A Hierarchical Structure for the Sharp Constants of Discrete Sobolev Inequalities on a Weighted Complete Graph

Takemura, Kazuo; Kametaka, Yoshinori; Nagai, Atsushi

doi:10.3390/sym10010001

Cited by 2 publications

(1 citation statement)

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“…Certain special types of connected graphs are also interesting to study and look for some applications, especially a complete graph which is a graph in which every two distinct vertices are adjacent. Some authors considered a complete graph for applying its structure to complete their research, see for examples [4,5]. Furthermore, an algebraic formation on connected graphs has been studied in the sense of defining some binary operations among a pair of such graphs.…”

Section: Introductionmentioning

confidence: 99%

On the Semigroup Whose Elements Are Subgraphs of a Complete Graph

et al. 2018

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Let K n be a complete graph on n vertices. Denote by SK n the set of all subgraphs of K n. For each G, H ∈ SK n , the ring sum of G and H is a graph whose vertex set is V(G) ∪ V(H) and whose edges are that of either G or H, but not of both. Then SK n is a semigroup under the ring sum. In this paper, we study Green's relations on SK n and characterize ideals, minimal ideals, maximal ideals, and principal ideals of SK n. Moreover, maximal subsemigroups and a class of maximal congruences are investigated. Furthermore, we prescribe the natural order on SK n and consider minimal elements, maximal elements and covering elements of SK n under this order.

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Section: Introductionmentioning

confidence: 99%

On the Semigroup Whose Elements Are Subgraphs of a Complete Graph

et al. 2018

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A Novel Disease Detection and Classification Method Using Improved Fusion Random Weight Support Vector Machine

Rani¹,

Selvam²

2021

j med imaging hlth inform

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Health informatics is one of the main branch of engineering which provides a solution to a variety of problems like delayed, missed or incorrect diagnoses with the help of computational techniques. With the help of technologies such as bio-computing, health informatics, the disaster impacts on both human health and biological factors can be reduced to a large extend. Using these computational technologies, the country’s economy can also get boosted up and due to increased disease-causing pathogens, which directly impact the human health system. In this research work, a different type of sugarcane disease is detected and classified because manual identification is difficult and time-consuming. So, the farmers couldn’t find a better solution, than on the whole, they go for stubble burning, which is an alarming issue both on human and environmental wellness. The burning of bagasse causes bagassois, an interstitial lung disease that affects the tissues present in the lung through the air sacs. So, this sugarcane disease detection needs to be done early to avoid various health and environmental issues. The proposed work consists of the detection of four types of sugarcane leaf disease directly from the field. The sequence of methods is capturing images with WSN nodes, pre-processing with image enhancement and noise removal (IENR), segmentation with Fuzzy membership function and clustering (FMFC), feature extraction using Gray Level Co-occurrence Matrix Vector (GLCMV) and classification using Support Vector Machine (SVM). With the help of the effective proposed method, the highest parameters like precision, accuracy, sensitivity, and specificity for sugarcane leaf disease have been obtained. Based on the successful implementation process, the accuracy stated for the four sugarcane diseases along with the execution time is given below as Smut disease (87.12, 1.01 sec), Rust disease (90.23, 1.02 sec), Grassy Shoot disease (95.34, 1.047 sec), Red Rot disease (95.51, 1.04 sec).

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A Hierarchical Structure for the Sharp Constants of Discrete Sobolev Inequalities on a Weighted Complete Graph

Cited by 2 publications

References 10 publications

On the Semigroup Whose Elements Are Subgraphs of a Complete Graph

On the Semigroup Whose Elements Are Subgraphs of a Complete Graph

A Novel Disease Detection and Classification Method Using Improved Fusion Random Weight Support Vector Machine

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