• Kyungpook Mathematical Journal
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• v.58 no.2
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• pp.231-242
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• 2018

We derive sharp upper bound on the initial coefficients and Hankel determinants for normalized analytic functions belonging to a class, introduced by Silverman, defined in terms of ratio of analytic representations of convex and starlike functions. A conjecture related to the coefficients for functions in this class is posed and verified for the first five coefficients.

• Structural Engineering and Mechanics
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• v.30 no.3
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• pp.351-368
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• 2008

The purpose of this paper is to propose a simple analysis method of axial deformation of base-isolation rubber bearings in a building subjected to earthquake loading and present its applicability to the analysis of the bound of the aspect ratio of base-isolated buildings. The base shear coefficient is introduced as a key parameter for the bound analysis. The bound of the aspect ratio of base-isolated buildings is analyzed based on the relationship of the following four quantities; (i) ultimate state of the tensile stress of rubber bearings based on a proposed simple recursive analysis for seismic loading, (ii) ultimate state of drift of the base-isolation story for seismic loading, (iii) ultimate state of the axial compressive stress of rubber bearings under dead loads, (iv) prediction of the overturning moment at the base for seismic loading. In particular, a new recursive analysis method of axial deformation of rubber bearings is presented taking into account the nonlinear tensile behavior of rubber bearings and it is shown that the relaxation of the constraint on the ultimate state of the tensile stress of rubber bearings increases the limiting aspect ratio.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.451-464
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• 2019

In the present paper, we find the sharp bound for the fourth coefficient of starlike functions f which are normalized by f(0) = 0 = f'(0) - 1 and satisfy the following two-sided inequality: $$1+{\frac{{\gamma}-{\pi}}{2\;{\sin}\;{\gamma}}}\;<\;{\Re}\{{\frac{zf^{\prime}(z)}{f(z)}}\}\;<\;1+{\frac{{\gamma}}{2\;{\sin}\;{\gamma}}},\;z{\in}{\mathbb{D}}$$, where ${\mathbb{D}}:=\{z{\in}{\mathbb{C}}:{\left|z\right|}<1\}$ is the unit disk and ${\gamma}$ is a real number such that ${\pi}/2{\leq}{\gamma}<{\pi}$. Moreover, the sharp bound for the fifth coefficient of f defined above with ${\gamma}$ in a subset of [${\pi}/2,{\pi}$) also will be found.

• Bulletin of the Korean Mathematical Society
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• v.61 no.2
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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.

• Journal of the Korean Geotechnical Society
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• v.28 no.12
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• pp.123-131
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• 2012

Recent earthquake records indicate that the vertical component of earthquake loading, generally neglected in seismic slope stability analysis, has a significant influence on the stability. This is particularly true for the earthquakes originating inside the continent, not from its boundaries. Therefore the design of geotechnical structures without consideration of vertical component of earthquake loading may result in unsafe design. In this study, with a consideration of the effect of vertical seismic loading, the horizontal yield seismic coefficients under various slope conditions are estimated, using the lower bound limit analysis. In addition, the equation for the determination of the critical direction (either upward or downward) of vertical seismic loading is proposed.

• Geomechanics and Engineering
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• v.10 no.1
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• pp.21-35
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• 2016

Employing non-associated flow rule and Power-Law failure criterion, the failure mechanisms of tunnel roof in homogeneous and layered soils are studied in present analysis. From the viewpoint of energy, limit analysis upper bound theorem and variation principle are introduced to study the influence of dilatancy on the collapse mechanism of rectangular tunnel considering effects of supporting force and seepage force. Through calculation, the collapsing curve expressions of rectangular tunnel which are excavated in homogeneous soil and layered soils respectively are derived. The accuracy of this work is verified by comparing with the existing research results. The collapsing surface shapes with different dilatancy coefficients are draw out and the influence of dilatancy coefficient on possible collapsing range is analyzed. The results show that, in homogeneous soil, the potential collapsing range decreases with the decrease of the dilatancy coefficient. In layered soils, the total height and the width on the layered position of possible collapsing block increase and the width of the falling block on tunnel roof decrease when only the upper soil's dilatancy coefficient decrease. When only the lower soil's dilatancy coefficient decrease or both layers' dilatancy coefficients decrease, the range of the potential collapsing block reduces.

