| Records |
Author  |
Wang, L.; Ratkowsky, D.A.; Gielis, J.; Ricci, P.E.; Shi, P. |
| Title |
Effects of the numerical values of the parameters in the Gielis equation on its geometries |
Type |
A1 Journal article |
| Year |
2022 |
Publication |
Symmetry |
Abbreviated Journal |
Symmetry-Basel |
| Volume |
14 |
Issue |
12 |
Pages |
2475-12 |
| Keywords |
A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
The Lamé curve is an extension of an ellipse, the latter being a special case. Dr. Johan Gielis further extended the Lamé curve in the polar coordinate system by introducing additional parameters (n1, n2, n3; m): rφ=1Acosm4φn2+1Bsinm4φn3−1/n1, which can be applied to model natural geometries. Here, r is the polar radius corresponding to the polar angle φ; A, B, n1, n2 and n3 are parameters to be estimated; m is the positive real number that determines the number of angles of the Gielis curve. Most prior studies on the Gielis equation focused mainly on its applications. However, the Gielis equation can also generate a large number of shapes that are rotationally symmetric and axisymmetric when A = B and n2 = n3, interrelated with the parameter m, with the parameters n1 and n2 determining the shapes of the curves. In this paper, we prove the relationship between m and the rotational symmetry and axial symmetry of the Gielis curve from a theoretical point of view with the condition A = B, n2 = n3. We also set n1 and n2 to take negative real numbers rather than only taking positive real numbers, then classify the curves based on extremal properties of r(φ) at φ = 0, π/m when n1 and n2 are in different intervals, and analyze how n1, n2 precisely affect the shapes of Gielis curves. |
| Address |
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| Corporate Author |
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Thesis |
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| Publisher |
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Place of Publication |
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Editor |
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| Language |
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Wos |
000904525700001 |
Publication Date |
2022-11-23 |
| Series Editor |
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Series Title |
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Abbreviated Series Title |
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| Series Volume |
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Series Issue |
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Edition |
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| ISSN |
2073-8994 |
ISBN |
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Additional Links |
UA library record; WoS full record |
| Impact Factor |
2.7 |
Times cited |
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Open Access |
OpenAccess |
| Notes |
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Approved |
Most recent IF: 2.7 |
| Call Number |
UA @ admin @ c:irua:191860 |
Serial |
7301 |
| Permanent link to this record |
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| Author |
Wang, L.; Shi, P.; Chen, L.; Gielis, J.; Niklas, K.J. |
| Title |
Evidence that Chinese white olive (Canarium album(Lour.) DC.) fruits are solids of revolution |
Type |
A1 Journal article |
| Year |
2023 |
Publication |
Botany letters |
Abbreviated Journal |
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| Volume |
|
Issue |
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Pages |
1-7 |
| Keywords |
A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
Although many fruit geometries resemble a solid of revolution, this assumption has rarely been rigorously examined. To test this assumption, 574 fruits of Canarium album (Lour.) DC. which appear to have an ellipsoidal shape, were examined to determine the validity of a general avian-based egg-shape equation, referred to as the explicit Preston equation (EPE). The assumption that the C. album fruit geometry is a solid of revolution is tested by applying the volume formula for a solid of revolution using the EPE. The goodness of fit of the EPE was assessed using the adjusted root-mean-square error (RMSEadj). The relationship between the observed volume (Vobs) of each fruit, as measured by water displacement in a graduated cylinder, and the predicted volumes (Vpre) based on the EPE was also evaluated using the equation Vpre = slope * Vobs. All the RMSEadj values were smaller than 0.05, which demonstrated the validity of the EPE based on C. album fruit profiles. The 95% confidence interval of the slope of Vpre vs. Vobs included 1.0, indicating that there was no significant difference between Vpre and Vobs. The data confirm that C. album fruits are solids of revolution. This study provides a new approach for calculating the volume and surface area of geometrically similar fruits, which can be extended to other species with similar fruit geometries to further explore the ontogeny and evolution of angiosperm reproductive organs. |
| Address |
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| Corporate Author |
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Thesis |
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| Publisher |
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Place of Publication |
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Editor |
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| Language |
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Wos |
001033135400001 |
Publication Date |
2023-07-25 |
| Series Editor |
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Series Title |
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Abbreviated Series Title |
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| Series Volume |
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Series Issue |
