• Journal of Digital Contents Society
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• v.5 no.4
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• pp.289-294
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• 2004

For the purpose of image analysis, we usually take the application method relying on the various mathematical theories. On the respect of image as two variable function one may uses the gradient vector or several type of energy functions induced by the conventional (partial) derivative. We also have used the tangent plane or curvature vector from the concept of differential geometry {**]. However, these mathematical tools my assume that the given function should be sufficiently smoothing enough to depict every local variation continuously. But the real application of these mathematical methods to the natural images or phenomena may occur the ill-posed problem. In this paper, we have defined the weak derivative as a loose form of the derivative so that it my applied to the irregular case with less ill-posed problem.

• Interaction and multiscale mechanics
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• v.1 no.2
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• pp.251-278
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• 2008

In this study, we investigate the discontinuous-derivative treatment at the gas-liquid interface in underwater explosion (UNDEX) problems by using the Moving Least Squares-Smoothed Particle Hydrodynamics (MLS-SPH) method, which is known as one of the particle methods suitable for problems where large deformation and inhomogeneity occur in the whole domain. Because the numerical oscillation of pressure arises from derivative discontinuity in the UNDEX analysis using the standard SPH method, the MLS shape function with Discontinuous-derivative Basis Function (DBF) that is able to represent the derivative discontinuity of field function is utilized in the MLS-SPH formulation in order to suppress the nonphysical pressure oscillation. The effectiveness of the MLS-SPH with DBF is demonstrated in comparison with the standard SPH and conventional MLS-SPH though a shock tube problem and benchmark standard problems of UNDEX of a trinitrotoluene (TNT) charge.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 2001.06a
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• pp.212-217
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• 2001

This paper presents the stability characteristics of a rotor-bearing system supported by actively controlled hydrodynamic journal bearing. The proportional and derivative controls including coupled motion are adopted for the control algorithm to control the hydrodynamic journal bearing with a circumferentially groove. Also, the cavitation algorithm implementing the Jakobsson-Floberg-Olsson boundary condition is adopted to predict cavitation regions in the fluid film more accurately than conventional analysis which uses the Reynolds condition. The stability characteristics are investigated with the Routh-Hurwitz criteria using the linear dynamic coefficients which are obtained from the perturbation method. The stability characteristics of the rotor-bearing system supported by active controlled hydrodynamic journal bearing are investigated for various control gain. It is found that the speed at onset of instability is increased for both proportional and derivative control of the bearing, and the proportional and derivative control of coupled motion is more effective than proportional and derivative control of uncoupled motion.

• Geomechanics and Engineering
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• v.37 no.6
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• pp.591-597
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• 2024

The purpose of this paper is to depict the effect of gravity on a nonlocal thermoelastic medium with initial stress. The Lord-Shulman and Green-Lindsay theories with fractional derivative order serve as the foundation for the formulation of the fundamental equations for the problem. To address the problem and acquire the exact expressions of physical fields, appropriate non-dimensional variables and normal mode analysis are used. MATLAB software is used for numerical calculations. The projected outcomes in the presence and absence of the gravitational field, along with a nonlocal parameter, are compared. Additional comparisons are made for various fractional derivative order values. It is evident that the variation of physical variables is significantly influenced by the fractional derivative order, nonlocal parameter and gravity field.

• Macromolecular Research
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• v.14 no.4
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• pp.443-448
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• 2006

A novel ${\beta}$-cyclodextrin derivative (CCD-C) was synthesized with chitosan and carboxymethyl-${\beta}$-cyclodextrin. Its structure was characterized by elemental analysis, infrared spectra analysis, and X-ray diffraction analysis. The adsorption properties for guanosine 5'-monophosphate, cytidine 5'-monophosphate and uridine 5'-monophosphate were studied. Experimental results demonstrated that CCD-C had higher adsorption capability for guanosine 5'-monophosphate, and that the adsorption capacity for guanosine 5'-monophosphate was 74.20mg/g. The adsorption capacity was greatly influenced by pH, time and temperature. The introduction of chitosan enhanced the adsorption ability and adsorption selectivity of ${\beta}$-cyclodextrin for guanosine 5'-monophosphate. This novel derivative of chitosan is expected to have wide applications in the separation, concentration and analysis of nucleotides in biological samples.

• Bulletin of the Korean Chemical Society
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• v.27 no.2
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• pp.302-304
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• 2006

• Natural Product Sciences
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• v.17 no.4
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• pp.350-353
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• 2011

A new daucosteryl derivative, verticilloside (1), was isolated from the seeds of Malva verticillata L. (Malvaceae). The structure was determined to be 3-O-[${\beta}$-D-(6'-linoleoyl)glucopyranosyl]-${\beta}$-sitosterol based on spectroscopic analyses ($^1H$ and $^{13}C$-NMR, DEPT, COSY, HMQC, and HMBC) and chemical reactions.

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.797-805
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• 2022

Let P(z) be a polynomial of degree n. A well-known inequality due to S. Bernstein states that if P ∈ P_n, then $$\max_{{\mid}z{\mid}=1}\,{\mid}P^{\prime}(z){\mid}\,{\leq}n\,\max_{{\mid}z{\mid}=1}\,{\mid}P(z){\mid}$$. In this paper, we establish some extensions and refinements of the above inequality to polar derivative and some other well-known inequalities concerning the polynomials and their ordinary derivatives.

• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.647-657
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• 2023

The aim of this paper is to study certain subclass ${\tilde{S^q_{\Sigma}}}({\lambda},\,{\alpha},\,t,\,s,\,p,\,b)$ of analytic and bi-univalent functions which are defined by using symmetric q-derivative operator. We estimate the second and third coefficients of the Taylor-Maclaurin series expansions belonging to the subclass and upper bounds for Feketo-Szegö inequality. Furthermore, some relevant connections of certain special cases of the main results with those in several earlier works are also pointed out.

• Nonlinear Functional Analysis and Applications
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• v.29 no.3
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• pp.753-767
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• 2024

In this paper, we developed the existence and uniqueness results by monotone method for non-linear fractional reaction-diffusion equation together with initial and boundary conditions. In this text the Hilfer fractional derivative is used to denote the time fractional derivative. The employment of monotone method generates two sequences of minimal and maximal solutions which converges to lower and upper solutions respectively.