• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.367-377
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• 2024

Let G = (V, E) be a graph with p-vertices and q-edges and let R^◦ be a finite zero ring of order n. An injective function f : V (G) → {r₁, r₂, _…, r_k}, where r_i ∈ R^◦ is called vertex pair sum k-zero ring labeling, if it is possible to label the vertices x ∈ V with distinct labels from R^◦ such that each edge e = uv is labeled with f(e = uv) = [f(u) + f(v)] (mod n) and the edge labels are distinct. A graph admits such labeling is called vertex pair sum k-zero ring graph. The minimum value of positive integer k for a graph G which admits a vertex pair sum k-zero ring labeling is called the vertex pair sum k-zero ring index denoted by 𝜓_pz(G). In this paper, we defined the vertex pair sum k-zero ring labeling and applied to some graphs.

• Journal of the Korean Society of Radiology
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• v.15 no.4
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• pp.473-479
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• 2021

The diagnostic criteria for diffuse thyroid disease are ambiguous and there are many errors due to the subjective diagnosis of experts. Also, studies on ultrasound imaging of thyroid nodules have been actively conducted, but studies on diffuse thyroid disease are insufficient. In this study, features were extracted by applying the GLCM algorithm to ultrasound images of normal and diffuse thyroid disease, and quantitative analysis was performed using the extracted feature values. Using the GLCM algorithm for thyroid ultrasound images of patients diagnosed at W hospital, 199 normal cases, 132 mild cases, and 99 moderate cases, a region of interest (50×50 pixel) was set for a total of 430 images, and Autocorrelation, Sum of squares, sum average, sum variance, cluster prominence, and energy were analyzed using six parameters. As a result, in autocorrelation, sum of squares, sum average, and sum variance four parameters, Normal, Mild, and Moderate were distinguished with a high recognition rate of over 90%. This study is valuable as a criterion for classifying the severity of diffuse thyroid disease in ultrasound images using the GLCM algorithm. By applying these parameters, it is expected that errors due to visual reading can be reduced in the diagnosis of thyroid disease and can be utilized as a secondary means of diagnosing diffuse thyroid disease.

• Journal of the Korean Society of Radiology
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• v.17 no.5
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• pp.735-742
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• 2023

Non-alcoholic fatty liver disease is an independent risk factor for the development of cardiovascular disease, diabetes, hypertension, and kidney disease, and the clinical importance of non-alcoholic fatty liver disease has recently been increasing. In this study, we aim to extract feature values by applying GLCM, a texture analysis method, to ultrasound images of patients with non-alcoholic fatty liver disease. By applying an artificial neural network model using extracted feature values, we would like to classify the degree of fat deposition in non-alcoholic fatty liver into normal liver, mild fatty liver, moderate fatty liver, and severe fatty liver. As a result of applying the GLCM algorithm, the parameters Autocorrelation, Sum of squares, Sum average, and sum variance showed a tendency for the average value of the feature values to increase as it progressed from mild fatty liver to moderate fatty liver to severe fatty liver. The four parameters of Autocorrelation, Sum of squares, Sum average, and sum variance extracted by applying the GLCM algorithm to ultrasound images of non-alcoholic fatty liver disease were applied as inputs to the artificial neural network model. The classification accuracy was evaluated by applying the GLCM algorithm to the ultrasound images of non-alcoholic fatty liver disease and applying the extracted images to an artificial neural network, showing a high accuracy of 92.5%. Through these results, we would like to present the results of this study as basic data when conducting a texture analysis GLCM study on ultrasound images of patients with non-alcoholic fatty liver disease.

• East Asian mathematical journal
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• v.16 no.1
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• pp.33-48
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• 2000

In this paper, for any ring R with an identity, in order to study prime ideals of the endomorphism ring $End_R$(M) of left R-module $_RM$, meet-prime submodules, prime radical, sum-prime submodules and the prime socle of a module are defined. Some relations of the prime radical, the prime socle of a module and the prime radical of the endomorphism ring of a module are investigated. It is revealed that meet-prime(or sum-prime) modules and semi-meet-prime(or semi-sum-prime) modules have their prime, semi-prime endomorphism rings, respectively.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.520-523
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• 1997

This paper presents FPGA implementation of fuzzy controller using Product-Sum inference method. Product-Sum inference method has much better performance than other inference methods. This fuzzy controller is composed of several digital modules, e.g. fuzzifier, rule base, adder, multiplier, select center and divider, and is operated by error and error variation. We synthesized the fuzzy controller and performed wave simulation using Xilinx VHDL tool(ViewLogic, ViewSim).

• Korean Journal of Mathematics
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• v.23 no.4
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• pp.571-590
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• 2015

Let a, b, q be integers with q > 0. The homogeneous Dedekind sum is dened by $$\Large S(a,b,q)={\sum_{r=1}^{q}}\(\({\frac{ar}{q}}\)\)\(\({\frac{br}{q}}\)\)$$, where $$\Large ((x))=\{x-[x]-{\frac{1}{2}},\text{ if x is not an integer},\\0,\hspace{75}\text{ if x is an integer.}$$ In this paper we study the mean value of S(a, b, q) by using mean value theorems of Dirichlet L-functions, and give some asymptotic formula.

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.601-607
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• 1996

For functions $f(z) = \sum_{n = 0}^{\infty}a_n z^n$ and $g(z) = \sum_{n = 0}^{\infty} b_n z^n$ analytic in the unit disk $\Delta = {z : $\mid$z$\mid$ < 1}$, the convolution $f * g$ is defined by $(f * g)(z) = \sum_{n = 0}^{\infty}a_n b_n z^n$. Let S denote the family of functions $f(z) = z + \cdots$ analytic and univalent in $\Delta$ and K, St, C the subfamilies that are respectively convex, starlike, and close-to-convex.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.599-609
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• 2017

We construct degenerated Euler polynomials of the second kind and find some basic properties of this polynomials. From this paper, we can see degenerated alternative power sum is defined and is related to degenerated Euler polynomials of the second kind. Using this power sum, we have a number of symmetric properties of degenerated Euler polynomials of the second kind.

• Bulletin of the Korean Mathematical Society
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• v.35 no.1
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• pp.33-43
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• 1998

Matlis posed the following question in 1958: if N is a direct summand of a direct sum M of indecomposable injectives, then is N itself a direct sum of indecomposable innjectives\ulcorner It will be proved that the Matlis problem has an affirmative answer when M is a multiplication module, and that a weaker condition then that of M being a multiplication module can be given to module M when M is a countable direct sum of indecomposable injectives.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.2061-2070
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• 2013

In this paper, we investigate the generalized HyersUlam-Rassias stability of the following additive functional equation $$2\sum_{j=1}^{n}f(\frac{x_j}{2}+\sum_{i=1,i{\neq}j}^{n}\;x_i)+\sum_{j=1}^{n}f(x_j)=2nf(\sum_{j=1}^{n}x_j)$$, in quasi-${\beta}$-normed spaces.