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Edition |
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| ISSN |
2381-8107; 2381-8115 |
ISBN |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
| Impact Factor |
1.5 |
Times cited |
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Open Access |
Not_Open_Access: Available from 24.01.2024 |
| Notes |
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Approved |
Most recent IF: 1.5; 2023 IF: NA |
| Call Number |
UA @ admin @ c:irua:198001 |
Serial |
8864 |
| Permanent link to this record |
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| Author |
Yao, W.; Hui, C.; Wang, L.; Wang, J.; Gielis, J.; Shi, P. |
| Title |
Comparison of the performance of two polar equations in describing the geometries of elliptical fruits |
Type |
A1 Journal article |
| Year |
2024 |
Publication |
Botany letters |
Abbreviated Journal |
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| Volume |
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Issue |
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Pages |
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| Keywords |
A1 Journal article; Antwerp engineering, PhotoElectroChemistry & Sensing (A-PECS) |
| Abstract |
In nature, the two-dimensional (2D) profiles of fruits from many plants often resemble ellipses. However, it remains unclear whether these profiles strictly adhere to the ellipse equation, as many natural shapes resembling ellipses are actually better described as superellipses. The superellipse equation, which includes an additional parameter n compared to the ellipse equation, can generate a broader range of shapes, with the ellipse being just a special case of the superellipse. To investigate whether the 2D profiles of fruits are better described by ellipses or superellipses, we collected a total of 751 mature and undamaged fruits from 31 naturally growing plants of Cucumis melo L. var. agrestis Naud. Our analysis revealed that most adjusted root-mean-square errors (> 92% of the 751 fruits) for fitting the superellipse equation to the fruit profiles were consistently less than 0.0165. Furthermore, there were 638 of the 751 fruits (ca. 85%) with the 95% confidence intervals of the estimated parameter n in the superellipse equation not including 2. These findings suggest that the profiles of C. melo var. agrestis fruits align more closely with the superellipse equation than with the ellipse equation. This study provides evidence for the existence of the superellipse in fruit profiles, which has significant implications for studying fruit geometries and estimating fruit volumes using the solid of revolution formula. Furthermore, this discovery may contribute to a deeper understanding of the mechanisms driving the evolution of fruit shapes. |
| Address |
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| Corporate Author |
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Thesis |
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| Publisher |
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Place of Publication |
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Editor |
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| Language |
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Wos |
001219634500001 |
Publication Date |
2024-05-08 |
| Series Editor |
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Series Title |
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Abbreviated Series Title |
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| Series Volume |
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Series Issue |
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Edition |
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| ISSN |
2381-8107; 2381-8115 |
ISBN |
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Additional Links |
UA library record; WoS full record |
| Impact Factor |
1.5 |
Times cited |
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Open Access |
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| Notes |
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Approved |
Most recent IF: 1.5; 2024 IF: NA |
| Call Number |
UA @ admin @ c:irua:205955 |
Serial |
9140 |
| Permanent link to this record |
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| Author |
Yao, W.; Niinemets, Ü.; Yao, W.; Gielis, J.; Schrader, J.; Yu, K.; Shi, P. |
| Title |
Comparison of two simplified versions of the Gielis equation for describing the shape of bamboo leaves |
Type |
A1 Journal article |
| Year |
2022 |
Publication |
Plants |
Abbreviated Journal |
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| Volume |
11 |
Issue |
22 |
Pages |
3058-11 |
| Keywords |
A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
Bamboo is an important component in subtropical and tropical forest communities. The plant has characteristic long lanceolate leaves with parallel venation. Prior studies have shown that the leaf shapes of this plant group can be well described by a simplified version (referred to as SGE-1) of the Gielis equation, a polar coordinate equation extended from the superellipse equation. SGE-1 with only two model parameters is less complex than the original Gielis equation with six parameters. Previous studies have seldom tested whether other simplified versions of the Gielis equation are superior to SGE-1 in fitting empirical leaf shape data. In the present study, we compared a three-parameter Gielis equation (referred to as SGE-2) with the two-parameter SGE-1 using the leaf boundary coordinate data of six bamboo species within the same genus that have representative long lanceolate leaves, with >300 leaves for each species. We sampled 2000 data points at approximately equidistant locations on the boundary of each leaf, and estimated the parameters for the two models. The root–mean–square error (RMSE) between the observed and predicted radii from the polar point to data points on the boundary of each leaf was used as a measure of the model goodness of fit, and the mean percent error between the RMSEs from fitting SGE-1 and SGE-2 was used to examine whether the introduction of an additional parameter in SGE-1 remarkably improves the model’s fitting. We found that the RMSE value of SGE-2 was always smaller than that of SGE-1. The mean percent errors among the two models ranged from 7.5% to 20% across the six species. These results indicate that SGE-2 is superior to SGE-1 and should be used in fitting leaf shapes. We argue that the results of the current study can be potentially extended to other lanceolate leaf shapes. |
