• Korean Journal of Mathematics
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• v.29 no.1
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• pp.179-191
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• 2021

In this paper we introduce generalised logarithmic proximate order, generalised logarithmic proximate type of an entire function and prove the corresponding existence theorems. Also we investigate some theorems on the application of generalised logarithmic proximate order.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.275-283
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• 2013

In this paper we investigate an initial boundary value problem of a logarithmic wave equation. We establish the global existence of weak solutions to the problem by using Galerkin method, logarithmic Sobolev inequality and compactness theorem.

• Journal of the Korean Society for Precision Engineering
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• v.20 no.9
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• pp.159-165
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• 2003

Most engineers interested in stress singularities have focused mainly on the research of power stress singularities for v-notched cracks in dissimilar materials. The logarithmic stress singularity was discussed a little in Bogy's paper. The power-logarithmic stress singularity was reported by Dempsey and Sinclair. It was indicated that the logarithmic singularity is only a special case of power-logarithmic stress singularities. Then, Dempsey reported specific cases which have power-logarithmic singularities even fur homogeneous boundary conditions. It was known that logarithmic stress singularities for v-notched cracks in dissimilar materials occurs when the surfaces of a v-notched crack have constant tractions. In this paper, using the complex potential method, the stresses and displacements having logarithmic stress singularities were obtained and the coefficients vectors were calculated by a numerical program code: Mathematica. It was shown that our analysis models don't have logarithmic stress singularities under the constant tractions, although the coefficient vectors are existing.

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.527-540
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• 2010

We characterize the boundedness and compactness of the weighted composition operator on the logarithmic Bloch space $\mathcal{L}\ss=\{f{\in}H(D):sup_D(1-|z|^2)ln(\frac{2}{1-|z|})|f'(z)|$<+$\infty$ and the little logarithmic Bloch space ${\mathcal{L}\ss_0$. The results generalize the known corresponding results on the composition operator and the pointwise multiplier on the logarithmic Bloch space ${\mathcal{L}\ss$ and the little logarithmic Bloch space ${\mathcal{L}\ss_0$.

• Korean Journal of Mathematics
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• v.29 no.1
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• pp.105-120
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• 2021

In this paper, we extend some results related to the growth rates of entire functions by introducing the relative logarithmic order ����g(f) of a nonconstant entire function f with respect to another nonconstant entire function g. Next we investigate some theorems related the behavior of ����g(f). We also define the relative logarithmic proximate order of f with respect to g and give some theorems on it.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.83-98
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• 2014

During the last decade, several papers have focused on linear q-difference equations of the form ${\sum}^n_{j=0}a_j(z)f(q^jz)=a_{n+1}(z)$ with entire or meromorphic coefficients. A tool for studying these equations is a q-difference analogue of the lemma on the logarithmic derivative, valid for meromorphic functions of finite logarithmic order ${\rho}_{log}$. It is shown, under certain assumptions, that ${\rho}_{log}(f)$ = max${{\rho}_{log}(a_j)}$ + 1. Moreover, it is illustrated that a q-Casorati determinant plays a similar role in the theory of linear q-difference equations as a Wronskian determinant in the theory of linear differential equations. As a consequence of the main results, it follows that the q-gamma function and the q-exponential functions all have logarithmic order two.

• Journal of the Korean Home Economics Association
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• v.28 no.4
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• pp.87-101
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• 1990

This study was undertaken to test to fit forms of the Engel curves to data. The comparisons were confined to the linear, semi-logarithmic and double-logarithmic forms. Data from the 1970-1987 Urban Household Economy Survey were used to estimate the Engel curves. The twelve categories of consumption expenditure were considered for investigation. Parameters of the Engel curves were derived from OLS and TSLS. In this paper the size of the family was used as the deflater. The results could be summarized as follows: 1. Comparing with the R2 of three foms, it could be concluded that, the linear form generally gave a better fit to data than the other forms did. Only for housing and clothing and foot wear, did the semi-logarithmic form give a better fit. Only for meals outside the home, fuel, light and water charges, and miscellaneous, did the double-logarithmic form give a better fit. 2. Comping with the income elasticities based on the alternative forms, it could be concluded that the differences between the estimates were since each form made different assumption as to the way in which elasticity varied. In general, the semi-logarithmic form gave the highest estimate and double-logarithmic form did the lowest estimate. The difference between semi-logarithmic and the other forms were greater than the those of linear and double-logarithmic form. 3. It was found that the income elasticity varied with the difinition of income used as an explanatory variable in Engel curves.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.325-332
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• 2009

Reducing the generalized logarithmic functional equations to differential equations in the sense of Schwartz distributions, we find the locally integrable solutions of the equations.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.2
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• pp.301-305
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• 2020

Logarithmic fractional Sobolev trace inequalities are derived as a generalization of the results in [6, 9].

• Journal of the Chungcheong Mathematical Society
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• v.32 no.2
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• pp.239-243
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• 2019

Logarithmic Sobolev trace inequalities are derived from the well known classical Sobolev trace inequalities as a limiting case.