• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.167-179
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• 2023

In this paper, we investigate solutions of equations which are linear (p, q)-difference equation of higher order by using (p, q)-derivative and integral. We also derive the solution of equation in the case of second order.

• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.331-357
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• 2020

Let p be an analytic function defined on the open unit disk 𝔻. We obtain certain differential subordination implications such as ψ(p) := p^λ(z)(α+βp(z)+γ/p(z)+δzp'(z)/p^j(z)) ≺ h(z) (j = 1, 2) implies p ≺ q, where h is given by ψ(q) and q belongs to 𝒫, by finding the conditions on α, β, γ, δ and λ. Further as an application of our derived results, we obtain sufficient conditions for normalized analytic function f to belong to various subclasses of starlike functions, or to satisfy |log(zf'(z)/f(z))| < 1, |(zf'(z)/f(z))² - 1| < 1 and zf'(z)/f(z) lying in the parabolic region v² < 2u - 1.

• Honam Mathematical Journal
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• v.41 no.1
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• pp.163-174
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• 2019

The veritable pursuit of this exegesis is to exhibit integrals affined with the Bessel-Struve kernel function, which are explicitly inscribed in terms of generalized (Wright) hypergeometric function and also the product of generalized (Wright) hypergeometric function with sum of two confluent hypergeometric functions. Somewhat integrals involving exponential functions, modified Bessel functions and Struve functions of order zero and one are also obtained as special cases of our chief results.

• 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 Environmental Science International
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• v.28 no.9
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• pp.785-795
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• 2019

In order to analyze the sensitivity of carbon dioxide flux by soil temperature in the grassplot, carbon dioxide flux and soil temperature were observed 24 times from March, 2010 to March, 2011 at nine sites in the grassplot. The average of $CO_2$ in the grassplot is $2.2{\sim}36.7^{\circ}C$, the highest in August, the lowest in January, and the average of carbon dioxide flux is $12{\sim}1479mgCO_2{\cdot}m^{-2}{\cdot}hr^{-1}$, and the carbon dioxide emission from the grassplot to the atmosphere was 10 times higher in summer than in winter. The temperature response coefficient estimated by the exponential function of carbon dioxide flux according to soil temperature was ranged from 0.1065 to 0.1274, and the increase tendency of $CO_2$ flux with soil temperature was linear at $0{\sim}20^{\circ}C$ and exponential at $20{\sim}40^{\circ}C$. The $Q_{10}$ values for each of nine observation sites on the grassplot was in the range of 2.901 ~ 3.575, and the $Q_{10}$ value using the total data observed in the lawn was estimated to be 3.374. In the homogeneous grassplot area, the average of $Q_{10}$ values by observation point and the $Q_{10}$ value by the total data were estimated similarly.

• Geotechnical Engineering
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• v.14 no.5
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• pp.39-52
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• 1998

The pupose of the present paper is to estimate the effects of constraint condition of pile head, ground condition(dry unit weight. $\gamma_4$) and embedded pile lengths on the behavior of single pile which is embedded in normally consolidated clay. BBperiment functions can be quantified to these effects obtained from the results of model teats. The ground of model tests is normally consolidated( NC ) clay under three kinds of effective vertical stress. The results of the model tests using the steel pile of two different embedded pile length and of free-head and fired-head show that the lateral load-deflection relationship is to be elasto plastic behavior below $\gamma_d/\gamma_{dmax}$: 0.84 and that the reduction of lateral load of beyond maximum lateral load($Q_{max}$) at each model test is significantly time-dependent. In this study, it is shown that the displacement relationship can be fitted to exponential function of time by model best results. The effect of ground conditions on the ultimate and yield lateral load is fitted to exponential function including the ratio of dry unit weight to maximum dry unit weight. When tests by results are compared with those from Broms and Budhu et at., the predicted results are over-estimated about 27-87 ayo. In effectivity of constraint condition of pile head on the lateral load-deflection response, the $Q_{fixed}/Q_{gree}-y/D$ relationship is highly non-linear and fitted to parabolic function.

• The Journal of Asian Finance, Economics and Business
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• v.4 no.1
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• pp.19-23
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• 2017

Based on a simultaneous-equation model consisting of aggregate demand and short-run aggregate supply, this paper estimates a reduced-form equation specifying that the equilibrium real GDP is a function of the real effective exchange rate, the government deficit as a percent of GDP, the real interest rate, foreign income, labor productivity, the real oil price, the expected inflation rate, and the interactive and intercept binary variables accounting for a potential change in the slope of the real effective exchange rate and shift in the intercept. Applying the exponential GARCH technique, it finds that aggregate output in Australia has a positive relationship with the real effective exchange rate during 2003.Q3 - 2013.Q2, the government deficit as a percent of GDP, U.S. real GDP, labor productivity and the real oil price and a negative relationship with the real effective exchange rate during 2013.Q3 - 2016.Q1, the real lending rate and the expected inflation rate. These results suggest that real appreciation was expansionary before 2013.Q3 whereas real depreciation was expansionary after 2013.Q2 and that more government deficit as a percent of GDP would be helpful to stimulate the economy. Hence, the impact of real appreciation or real depreciation on real GDP may change overtime.

