications of the Korean Mathematical Society
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• v.36 no.4
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• pp.743-757
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• 2021

We consider a different version of Schwarz Lemma for λ-spirallike function of complex order at the boundary of the unit disc D. We estimate the modulus of the angular derivative of the function $\frac{zf^{\prime}(z)}{f(z)}$ from below for λ-spirallike function f(z) of complex order at the boundary of the unit disc D by taking into account the zeros of the function f(z)-z which are different from zero. We also estimate the same function with the second derivatives of the function f at the points z = 0 and z = z₀ ≠ 0. We show the sharpness of these estimates and present examples.

• Journal of Ocean Engineering and Technology
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• v.15 no.4
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• pp.92-100
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• 2001

It is very important to determine the coefficient of earth pressure at rest accurately in order to estimate the behavior of soil structure. For estimation of K/sub 0/-value depending upon the stress history of dry sand, a new type of K/sub 0/-oedeometer apparatus is devised, and the horizontal earth pressure is accurately measured. For this study, 2 types of one-cyclic K/sub 0/-Loading/unloading models have been studied experimentally using four relative densities of the sand. The results obtained in this test are as follows : K/sub on'/ the coefficient of earth pressure at - rest for virgin loading is a function of the angle of internal friction Φ' of the sand and is determined as K/sub on/=1 - 0.914 sin Φ', K/sub ou'/ the coefficient of earth pressure at rest for virgin unloading is a function of K/sub on/ and over consolidation ratio(OCR), and is determined as K/sub ou/=K/sub on/(OCR)K/sup a/. The exponent α, increases as the relative density increases. K/sub or'/ the coefficient of earth pressure at rest for virgin reloading decreases in hyperbola type as the vertical stress, σ/sub v/’, increases. And, the stress path at virgin reloading leads to the maximum prestress point, independent upon the value of the minimum unloading stress. The gradient of this curve, m/sub r/ increases as OCR increases.

• Bulletin of the Korean Chemical Society
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• v.25 no.5
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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.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.19 no.2
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• pp.125-129
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• 1983

It is customary to assume that the resistance of a jull at uniform speed may be regarded as the sum of viscous and wavemaking component resistance, or C sub(i)=C sub(v)+C sub(w), where C sub(v) is regarded as a function of Reynolds Number R and C sub(w) a function of Froude Number F. Formulae have been obtained for ∂C sub(w)/∂R, ∂C sub(v)/∂F which may be relevant in seeking theoretical grounds for possible interaction between viscous and wavemaking component resistances. The values of ∂C sub(w)/∂R are small. In general they are smaller than corresponding values of ∂C sub(v)/∂R. But although these values are small it does not follow that they are entirely negligible. The Froude assumption that the rate of change of C sub(w) with R is zero must bel regarded as incorrect.

• Kyungpook Mathematical Journal
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• v.52 no.3
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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.

• Bulletin of the Korean Mathematical Society
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• v.59 no.2
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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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• v.28 no.2
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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.

• The Pure and Applied Mathematics
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• v.22 no.3
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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.

• Journal of Sensor Science and Technology
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• v.29 no.6
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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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• v.24 no.3
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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.