| Address |
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| Corporate Author |
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Thesis |
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| Publisher |
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Place of Publication |
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Editor |
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| Language |
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Wos |
000887783400001 |
Publication Date |
2022-11-14 |
| Series Editor |
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Series Title |
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Abbreviated Series Title |
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| Series Volume |
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Series Issue |
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Edition |
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| ISSN |
2223-7747 |
ISBN |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
| Impact Factor |
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Times cited |
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Open Access |
OpenAccess |
| Notes |
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Approved |
Most recent IF: NA |
| Call Number |
UA @ admin @ c:irua:191859 |
Serial |
7289 |
| Permanent link to this record |
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| Author |
Zhang, L.; Quinn, B.K.; Hui, C.; Lian, M.; Gielis, J.; Gao, J.; Shi, P. |
| Title |
New indices to balance α-diversity against tree size inequality |
Type |
A1 Journal article |
| Year |
2024 |
Publication |
Journal of forestry research |
Abbreviated Journal |
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| Volume |
35 |
Issue |
1 |
Pages |
31-39 |
| Keywords |
A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
The number and composition of species in a community can be quantified with alpha-diversity indices, including species richness (R), Simpson's index (D), and the Shannon-Wiener index (HGREEK TONOS). In forest communities, there are large variations in tree size among species and individuals of the same species, which result in differences in ecological processes and ecosystem functions. However, tree size inequality (TSI) has been largely neglected in studies using the available diversity indices. The TSI in the diameter at breast height (DBH) data for each of 999 20 m x 20 m forest census quadrats was quantified using the Gini index (GI), a measure of the inequality of size distribution. The generalized performance equation was used to describe the rotated and right-shifted Lorenz curve of the cumulative proportion of DBH and the cumulative proportion of number of trees per quadrat. We also examined the relationships of alpha-diversity indices with the GI using correlation tests. The generalized performance equation effectively described the rotated and right-shifted Lorenz curve of DBH distributions, with most root-mean-square errors (990 out of 999 quadrats) being < 0.0030. There were significant positive correlations between each of three alpha-diversity indices (i.e., R, D, and H') and the GI. Nevertheless, the total abundance of trees in each quadrat did not significantly influence the GI. This means that the TSI increased with increasing species diversity. Thus, two new indices are proposed that can balance alpha-diversity against the extent of TSI in the community: (1 – GI) x D, and (1 – GI) x H'. These new indices were significantly correlated with the original D and HGREEK TONOS, and did not increase the extent of variation within each group of indices. This study presents a useful tool for quantifying both species diversity and the variation in tree sizes in forest communities, especially in the face of cumulative species loss under global climate change. |
| Address |
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| Corporate Author |
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Thesis |
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| Publisher |
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Place of Publication |
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Editor |
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| Language |
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Wos |
001131698000001 |
Publication Date |
2023-12-28 |
| Series Editor |
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Series Title |
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Abbreviated Series Title |
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| Series Volume |
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Series Issue |
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Edition |
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| ISSN |
1007-662x; 1993-0607 |
ISBN |
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Additional Links |
UA library record; WoS full record |
| Impact Factor |
3 |
Times cited |
|
Open Access |
Not_Open_Access |
| Notes |
|
Approved |
Most recent IF: 3; 2024 IF: 0.774 |
| Call Number |
UA @ admin @ c:irua:201972 |
Serial |
9061 |
| Permanent link to this record |