• Structural Engineering and Mechanics
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• v.72 no.3
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• pp.313-327
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• 2019

Damage evolution in the form of void nucleation, propagation and coalescence is the primary cause that is responsible for the ductile failure of microalloyed steels. The Gurson-Tvergaard-Needleman (GTN) damage model has proven to be extremely robust for characterizing the microscopic damage behavior of ductile metals. Nonetheless, successful applications of the model on a given metal type are limited by the correct identification of damage parameters as well as the validation of the calculated void growth rate. The purpose of this study is two-fold. First, we aim to identify the damage parameters of the GTN model for Q345 steel (Chinese code), due to its extensive application in mechanical and civil industries in China. The identification of damage parameters is facilitated by the well-suited response surface methodology, followed by a complete analysis of variance for evaluating the statistical significance of the identified model. Second, taking notched Q345 cylinders as an example, finite element simulations implemented with the identified GTN model are performed in order to analyze their microscopic damage behavior. In particular, the void growth rate predicted from the simulations is successfully correlated with experimentally measured acoustic emissions. The quantitative correlation suggests that during the yielding stage the void growth rate increases linearly with the acoustic emissions, while in the strain-hardening and softening period the dependence becomes an exponential function. The combined experimental and finite element approach provides a means for validating simulated void growth rate against experimental measurements of acoustic emissions in microalloyed steels.

• Wind and Structures
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• v.21 no.2
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• pp.119-158
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• 2015

The characteristics of the coherence functions of X axial, Y axial, and RZ axial (i.e., body axis) wind forces on the Shanghai World Trade Centre - a 492 m super-tall building with section varying along height are studied via a synchronous multi-pressure measurement of the rigid model in wind tunnel simulating of the turbulent, and the corresponding mathematical expressions are proposed there from. The investigations show that the mathematical expressions of coherence functions in across-wind and torsional-wind directions can be constructed by superimposition of a modified exponential decay function and a peak function caused by turbulent flow and vortex shedding respectively, while that in along-wind direction need only be constructed by the former, similar to that of wind speed. Moreover, an inductive analysis method is proposed to summarize the fitted parameters of the wind force coherence functions of every two measurement levels of altitudes. The comparisons of the first three order generalized force spectra show that the proposed mathematical expressions accord with the experimental results well. Later, the influences of coherence functions on wind-induced dynamic responses are analyzed in detail based on the proposed mathematical expressions and the frequency-domain method of random vibration theory.

• Journal of the Korean Geotechnical Society
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• v.35 no.3
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• pp.17-24
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• 2019

The purpose of this study is to understand the characteristics of bearing capacity of shallow foundation on the grounds. We made a comparative study of existing bearing capacity theory, based on the three-dimensional finite element analysis with a variety of conditions such as ground condition, foundation scale and foundation shape. In the finite element analysis, the ultimate bearing capacity showed a gradual convergence in the form of exponential function or logarithm function according to the foundation scale. Although the shear strength increased, the bearing capacity tended not to increase but change linearly. In the results of comparative study of existing bearing capacity theory, bearing capacity ratio ($q_{u(FEA)}/q_{u(theory)}$) of pure sand has the outcome closest to those of the Terzaghi method. Pure clay turned out to be about 0.4~0.6 while normal soil was changed in a range of 0.3~1.3. As shear strength is increased, the results turned out to be less than 1.0. Bearing capacity ratio ($q_u/q_{u(1.0)}$), normalized at 1.0m bearing capacity, was about 35%, 15% and 5% of theoretical formula under the condition of ${\phi}=25^{\circ}$, $30^{\circ}$ and $35^{\circ}$ of pure sand; no scale effect was found with pure clay and the normal soil with lower soil strength level showed less than 10% of the theoretical formula of pure sand. Bearing capacity ratio of each case, in accordance with, the shear strength increase, was largely influenced by the internal friction angle. Shape factor of bearing capacity ratios classified by foundation shapes have different results according to the shapes; the shape factor of circular foundation is 1.50, square foundation is 1.30, rectangular and continuous foundations are 1.1~1.0.