• Journal of applied mathematics & informatics
• /
• v.42 no.1
• /
• pp.189-197
• /
• 2024

The purpose of this paper is to introduce and study the new class of spaces called the fuzzy 𝛽-Volterra spaces with the help of fuzzy β-dense and fuzzy 𝛽-G_𝛿 sets. Examples are given to illustrate the concept. Some interesting characterizations of the fuzzy 𝛽-Volterra spaces are established in this paper.

• Kyungpook Mathematical Journal
• /
• v.32 no.1
• /
• pp.31-43
• /
• 1992

• Kyungpook Mathematical Journal
• /
• v.45 no.2
• /
• pp.199-209
• /
• 2005

An ideal space is ${\cal{I}}-resolvable$ if it has two disjoint ${\cal{I}}-dense$ subsets. We answer the question: If X is ${\cal{I}}-resolvable$, then is X (${\cal{I}}\;{\cup}\;{\cal{N}$)-resolvable?, posed by Dontchev, Ganster and Rose. We give three generalizations of the well known Banach Category Theorem and deduce the Banach category Theorem as a corollary. Characterizations of completely codense ideals and ${\cal{I}-locally$ closed sets are given and their properties are discussed.

• Journal of applied mathematics & informatics
• /
• v.3 no.2
• /
• pp.279-290
• /
• 1996

In the present paper we study the Cauchy problem in a Banach space E for an abstract nonlinear differential equation of form $$\frac{d^2u}{dt^2}=-A{\frac{du}{dt}}+B(t)u+f(t, W)$$ where W=($A_1$(t)u, A_2(t)u)..., A_{\nu}(t)u), A_{i}(t),\;i=1,2,...{\nu}$,(B(t), t{\in}I$=[0, b]) are families of closed operators defined on dense sets in E into E, f is a given abstract nonlinear function on $I{\times}E^{\nu}$ into E and -A is a closed linar operator defined on dense set in e into E which generates a semi-group. Further the existence and uniqueness of the solution of the considered Cauchy problem is studied for a wide class of the families ($A_{i}$(t), i =1.2...${\nu}$), (B(t), $t{\in}I$) An application and some properties are also given for the theory of partial diferential equations.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.1
• /
• pp.29-41
• /
• 2014

In this paper, we prove that infinite-dimensional vector spaces of -dense curves are generated by means of the functional equations f(x)+f(2x)+${\cdots}$+f(nx) = 0, with $n{\geq}2$, which are related to the partial sums of the Riemann zeta function. These curves ${\alpha}$-densify a large class of compact sets of the plane for arbitrary small ${\alpha}$, extending the known result that this holds for the cases n = 2, 3. Finally, we prove the existence of a family of solutions of such functional equation which has the property of quadrature in the compact that densifies, that is, the product of the length of the curve by the $n^{th}$ power of the density approaches the Jordan content of the compact set which the curve densifies.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.13 no.6
• /
• pp.2986-2999
• /
• 2019

The uncertainties of the uncertain graph make the traditional definition and algorithms on mining dense graph for certain graph not applicable. The subgraph obtained by maximizing expected density from an uncertain graph always has many low edge-probability data, which makes it low reliable and low expected edge density. Based on the concept of ${\beta}$-subgraph, to overcome the low reliability of the densest subgraph, the concept of optimal ${\beta}$-subgraph is proposed. An efficient greedy algorithm is also developed to find the optimal ${\beta}$-subgraph. Simulation experiments of multiple sets of datasets show that the average edge-possibility of optimal ${\beta}$-subgraph is improved by nearly 40%, and the expected edge density reaches 0.9 on average. The parameter ${\beta}$ is scalable and applicable to multiple scenarios.

• Bulletin of the Korean Mathematical Society
• /
• v.61 no.1
• /
• pp.195-205
• /
• 2024

In this paper, we consider the set of periodic shadowable points for homeomorphisms of a compact metric space, and we prove that this set satisfies some properties such as invariance and being a G_δ set. Then we investigate implication relations related to sets consisting of shadowable points, periodic shadowable points and uniformly expansive points, respectively. Assume that the set of periodic points and the set of periodic shadowable points of a homeomorphism on a compact metric space are dense in X. Then we show that a homeomorphism has the periodic shadowing property if and only if so is the restricted map to the set of periodic shadowable points. We also give some examples related to our results.

• Journal of the Korean Mathematical Society
• /
• v.38 no.5
• /
• pp.937-954
• /
• 2001

This paper is a natural continuation of [2], [3], [4] and [5]. Localization techniques for modular lattices are developed. These techniques are applied to study liftings of linear order types from quotient lattices and to find Г-dense sets in certain lattices without Г-deviation in the sense of [4], where Г is a set of indecomposable linear order types.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
• /
• v.38 no.1
• /
• pp.23-33
• /
• 2020

Recently, high-resolution images can be easily acquired using UAV (Unmanned Aerial Vehicle), so that it is possible to produce small area observation and spatial information at low cost. In particular, research on the generation of cover maps in crop production areas is being actively conducted for monitoring the agricultural environment. As a result of comparing classification performance by applying RF(Random Forest), SVM(Support Vector Machine) and CNN(Convolutional Neural Network), deep learning classification method has many advantages in image classification. In particular, land cover classification using satellite images has the advantage of accuracy and time of classification using satellite image data set and pre-trained parameters. However, UAV images have different characteristics such as satellite images and spatial resolution, which makes it difficult to apply them. In order to solve this problem, we conducted a study on the application of deep learning algorithms that can be used for analyzing agricultural lands where UAV data sets and small-scale composite cover exist in Korea. In this study, we applied DeepLab V3 +, FC-DenseNet (Fully Convolutional DenseNets) and FRRN-B (Full-Resolution Residual Networks), the semantic image classification of the state-of-art algorithm, to UAV data set. As a result, DeepLab V3 + and FC-DenseNet have an overall accuracy of 97% and a Kappa coefficient of 0.92, which is higher than the conventional classification. The applicability of the cover classification using UAV images of small areas is shown.

• Geomechanics and Engineering
• /
• v.19 no.4
• /
• pp.307-314
• /
• 2019

Light construction waste (LCW) particles are pieces of light concrete or insulation wall with light quality and certain strength, containing rich isolated and disconnected pores. Mixing LCW particles with soil can be one of the alternative lightweight soils. It can lighten and stabilize the deep-thick soft soil in-situ. In this study, the unconfined compressive strength (UCS) and its mechanism of Construction Waste Stabilized Lightweight Soil (CWSLS) are investigated. According to the prescription design, totally 35 sets of specimens are tested for the index of dry density (DD) and unconfined compressive strength (UCS). The results show that the DD of CWSLS is mainly affected by LCW content, and it decreases obviously with the increase of LCW content, while increases slightly with the increase of cement content. The UCS of CWSLS first increases and then decreases with the increase of LCW content, existing a peak value. The UCS increases linearly with the increase of cement content, while the strength growth rate is dramatically affected by the different LCW contents. The UCS of CWSLS mainly comes from the skeleton impaction of LCW particles and the gelation of soil-cement composite slurry. According to the distribution of LCW particles and soil-cement composite slurry, CWSLS specimens are divided into three structures: "suspend-dense" structure, "framework-dense" structure and "framework-pore" structure.