• Journal of the Korean Mathematical Society
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• v.57 no.1
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• pp.145-169
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• 2020

Let k be a field of characteristic 0. Let ${\mathfrak{C}}=Spec(k[x,y]/{\langle}f{\rangle})$ be a weighted homogeneous plane curve singularity with tangent space ${\pi}_{\mathfrak{C}}:T_{{\mathfrak{C}}/k}{\rightarrow}{\mathfrak{C}$. In this article, we study, from a computational point of view, the Zariski closure ${\mathfrak{G}}({\mathfrak{C}})$ of the set of the 1-jets on ${\mathfrak{C}}$ which define formal solutions (in F[[t]]² for field extensions F of k) of the equation f = 0. We produce Groebner bases of the ideal ${\mathcal{N}}_1({\mathfrak{C}})$ defining ${\mathfrak{G}}({\mathfrak{C}})$ as a reduced closed subscheme of $T_{{\mathfrak{C}}/k}$ and obtain applications in terms of logarithmic differential operators (in the plane) along ${\mathfrak{C}}$.

• Journal of Integrative Natural Science
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• v.7 no.4
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• pp.273-277
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• 2014

In this article, we consider a singular and a degenerate elliptic operators in a divergence form. The singularities exist on a part of boundary, and comparable to the logarithmic distance function or its inverse. If we assume that the operator can be treated in a pointwise sense than distribution sense, with this operator we obtain a priori Harnack continuity near the boundary. In the proof we transform the singular elliptic operator to uniformly bounded elliptic operator with unbounded first order terms. We study this type of estimations considering a De Giorgi conjecture. In his conjecture, he proposed a certain ellipticity condition to guarantee a continuity of a solution.

• The Transactions of the Korean Institute of Electrical Engineers P
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• v.53 no.2
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• pp.82-88
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• 2004

In this study, an intelligent solenoid valve controller has been developed for efficient maintaining of filters in a dust collecting system. This controller has automatic controllability of solenoid valves' ON/OFF time depending on the clogging status of filters, and then it can extend the filters' lifetimes, decrease the power consumption, and make effective operation of the system possible. This controllability has been executed by the fuzzy theory that utilizes the workers' experimental knowledges, the control expert's knowledges and the differential pressures between the inlets and outlets measured by the sensors. The system's operation is under the continuous surveillance by using a current transformer, which warns the operators and lets them take necessary actions in case of abnormal operation.

• Communications of the Korean Mathematical Society
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• v.31 no.4
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• pp.827-844
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• 2016

Here, in this paper, we aim at establishing some new unified integral and differential formulas associated with the $\bar{H}$-function. Each of these formula involves a product of the $\bar{H}$-function and Srivastava polynomials with essentially arbitrary coefficients and the results are obtained in terms of two variables $\bar{H}$-function. By assigning suitably special values to these coefficients, the main results can be reduced to the corresponding integral formulas involving the classical orthogonal polynomials including, for example, Hermite, Jacobi, Legendre and Laguerre polynomials. Furthermore, the $\bar{H}$-function occurring in each of main results can be reduced, under various special cases.

• Kyungpook Mathematical Journal
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• v.59 no.2
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• pp.301-314
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• 2019

The aim of this article is to make a connection between the Pascal distribution series and some subclasses of normalized analytic functions whose coefficients are probabilities of the Pascal distribution. For these functions, for linear combinations of these functions and their derivatives, for operators defined by convolution products, and for the Alexander-type integral operator, we find simple sufficient conditions such that these mapping belong to a general class of functions defined and studied by Goodman, Rønning, and Bharati et al.

• Journal of the Korean Mathematical Society
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• v.56 no.1
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• pp.149-167
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• 2019

In this work, we study the existence, uniqueness and stability in the ${\alpha}$-norm of solutions for some stochastic partial functional integrodifferential equations. We suppose that the linear part has an analytic resolvent operator in the sense given in Grimmer [8] and the nonlinear part satisfies a $H{\ddot{o}}lder$ type condition with respect to the ${\alpha}$-norm associated to the linear part. Firstly, we study the existence of the mild solutions. Secondly, we study the exponential stability in pth moment (p > 2). Our results are illustrated by an example. This work extends many previous results on stochastic partial functional differential equations.

• Journal of applied mathematics & informatics
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• v.37 no.5_6
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• pp.341-349
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• 2019

This paper is concerned to investigate M-Wright function, which was earlier known as transcendental function of the Wright type. M-Wright function is a special case of the Wright function given by British mathematician (E.Maitland Wright) in 1933. We have explored the cosequences of Riemann-Liouville Integral and Differential operators on M-Wright function. We have also evaluated integral transforms of the M-Wright function.

• Nonlinear Functional Analysis and Applications
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• v.26 no.3
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• pp.497-512
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• 2021

In this paper, we study the analytical and approximate solutions for a fractional quadratic integral equation involving Katugampola fractional integral operator. The existence and uniqueness results obtained in the given arrangement are not only new but also yield some new particular results corresponding to special values of the parameters 𝜌 and ϑ. The main results are obtained by using Banach fixed point theorem, Picard Method, and Adomian decomposition method. An illustrative example is given to justify the main results.

• Structural Monitoring and Maintenance
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• v.11 no.1
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• pp.19-40
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• 2024

The elastic theory of beams is fundamental in engineering of design and structure. In this study, we construct Green's function for inhomogeneous fourth-order differential operators subjected to associated constraints that arises in dealing with dynamic problems in the Rayleigh beam. We obtain solutions for homogeneous and completely inhomogeneous beam problems using Green's function. This enables us to consider rotational influences in determining the eigenfrequency of beam vibrations. Additionally, we investigate the dynamic vibration model of inhomogeneous beams incorporating rotational effects. The eigenvalues of Rayleigh beams, including first-order correction terms, are also computed and displayed in tabular forms.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.7
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• pp.939-944
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• 2007

Edge is a significant element to represent boundary information between objects in images. There are various edge detection methods, which are based on differential operation, such as Sobel, Prewitt, Roberts, Canny, Laplacian, and etc. However the conventional methods have drawbacks as follow : (i) insensitivity to edges with gentle curve intensity, (ii) detection of double edges for edges with one pixel width. For the detection of edges, not only development of the effective operators but also that of appropriate thresholding methods are necessary. But it is very complicate problem to find an appropriate threshold. In this paper, we propose an edge detection method based on the region separateness between objects to overcome the drawbacks of the conventional methods, and a thresholding method for the proposed edge detection method. We show the effectiveness of the proposed method through experimental results obtained by applying the proposed and the conventional methods to well-known test images.