• Transactions of Materials Processing
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• v.3 no.1
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• pp.97-109
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• 1994

Closed-die forging of the spur gears with circular are fillet has been analyses by using the upper-bound method. A kinematically admissible velocity field has been developed, wherein, the tooth profile consists of the involute curve and the circular arc fillet. In the analysis, the deformation regions have been divided into eight zones. A constant frictional stress has been assumed on the contacting surfaces Utilizing the formulated velocity field, numerical calculations have been carried out to investigate the effects of various parameters, such as module, number of teeth, addendum modification coefficient and friction factor, on the relative forging pressure of spur gears. As the result of numerical calculations, the relative forging pressure does not change so much against the variation of module. On the other hand, the relative forging pressure increases at the final filling stage as the addendum modification coefficient increases.

• Geomechanics and Engineering
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• v.8 no.5
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• pp.741-756
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• 2015

The prediction of impending collapse of deep tunnel is one of the most difficult problems. Collapse mechanism of deep tunnel in layered soils is derived using a new curved failure mechanism within the framework of upper bound theorem, and effects of seepage forces are considered. Nonlinear failure criterion is adopted in the present analysis, and the possible collapse shape of deep tunnel in the layered soils is discussed in this paper. In the layered soils, the internal energy dissipations along velocity discontinuity are calculated, and the external work rates are produced by weight, seepage forces and supporting pressure. With upper bound theorem of limit analysis, two different curve functions are proposed for the two different soil stratums. The specific shape of collapse surface is discussed, using the proposed curve functions. Effects of nonlinear coefficient, initial cohesion, pore water pressure and unit weight on potential collapse are analyzed. According to the numerical results, with the nonlinear coefficient increase, the shape of collapse block will increase. With initial cohesion of the upper soil increase, the shape of failure block will be flat, and with the lower soil improving, the size of collapsing will be large. Furthermore, the shape of collapsing will decrease with the unit weight decrease.

• Environmental Engineering Research
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• v.11 no.1
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• pp.33-44
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• 2006

The objective of this study was to develop and assess a method for estimating the rain scavenging ratios (RSRs) of particle-bound PAHs and PCBs using measured scavenging ratio of particulate matters (PM) and routinely available data of physico-chemical properties of PM. Paired atmospheric and rainwater sampling was conducted for a total of 4 rain events. Assuming equilibrium partitioning in rainwater-gas-PM system, an equation was derived for estimating the RSR of particle-bound chemicals as a function of RSR of PM and three equilibrium partition constants (i.e. dimensionless Henry's law constant, gas-particle partition coefficient, and water-particle partition coefficient). For all PAHs, the model significantly under-predicted the RSR while the model prediction for PCBs agreed with observation mostly within a factor of 5. The RSR model for the chemicals is of limited use as its accuracy critically depends on how close the observed partitioning of the chemicals in the gas-PM-rainwater system is to that estimated under the equilibrium assumption.

• Journal of the Korean Operations Research and Management Science Society
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• v.19 no.2
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• pp.1-19
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• 1994

A generalized network problem is a special class of linear programming problem whose coefficient matrix contains at most two nonzero elements per column. A generalized network problem with 0-1 flow restrictions is called an integer generalized network(IGN) problem. In this paper, we presented a branch and bound algorithm for the IGN that uses network relaxation. To improve the procedure, we develop various strategies, each of which employs different node selection criterion and/or branching variable selection criterion. We test these solution strategies and compare their efficiencies with LINDO on 70 randomly generated problems.