Poisson-Voronoi tessellations in three-dimensional hyperbolic spaces

2000 ◽  
Vol 32 (03) ◽  
pp. 648-662
Author(s):  
Yukinao Isokawa
Keyword(s):  
Surface Area ◽  
Three Dimensional ◽  
Hyperbolic Spaces ◽  
Euclidean Spaces ◽  
Voronoi Tessellations ◽  
Euclidean Case ◽  
Absolute Value ◽  
The Absolute ◽  
Explicit Expressions

We study Poisson-Voronoi tessellations in three-dimensional hyperbolic spaces, and give explicit expressions for mean surface area, mean perimeter length, and mean number of vertices of their cells. Furthermore we compare these mean characteristics with those for Poisson-Voronoi tessellations in three-dimensional Euclidean spaces. It is shown that, as the absolute value of the curvature of hyperbolic spaces increases from zero to infinity, these mean characteristics increase monotonically from those for the Euclidean case to infinity.

Poisson-Voronoi tessellations in three-dimensional hyperbolic spaces

2000 ◽  
Vol 32 (3) ◽  
pp. 648-662 ◽  
Author(s):  
Yukinao Isokawa
Keyword(s):  
Surface Area ◽  
Three Dimensional ◽  
Hyperbolic Spaces ◽  
Euclidean Spaces ◽  
Voronoi Tessellations ◽  
Euclidean Case ◽  
Absolute Value ◽  
The Absolute ◽  
Explicit Expressions

We study Poisson-Voronoi tessellations in three-dimensional hyperbolic spaces, and give explicit expressions for mean surface area, mean perimeter length, and mean number of vertices of their cells. Furthermore we compare these mean characteristics with those for Poisson-Voronoi tessellations in three-dimensional Euclidean spaces. It is shown that, as the absolute value of the curvature of hyperbolic spaces increases from zero to infinity, these mean characteristics increase monotonically from those for the Euclidean case to infinity.

scholarly journals MORE ON THEORETICAL MORPHOSPACE AND ITS RELATION TO FRESHWATER GOMPHONEMOID-CYMBELLOID DIATOM (BACILLARIOPHYTA) LINEAGES

2008 ◽  
Vol 16 (01) ◽  
pp. 119-137 ◽  
Author(s):  
JANICE L. PAPPAS
Keyword(s):  
Three Dimensional ◽  
Cladistic Analysis ◽  
Absolute Value ◽  
3D Space ◽  
Riemann Sum ◽  
Evolutionary Pathways ◽  
The Absolute

All forms from hypothesized gomphonemoid-cymbelloid lineages were constructed using three-dimensional (3D) parametric equations with the same boundary intervals for all forms. To construct a theoretical morphospace, the absolute value of the Riemann sum of differences between pairs of forms in terms of surfaces in the x-, y- and z-directions was determined and plotted in 3D space. In general, naviculoid forms occupied the lowest valued morphospace, and cymbelloid and gomphonemoid forms occupied different higher valued morphospaces. In particular, Anomoeoneis, Brebissonia and Placoneis were basal to cymbelloid and gomphonemoid forms. Brebissonia was found to be more closely related to gomphonemoid forms, and Placoneis was found to be more closely related to cymbelloid forms. Reimeria was found to be in lower valued morphospace than other cymbelloid forms, including Encyonema. Didymosphenia was found to be more closely associated with cymbelloid morphospace. Gomphocymbelloid forms were more closely associated with gomphonemoid forms. These results are complementary to the previous study and mostly supported Kociolek and Stoermer's cladistic analysis of gomphonemoid-cymbelloid lineages. In addition, some ideas concerning evolutionary pathways and ontogeny with respect to theoretical morphospaces were explored.

scholarly journals THE INVARIATOR DESIGN: AN UPDATE

2015 ◽  
Vol 34 (3) ◽  
pp. 147 ◽  
Author(s):  
Luis Manuel Cruz-Orive ◽  
Ximo Gual-Arnau
Keyword(s):  
Fixed Point ◽  
Surface Area ◽  
Test Line ◽  
Dimensional Space ◽  
Three Dimensional ◽  
A Posteriori ◽  
Euclidean Spaces ◽  
Oriented Plane ◽  
Three Dimensional Space ◽  
Area And Volume

