• Journal of applied mathematics & informatics
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• v.41 no.4
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• pp.861-868
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• 2023

Nonlinear network creates complex homotopy structural communication in wireless network medium because of complex distribution approach. Due to this multicast topological connection structure, the queuing probability was non regular principles to create routing structures. To resolve this problem, we propose a Co-cluster homotopy queuing model (Co-CHQT) for Nonlinear Algebraic Topological Structure (NLTS-) for improving poison distribution network communication. Initially this collects the routing propagation based on Nonlinear Distance Theory (NLDT) to estimate the nearest neighbor network nodes undernon linear at x_(a,b)→ax²+bx² = c. Then Quillen Network Decomposition Theorem (QNDT) was applied to sustain the non-regular routing propagation to create cluster path. Each cluster be form with co variance structure based on Two unicast 2(n+1)-Z2(n+1)-Z network. Based on the poison distribution theory X_(a,b) ≠ µ(C), at number of distribution routing strategies weights are estimated based on node response rate. Deriving shorte;'l/st path from behavioral of the node response, Hilbert -Krylov subspace clustering estimates the Cluster Head (CH) to the routing head. This solves the approximation routing strategy from the nonlinear communication depending on Max- equivalence theory (Max-T). This proposed system improves communication to construction topological cluster based on optimized level to produce better performance in distance theory, throughput latency in non-variation delay tolerant.

• East Asian mathematical journal
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• v.22 no.1
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• pp.79-91
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• 2006

In this paper, we will show some relations between decomposition series {$\pi^{\alpha}q\;:\;{\alpha}$ is an ordinal} and topological series {$\tau_{\alpha}q\;:\;{\alpha}$ is an ordinal} for a convergence structure q and the formular ${\pi}^{\beta}(\tau_{\alpha}q)={\pi}^{{\omega^{\alpha}\beta}}q$, where $\omega$ is the first limit ordinal and $\alpha$ and $\beta({\geq}1)$ are ordinals.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.8
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• pp.3950-3964
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• 2017

With the increasing popularity of 3D technology such as 3D printing, 3D modeling, etc., there is a growing need to search for similar models on the internet. Matching non-rigid shapes has become an active research field in computer graphics. In this paper, we present an efficient and effective non-rigid model retrieval method based on topological structure and local volume. The integral geodesic distances are first calculated for each vertex on a mesh to construct the topological structure. Next, each node on the topological structure is assigned a local volume that is calculated using the shape diameter function (SDF). Finally, we utilize the Hungarian algorithm to measure similarity between two non-rigid models. Experimental results on the latest benchmark (SHREC' 15 Non-rigid 3D Shape Retrieval) demonstrate that our method works well compared to the state-of-the-art.

• Communications of the Korean Mathematical Society
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• v.25 no.3
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• pp.335-342
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• 2010

The structure of fuzzy topological spaces based on WFI-algebras is considered. The notions of WFI-fuzzy topological spaces and WFI-fuzzy continuous mappings are introduced, and several properties are investigated. A relation between WFI-homomorphism and WFI-fuzzy continuous mapping is given.

• Journal for History of Mathematics
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• v.14 no.2
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• pp.13-20
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• 2001

The topological structure of a topological space is completely determined by the data of convergence of filters on the space. We study the origin of convergence structure in the setting of filters and nets and their ramifications.

• Elastomers and Composites
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• v.37 no.4
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• pp.234-243
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• 2002

A general scheme of a rubber structure is proposed. Using the thermomechanical method(TMA), some changes in the molecular and topological structures for uncured and cured, and unfilled and filled rubbers during processing are shown. In our investigations as region it is understood a complex structure, which is expressed at the thermomechanical curve(TMC) as a zone differed from others in thermal expansion properties. This zone is between the noticed temperatures of relaxation transitions, usually on the level like those determined by DMTA at 1Hz. These regions, which shares, are not stable, and differ in molecular-weight distribution(MWD) of chain fragments between the junctions. Differences in dynamics of the formation of the molecular and topological structures of a vulcanizate are dependent on the rubber formulation, mixing technology and curing time. Some of characteristics of these regions correlate with mechanical properties of vulcanizates what is shown for NR rubbers containing ENR or CPE as a polymeric additive. It is well known that the state of order influences diffusivity of low-molecular substances into the polymer matrix. Because of this, the two topological amorphous regions should influence the distribution of the ingredients and resulting in rubber compounds' heterogeneity, and related properties of cured rubber. Investigation of this problem is expected to be, in the future, one of the essential factors in determining further improvement of polymeric materials properties by compounding with additives and in reprocessing of rubber scrap.

• Honam Mathematical Journal
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• v.34 no.4
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• pp.559-570
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• 2012

We construct a new definition of a base for ordinary smooth topological spaces and introduce the concept of a neighborhood structure in ordinary smooth topological spaces. Then, we state some of their properties which are generalizations of some results in classical topological spaces.

• International Journal of CAD/CAM
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• v.5 no.1
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• pp.59-68
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• 2005

Euclidean Voronoi diagram of spheres in 3-dimensional space has not been explored as much as it deserves even though it has significant potential impacts on diverse applications in both science and engineering. In addition, studies on the data structure for its topology have not been reported yet. Presented in this, paper is the topological representation for Euclidean Voronoi diagram of spheres which is a typical non-manifold model. The proposed representation is a variation of radial edge data structure capable of dealing with the topological characteristics of Euclidean Voronoi diagram of spheres distinguished from those of a general non-manifold model and Euclidean Voronoi diagram of points. Various topological queries for the spatial reasoning on the representation are also presented as a sequence of adjacency relationships among topological entities. The time and storage complexities of the proposed representation are analyzed.

• Korean Journal of Computational Design and Engineering
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• v.2 no.3
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• pp.150-160
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• 1997

Existing non-manifold data structures which use the ordered topological representation method, are designed based on a "Model" which is the highest topological entity. Their non-manifold information is always included in edges and vertices even if they are in the manifold situation. Thus they require large storage spaces than manifold data structures. The proposed data structure reduces its storage space by removing unnecessary information stored in edges and vertices. Topological information is classified into manifold and non-manifold information. The main non-manifold information is radial cycles and disk cycles. The proposed data structure always stores manifold information. For the non-manifold situation, the edge stores radial cycles, and the vertex stores disk cycles. The storage space can be reduced in the later stage of CAD design when the ratio of non-manifold to manifold entities is small.

• International Journal of CAD/CAM
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• v.6 no.1
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• pp.125-137
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• 2006

Nowadays, many commercial CAD systems support history-based, constraint-based and feature-based modeling. Unfortunately, most systems fail during the re-evaluation phase when various kind of topological changes occur. This issue is known as "persistent naming" which refers to the problem of identifying entities in an initial parametric model and matching them in the re-evaluated model. Most works in this domain focus on the persistent naming of atomic entities such as vertices, edges or faces. But very few of them consider the persistent naming of aggregates like shells (any set of faces). We propose in this paper a complete framework for identifying and matching any kind of entities based on their underlying topology, and particularly shells. The identifying method is based on the invariant structure of each class of form features (a hierarchical structure of shells) and on its topological evolution (an historical structure of faces). The matching method compares the initial and the re-evaluated topological histories, and computes two measures of topological similarity between any couple of entities occurring in both models. The naming and matching method has been implemented and integrated in a prototype of commercial CAD Software (Topsolid).