• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.25 no.1
• /
• pp.16-25
• /
• 2021

This paper is studied the existence of a solution for the impulsive Cauchy problem involving the Caputo fractional derivative in Banach space by using topological structures. We based on using topological degree method and fixed point theorem with some suitable conditions. Further, some topological properties for the set of solutions are considered. Finally, an example is presented to demonstrate our results.

• Journal of the Korean Mathematical Society
• /
• v.37 no.6
• /
• pp.1043-1057
• /
• 2000

This paper is devoted to the investigation of mixed Fourier-Bessel transformation (※Equations, See Full-text) We apply the method of [6] which provides the estimate for weighted L(sub)$\infty$-norm of the spherical mean of │f│$^2$ via its weighted L$_1$-norm (generally it is wrong without the requirement of the non-negativity of f). We prove that in the case of Fourier-Bessel transformatin the mentioned method provides (in dependence on the relation between the dimension of the space of non-special variables n and the length of multiindex ν) similar estimates for weighted spherical means of │f│$^2$, the allowed powers of weights are also defined by multiindex ν. Further those estimates are applied to partial differential equations with singular Bessel operators with respect to y$_1$, …, y(sub)m and we obtain the corresponding estimates for solutions of the mentioned equations.

• Journal of the Korean Society of Clothing and Textiles
• /
• v.24 no.2
• /
• pp.277-285
• /
• 2000

The purpose of this study was to quantify the relationship between the sense of touch and mechanical properties of man-made leather. The first was to develop the five conversion equations which convert mechanical properties of man-made leather into five factor scores, which express five factors of the sense of touch(surface property, stretchiness, thickness & weight, thermal property(warmth & coolness), and moisture property(sticky & clingy)). The second was to develop the conversion equation which converts five factor scores into score of the sense of touch. Five factor scores were predicted by the following mechanical properties; surface property factor by log2HB and (log2HB)2, stretchiness factor by logEM, thickness & weight factor by logT, log2HB, logW, thermal property factor by logT, logHB, logSMd, and moisture property factor by logMMD, RC, RC2, (logEM)2, RT2. Subsequently, these five factor scores were converted into score of the sense of touch. The predictive abilities of the developed equations were satisfied.

• Journal of Industrial Technology
• /
• v.34
• /
• pp.53-59
• /
• 2014

The single regression method was used to analyze the correlationship between the compression index with mechanical properties for reclaimed marine clays in the southern coast of Korea. As results of performing regression analysis for 200 samples about reclaimed marine clays in the southern coast of Korea, linear regression lines between compression index and natural water content, void ratio in situ, and liquid limit respectively wer obtained. The changed properties of soil due to disturbance during dredging and reclaiming could be investigated by comparing with the existing empirical correlation equations for the original ground where dredging was performed. These regression equations might be rationally used in the preliminary evaluation of settlement of dredged and reclaimed marine clayey ground in the southern coast of Korea.

• Journal of the Korean Society of Propulsion Engineers
• /
• v.26 no.5
• /
• pp.24-34
• /
• 2022

In order to predict the cooling performance of a regenerative cooling channel using hydrocarbon fuel operating in the supercritical region, it is essential to predict the thermodynamic properties. In this study, a comparative analysis was performed on two-parameter equations of state (SRK(Soave-Redlich-Kwong), PR(Peng-Robinson) equations of state) and three-parameter equations of state (RK-PR equations of state) to appropriately predict density and specific heat according to the critical compressibility factor of polymer hydrocarbons. Representatively, n-dodecane fuel with low critical compressibility factor and JP-10 fuel with high critical compressibility factor were selected, and an appropriate equation of state was presented when predicting the thermodynamic properties of the two fuels. Finally, the prediction results of density and specific heat were compared and verified with NIST REFPROP data.

• Kyungpook Mathematical Journal
• /
• v.16 no.2
• /
• pp.267-279
• /
• 1976

• Steel and Composite Structures
• /
• v.19 no.6
• /
• pp.1421-1447
• /
• 2015

In this paper, the effect of material-temperature dependent on the wave propagation of a cantilever beam composed of functionally graded material (FGM) under the effect of an impact force is investigated. The beam is excited by a transverse triangular force impulse modulated by a harmonic motion. Material properties of the beam are temperature-dependent and change in the thickness direction. The Kelvin-Voigt model for the material of the beam is used. The considered problem is investigated within the Euler-Bernoulli beam theory by using energy based finite element method. The system of equations of motion is derived by using Lagrange's equations. The obtained system of linear differential equations is reduced to a linear algebraic equation system and solved in the time domain and frequency domain by using Newmark average acceleration method. In order to establish the accuracy of the present formulation and results, the comparison study is performed with the published results available in the literature. Good agreement is observed. In the study, the effects of material distributions and temperature rising on the wave propagation of the FGM beam are investigated in detail.

• Journal for History of Mathematics
• /
• v.36 no.1
• /
• pp.1-17
• /
• 2023

Paper folding is a versatile tool that can be used not only as a mathematical model for analyzing the geometric properties of plane and spatial figures but also as a visual method for finding the real roots of polynomial equations. The historical evolution of origami's geometric and algebraic techniques has led to the discovery of definitions and properties that can enhance one's cognitive understanding of mathematical concepts and generate mathematical interest and motivation on an emotional level. This paper aims to examine the history of origami geometry, the utilization of origami for solving polynomial equations, and the process of determining the real roots of quadratic, cubic, and quartic equations through origami techniques.

• Structural Engineering and Mechanics
• /
• v.70 no.2
• /
• pp.179-197
• /
• 2019

In this article, the effect of different geometrical, materials and load parameters on the transient response of axisymmetric viscoelastic functionally graded annular plates with different boundary conditions are studied. The behavior of the plate is assumed the elastic in bulk and viscoelastic in shear with the standard linear solid model. Also, the graded properties vary through the thickness according to a power law function. Three types of mostly applied transient loading, i.e., step, impulse, and harmonic with different load distribution respect to radius coordinate are examined. The motion equations and the corresponding boundary conditions are extracted by applying the first order shear deformation theory which are three coupled partial differential equations with variable coefficients. The resulting motion equations are solved analytically using the perturbation technique and the generalized Fourier series. The sensitivity of the response to the graded indexes, different transverse loads, aspect ratios, boundary conditions and the material properties are investigated too. The results are compared with the finite element analysis.

• Coupled systems mechanics
• /
• v.5 no.3
• /
• pp.255-267
• /
• 2016

To investigate the surface effects on vibration of embedded circular curved nanosize beams, nonlocal elasticity model is used in combination with surface properties including surface elasticity, surface tension and surface density for modeling the nano scale effect. The governing equations are determined via the energy method. Analytically Navier method is utilized to solve the governing equations for simply supported at both ends. Solving these equations enables us to estimate the natural frequency for circular curved nanobeam including Winkler and Pasternak elastic foundations. The results determined are verified by comparing the results by available ones in literature. The effects of various parameters such as nonlocal parameter, surface properties, Winkler and Pasternak elastic foundations and opening angle of circular curved nanobeam on the natural frequency are successfully studied. The results reveal that the natural frequency of circular curved nanobeam is significantly influenced by these effects.