The invariator is a method to generate a test line within an isotropically oriented plane through a fixed point, in such a way that the test line is effectively motion invariant in three dimensional space. Generalizations exist for non Euclidean spaces. The invariator design is convenient to estimate surface area and volume simultaneously. In recent years a number of new results have appeared which call for an updated survey. We include two new estimators, namely the a posteriori weighting estimator for surface area and volume, and the peak-and-valley formula for surface area.

scholarly journals THEORETICAL MORPHOSPACE AND ITS RELATION TO FRESHWATER GOMPHONEMOID–CYMBELLOID DIATOM (BACILLARIOPHYTA) LINEAGES

2005 ◽  
Vol 13 (04) ◽  
pp. 385-398 ◽  
Author(s):  
JANICE L. PAPPAS
Keyword(s):  
Three Dimensional ◽  
Absolute Value ◽  
Riemann Sum ◽  
The Absolute

A number of basic forms in the gomphonemoid–cymbelloid diatom lineages were generated using three-dimensional (3D) parametric equations. The same boundary intervals and differentials for the parameters were used for all forms. From this, the absolute value of the Riemann sum of differences was determined for each variable between pairs of forms. The results were coordinate triplets, and they were plotted in 3D morphospace. Naviculoid forms occupied lower-valued morphospace in contrast to gomphonemoid and cymbelloid morphospaces. However, gomphonemoid and cymbelloid forms occupied different morphospaces. Forms representing Brebissonia occupied morphospace at the base of gomphonemoid forms, but occupied high-valued morphospace with respect to cymbelloid forms. Forms representing Encyonema had lower-valued coordinates compared to other cymbelloid forms. These results support hypotheses of Kociolek and Stoermer that state that naviculoid forms (and in particular, Placoneis) are ancestral to gomphonemoid and cymbelloid forms, Brebissonia is basal to gomphonemoid (but not cymbelloid) forms, and Encyonema is more primitive than other cymbelloid forms. This approach was useful in inferring the relation between theoretical morphospace and hypothesized phylogenies in the gomphonemoid–cymbelloid diatom lineages.

Low-Degree Tibial Slope Angle Prevents Component Overhang by Enlarging the Lateral Plateau Surface Area in Total Knee Arthroplasty

2020 ◽  
Author(s):  
Mehmet Emin Simsek ◽  
Mustafa Akkaya ◽  
Safa Gursoy ◽  
Özgür Kaya ◽  
Murat Bozkurt
Keyword(s):  
Total Knee Arthroplasty ◽  
Surface Area ◽  
Knee Arthroplasty ◽  
Tibial Plateau ◽  
Slope Angle ◽  
Three Dimensional ◽  
Tibial Slope ◽  
Total Knee ◽  
Lateral Plateau ◽  
Gender Groups

AbstractThis study aimed to investigate whether overhang or underhang around the tibial component that occurs during the placement of tibial baseplates was affected by different slope angles of the tibial plateau and determine the changes in the lateral and medial plateau diameters while changing the slope angle in total knee arthroplasty. Three-dimensional tibia models were reconstructed using the computed tomography scans of 120 tibial dry bones. Tibial plateau slope cuts were performed with 9, 7, 5, 3, and 0 degrees of slope angles 2-mm below the subchondral bone in the deepest point of the medial plateau. Total, lateral, and medial tibial plateau areas and overhang/underhang rates were measured at each cut level. Digital implantations of the asymmetric and symmetric tibial baseplates were made on the tibial plateau with each slope angles. Following the implantations, the slope angle that prevents overhang or underhang at the bone border and the slope angle that has more surface area was identified. A significant increase was noted in the total tibial surface area, lateral plateau surface area, and lateral anteroposterior distance, whereas the slope cut angles were changed from 9 to 0 degrees in both gender groups. It was found that the amount of posteromedial underhang and posterolateral overhang increased in both the asymmetric and symmetric tibial baseplates when the slope angle was changed from 0 to 9 degrees. Although the mediolateral diameter did not change after the proximal tibia cuts at different slope angles, the surface area and anteroposterior diameter of the lateral plateau could change, leading to increased lateral plateau area. Although prosthesis designs are highly compatible with the tibial surface area, it should be noted that the component overhangs, especially beyond the posterolateral edge, it can be prevented by changing the slope cut angle in males and females.

