• Computational Structural Engineering
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• v.10 no.3
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• pp.175-184
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• 1997

The objective of this paper is to study arelationship between maximum response and its standard deviation of rotational shells that are subjected to uneven settlements. For this, the ratio, .eta, of the maximum response to standard deviation and it's approximate, .eta./sub apr/, are investigated by stochastic methods. Also, an equation for .eta./sub apr/, that is a function of predominant harmonic number is suggested. The settlements are represented by the Fourier series. Each term in the series contains two coefficients; the amplitude and the phase angle. It is assumed that phase angles are random variables and amplitudes are deterministic. To investigate the characteristics of .eta. and .eta./sub apr/, 100 phase angles for two types of artificial amplitudes spectra are used in the analysis. .eta. and .eta./sub apr/, are almost constant regardless of amplitude type, position of a shell or type of responses; they fall into from 2.0 to 2.5. .eta./sub apr/ is always close to .eta., but tends to be somewhat greater. It may be concluded that a maximum responses of rotational shells subjected to uneven settlements are .eta./sub apr/ (about 2.5) times of its standard deviation. It is considered that this result is used when we design rotational shell structures subjected to differential settlements.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.27-41
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• 2019

We determine explicit formulas for the number of representations of a positive integer n by quaternary quadratic forms with coefficients 1, 2, 5 or 10. We use a modular forms approach.

• Kyungpook Mathematical Journal
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• v.59 no.3
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• pp.377-389
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• 2019

We evaluate the convolution sum $W_{a,b}(n):=\sum_{al+bm=n}{\sigma}(l){\sigma}(m)$ for (a, b) = (1, 28),(4, 7),(2, 7) for all positive integers n. We use a modular form approach. We also re-evaluate the known sums $W_{1,14}(n)$ and $W_{1,7}(n)$ with our method. We then use these evaluations to determine the number of representations of n by the octonary quadratic form $x^2_1+x^2_2+x^2_3+x^2_4+7(x^2_5+x^2_6+x^2_7+x^2_8)$. Finally we express the modular forms ${\Delta}_{4,7}(z)$, ${\Delta}_{4,14,1}(z)$ and ${\Delta}_{4,14,2}(z)$ (given in [10, 14]) as linear combinations of eta quotients.

• Bulletin of the Korean Mathematical Society
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• v.30 no.2
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• pp.229-238
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• 1993

Let M be an n-dimensional compact Riemannian manifold with boundary .part.M. We consider the Neumann eigenvalue problem on M of the equation (Fig.) where .upsilon. is the unit outward normal vector to the boundary .part.M. due to the importance of Poincare inequality for analysis on manifolds, one wishes to obtain the lower bound of the first non-zero eigenvalue .eta.$_{1}$ of (1.1). For the purpose of applications, it is important to relax the dependency of the lower bound on the geometric quantities. For general compact manifolds with convex boundary, Li-Yau [3] obtained the lower bound of .eta.$_{1}$. Recently, Roger Chen [1] investigated the lower bound of the first Neumann eigenvalue .eta.$_{1}$ on compact manifold M with nonconvex boundary. We investigate the lower bound .eta.$_{1}$ with the same conditions as those of Roger chen. But, using the different auxiliary function, we have the following theorem.

• 전기의세계
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• v.27 no.2
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• pp.69-74
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• 1978

There have been a number of experimental or theorethical investigations of transport coefficient for electrons in the field of gas. In this paper the authors present the method by which Townsend first ionization doefficient (.alpha.) or attachment coefficient (.eta.) can be deduced easily and precisely by means of analyzing Townsend equation based on linealized least squares method. The apparent ionization coefficient (.alpha.-.eta.)/p have been analyzed from the experimental data by applying the new method above mentioned. And the values of (.alpha.-.eta.)/p in SF$_{6}$ as a function of E/p were agreement with the values measured by Bhalla et al. who analyzed th experimental pre-breakdown currents. In the same way (.alpha.-.eta.)/p in N$_{2}$O had a same tendency to that of Folkard et al.l.

• Polymer(Korea)
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• v.34 no.5
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• pp.415-423
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• 2010

Poly(vinyl alcohol)(PVA) with high degree of hydrolysis of above 98% was dissolved in dimethyl sulfoxide(DMSO), and the shear viscosity was measured up to $C{\simeq}0.14\;g/mL$ in the semi-dilute solution regime. Next, as probe particle, polystyrene(PS) latex was introduced into this matrix system and its delayed diffusion due to polymer concentration was investigated by means of dynamic light scattering. When the solution viscosity of PVA/DMSO was plotted against the reduced concentration $C[{\eta}]$, which is scaled by the intrinsic viscosity, the molecular weight dependence was strongly appeared at C$[{\eta}]$ >2. Some heterogeneties in polymer solution were considered as its source. Contrary, the diffusion of probe particle in the matrix solution was observed as a single mode motion at whole concentration range but its ratio of its diffusion coefficient at solution to that at solvent, D/Do did not show any molecular weight dependence at all. However, the application limit of the stretched exponential function was disclosed at C$[{\eta}]$ >2.5.

• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.237-255
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• 2023

In this article, we find bases for the spaces of modular forms $M_2({\Gamma}_0(88),\;({\frac{d}{\cdot}}))$ for d = 1, 8, 44 and 88. We then derive formulas for the number of representations of a positive integer by the diagonal quaternary quadratic forms with coefficients 1, 2, 11 and 22.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.329-338
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• 2014

In this paper, we study the method of upper and lower solutions and develop the generalized quasilinearization technique for the existence and approximation of solutions to some three-point nonlocal boundary value problems associated with higher order fractional differential equations of the type $$^c{\mathcal{D}}^q_{0+}u(t)+f(t,u(t))=0,\;t{\in}(0,1)$$ $$u^{\prime}(0)={\gamma}u^{\prime}({\eta}),\;u^{\prime\prime}(0)=0,\;u^{\prime\prime\prime}(0)=0,{\ldots},u^{(n-1)}(0)=0,\;u(1)={\delta}u({\eta})$$, where, n-1 < q < n, $n({\geq}3){\in}\mathbb{N}$, 0 < ${\eta},{\gamma},{\delta}$ < 1 and $^c\mathcal{D}^q_{0+}$ is the Caputo fractional derivative of order q. The nonlinear function f is assumed to be continuous.

• Korean Journal of Mathematics
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• v.26 no.3
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• pp.483-501
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• 2018

In this paper, we present some recent results on weighted pointwise convergence and the rate of pointwise convergence for the family of nonlinear double singular integral operators in the following form: $$T_{\eta}(f;x,y)={\int}{\int\limits_{{\mathbb{R}^2}}}K_{\eta}(t-x,\;s-y,\;f(t,s))dsdt,\;(x,y){\in}{\mathbb{R}^2},\;{\eta}{\in}{\Lambda}$$, where the function $f:{\mathbb{R}}^2{\rightarrow}{\mathbb{R}}$ is Lebesgue measurable on ${\mathbb{R}}^2$ and ${\Lambda}$ is a non-empty set of indices. Further, we provide an example to support these theoretical results.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1323-1329
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• 2010

In this paper, a new fixed point theorem in cone is applied to obtain the existence of at least one positive pseudo-symmetric solution for the second order three-point boundary value problem {x" + f(t, x, x')=0, t $\in$ (0, 1), x(0)=0, x(1)=x($\eta$), where f is nonnegative continuous function; ${\eta}\;{\in}$ (0, 1) and f(t, u, v) = f(1+$\eta$-t, u, -v).