The Strong Slope Conjecture for twisted generalized Whitehead doubles

Kenneth Baker; Kimihiko Motegi; Toshie Takata

doi:10.4171/qt/242

Análise das feições de dissecação do relevo na folha topográfica de São Pedro do Sul - RS

Ciência e Natura ◽

10.5902/2179460x27229 ◽

2002 ◽

Vol 24 (24) ◽

pp. 101

Author(s):

Jair Antônio Raffaelli ◽

Mauro Kumpfer Werlang

Keyword(s):

Rio Grande ◽

Topographic Map ◽

Rio Grande Do Sul ◽

Central Depression ◽

Strong Slope

The investigation purpose was to observe, to localize, to analyse and to catalogue the different kinds of relieve, with its area and spacial distribution, based on the relieve dissection indexes of the São Pedro do Sul-RS topographic map, using the metodology first formulated by RADAMBRASIL PROJECT (1986) and after adapted by ROSS (1992 and 1996), to the relieve dissection study. The metodology was adapted to the survey scale (1:50000) and was shawed as efficient to these types of studies. It basically consider the interfluvial dimension and the fluvial channels carving degree. The study area is located on two distincts parts: the Central Depression of the Rio Grande do Sul and the edge Rio Grande do Sul Central Depression and the Brazilian Meridional Tableland edge. The first part has mainly areas with a plane os smooth wavy and the second part with strong slope and rugged. The areas observed with less dissection degree are situated mainly at the Central Depression part, whereas the sectors that shows a bitter dissection degree are located at the tableland edge. The results obtained shows that the area has predominantly medium to weak dissection indexes.

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Normal and Jones surfaces of knots

Journal of Knot Theory and Its Ramifications ◽

10.1142/s0218216518500396 ◽

2018 ◽

Vol 27 (06) ◽

pp. 1850039 ◽

Cited By ~ 1

Author(s):

Efstratia Kalfagianni ◽

Christine Ruey Shan Lee

Keyword(s):

Experimental Evidence ◽

Jones Polynomial ◽

Normal Surface ◽

Colored Jones Polynomial ◽

Open Questions ◽

Strong Slope ◽

Open Question

We describe a normal surface algorithm that decides whether a knot, with known degree of the colored Jones polynomial, satisfies the Strong Slope Conjecture. We also discuss possible simplifications of our algorithm and state related open questions. We establish a relation between the Jones period of a knot and the number of sheets of the surfaces that satisfy the Strong Slope Conjecture (Jones surfaces). We also present numerical and experimental evidence supporting a stronger such relation which we state as an open question.

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THE SPECTRUM OF THE 1-LAPLACE OPERATOR

Communications in Contemporary Mathematics ◽

10.1142/s0219199709003570 ◽

2009 ◽

Vol 11 (05) ◽

pp. 865-894 ◽

Cited By ~ 18

Author(s):

KUNG CHING CHANG

Keyword(s):

Variational Problem ◽

Critical Point ◽

Laplace Operator ◽

Strong Slope

The eigenfunction of the 1-Laplace operator is defined to be a critical point in the sense of the strong slope for a nonsmooth constraint variational problem. We completely write down all these eigenfunctions for the 1-Laplace operator on intervals.

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Apriori association rule and K-means clustering algorithms for interpretation of pre-event landslide areas and landslide inventory mapping

Open Geosciences ◽

10.1515/geo-2020-0299 ◽

2021 ◽

Vol 13 (1) ◽

pp. 1226-1244

Author(s):

Lutfiye Kusak ◽

Fatma Bunyan Unel ◽

Aydın Alptekin ◽

Mehmet Ozgur Celik ◽

Murat Yakar

Keyword(s):

Spatial Data ◽

Association Rule ◽

Performance Metrics ◽

Clustering Algorithms ◽

Spatial Data Mining ◽

Stream Line ◽

Apriori Algorithm ◽

Average Accuracy ◽

Aerial Vehicle ◽

Strong Slope

Abstract In this paper, an inventory of the landslide that occurred in Karahacılı at the end of 2019 was created and the pre-landslide conditions of the region were evaluated with traditional statistical and spatial data mining methods. The current orthophoto of the region was created by unmanned aerial vehicle (UAV). In this way, the landslide areas in the region were easily determined. According to this, it was determined that the areas affected by the landslides had an average slide of 26.56 m horizontally. The relationships among the topographic, hydrographic, and vegetative factors of the region were revealed using the Apriori algorithm. It was determined that the areas with low vegetation in the study area with 55% confidence were of a Strong Slope feature from the Apriori algorithm. In addition, the cluster distributions formed by these factors were determined by K-means. Among the five clusters created with K-means, it was determined that the study area was 38% in the southeast, had a Strong Slope, Low Vegetation, Non-Stream Line, and a slope less than 140 m. K-means results of the study were made with performance metrics. Average accuracy, recall, specificity, precision, and F-1 score were found as 0.77, 0.69, 0.84, and 0.73 respectively.

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