3D reconstruction and calculation of surface area and volume of bell pepper

2007 ◽  
Vol 3 (1) ◽  
pp. 89-113
Author(s):  
Zoltán Gillay ◽  
László Fenyvesi
Keyword(s):  
3D Reconstruction ◽  
Surface Area ◽  
Three Dimensional ◽  
Reference Method ◽  
Bell Pepper ◽  
Three Dimensional Model ◽  
Acceptable Error ◽  
Volume Calculation ◽  
Bell Peppers ◽  
Area And Volume

There was a method developed that generates the three-dimensional model of not axisymmetric produce, based on an arbitrary number of photos. The model can serve as a basis for calculating the surface area and the volume of produce. The efficiency of the reconstruction was tested on bell peppers and artificial shapes. In case of bell peppers 3-dimensional reconstruction was created from 4 images rotated in 45° angle intervals. The surface area and the volume were estimated on the basis of the reconstructed area. Furthermore, a new and simple reference method was devised to give precise results for the surface area of bell pepper. The results show that this 3D reconstruction-based surface area and volume calculation method is suitable to determine the surface area and volume of definite bell peppers with an acceptable error.

scholarly journals Incentive Function of Audit Opinion for the Increase of Regional Operational Expenditure and Own-Source Revenues Through Sensitivity Analysis in Indonesia

2020 ◽  
Vol 11 (1) ◽  
pp. 20
Author(s):  
Muhammad Ikbal Abdullah ◽  
Andi Chairil Furqan ◽  
Nina Yusnita Yamin ◽  
Fahri Eka Oktora
Keyword(s):  
Sensitivity Analysis ◽  
Significant Influence ◽  
Provincial Government ◽  
Sensitivity Testing ◽  
Audit Opinion ◽  
Absolute Value ◽  
Operating Expenditure ◽  
The Absolute ◽  
Operational Expenditure

This study aims to analyze the sensitivity testing using measurements of realization of regional own-source revenues and operating expenditure and to analyze the extent of the effect of sample differences between Java and non-Java provinces by using samples outside of Java. By using sensitivity analysis, the results found the influence of audit opinion on the performance of the provincial government mediated by the realization of regional operating expenditure. More specifically, when using the measurement of the absolute value of the realization of regional operating expenditure it was found that there was a direct positive and significant influence of audit opinion on the performance of the Provincial Government. However, no significant effect of audit opinion was found on the realization value of regional operating expenditure and the effect of the realization value of regional operating expenditure on the performance of the Provincial Government. This result implies that an increase in audit opinion will be more likely to be used as an incentive for the Provincial Government to increase the realization of regional operating expenditure.

Die Bedeutung der Homogenisationsart und -intensität für die Größe und Konstanz der Sauerstoffaufnahme von Meerschweinchen-Leberhomogenat / The Influence of Mode and Intensity of Homogenization on the Absolute Value and Stability of Oxygen Consumption of Guinea Pig Liver Homogenates

1977 ◽  
Vol 32 (11-12) ◽  
pp. 908-912 ◽  
Author(s):  
H. J. Schmidt ◽  
U. Schaum ◽  
J. P. Pichotka
Keyword(s):  
Oxygen Uptake ◽  
Guinea Pig ◽  
Measuring Time ◽  
Pig Liver ◽  
Absolute Value ◽  
Modified Method ◽  
Simultaneous Measurements ◽  
Liver Homogenates ◽  
The Absolute ◽  
Guinea Pig Liver

Abstract The influence of five different methods of homogenisation (1. The method according to Potter and Elvehjem, 2. A modification of this method called Potter S, 3. The method of Dounce, 4. Homogenisation by hypersonic waves and 5. Coarce-grained homogenisation with the “Mikro-fleischwolf”) on the absolute value and stability of oxygen uptake of guinea pig liver homogenates has been investigated in simultaneous measurements. All homogenates showed a characteristic fall of oxygen uptake during measuring time (3 hours). The modified method according to Potter and Elvehjem called Potter S showed reproducible results without any influence by homogenisation intensity.

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