| Records |
Author  |
Gielis, J.; Caratelli, D.; de Jong van Coevorden, M.; Ricci, P.E. |
| Title |
The common descent of biological shape description and special functions |
Type |
H1 Book chapter |
| Year |
2018 |
Publication |
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Abbreviated Journal |
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| Volume |
230 |
Issue |
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Pages |
119-131
T2 - Differential and difference equations |
| Keywords |
H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
Gielis transformations, with their origin in botany, are used to define square waves and trigonometric functions of higher order. They are rewritten in terms of Chebyshev polynomials. The origin of both, a uniform descriptor and the origin of orthogonal polynomials, can be traced back to a letter of Guido Grandi to Leibniz in 1713 on the mathematical description of the shape of flowers. In this way geometrical description and analytical tools are seamlessly combined. |
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Wos |
000451375900010 |
Publication Date |
2018-05-08 |
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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 |
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ISBN |
978-3-319-75646-2; 2194-1009; 978-3-319-75647-9; 978-3-319-75646-2 |
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 |
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| Notes |
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Approved |
no |
| Call Number |
UA @ admin @ c:irua:150949 |
Serial |
7685 |
| Permanent link to this record |
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| Author |
Gielis, J.; Caratelli, D.; Fougerolle, Y.; Ricci, P.E.; Gerats, T. |
| Title |
A biogeometrical model for corolla fusion in Asclepiad flowers |
Type |
H1 Book chapter |
| Year |
2017 |
Publication |
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Abbreviated Journal |
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| Volume |
2 |
Issue |
|
Pages |
83-105
T2 - Modeling in mathematics : proceedings |
| Keywords |
H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
The molecular genetics of flower development have been studied extensively for more than two decades. Fusion of organs and the tendency to oligomery, important characteristics of flower evolution, so far have remained fairly elusive. We present a geometric model for shape and fusion in the corolla of Asclepiads. Examples demonstrate how fusion of petals creates stable centers, a prerequisite for the formation of complex pollination structures via congenital and postgenital fusion events, with the formation of de novo organs, specific to Asclepiads. The development of the corolla reduces to simple inequalities from the MATHS-BOX. The formation of stable centers and of bell and tubular shapes in flowers are immediate and logical consequences of the shape. Our model shows that any study on flowers, especially in evo-devo perspective should be performed within the wider framework of polymery and oligomery and of fusion and synorganization. |
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Wos |
000442076400007 |
Publication Date |
2017-04-20 |
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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 |
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ISBN |
978-94-6239-260-1; 978-94-6239-261-8; 2543-0300; 978-94-6239-260-1 |
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 |
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| Notes |
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Approved |
no |
| Call Number |
UA @ admin @ c:irua:144551 |
Serial |
7561 |
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| Author |
Gielis, J.; Caratelli, D.; Fougerolle, Y.; Ricci, P.E.; Tavkelidze, I.; Gerats, T. |
| Title |
Universal natural shapes : from unifying shape description to simple methods for shape analysis and boundary value problems |
Type |
A1 Journal article |
| Year |
2012 |
Publication |
PLoS ONE |
Abbreviated Journal |
|
| Volume |
7 |
Issue |
9 |
Pages |
e29324-11 |
| Keywords |
A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
Gielis curves and surfaces can describe a wide range of natural shapes and they have been used in various studies in biology and physics as descriptive tool. This has stimulated the generalization of widely used computational methods. Here we show that proper normalization of the Levenberg-Marquardt algorithm allows for efficient and robust reconstruction of Gielis curves, including self-intersecting and asymmetric curves, without increasing the overall complexity of the algorithm. Then, we show how complex curves of k-type can be constructed and how solutions to the Dirichlet problem for the Laplace equation on these complex domains can be derived using a semi-Fourier method. In all three methods, descriptive and computational power and efficiency is obtained in a surprisingly simple way. |
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Wos |
000309517500001 |
Publication Date |
2012-09-30 |
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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 |
1932-6203 |
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 |
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| Notes |
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Approved |
no |
| Call Number |
UA @ admin @ c:irua:102202 |
Serial |
8711 |
| Permanent link to this record |
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| Author |
Gielis, J.; Caratelli, D.; Shi, P.; Ricci, P.E. |
| Title |
A note on spirals and curvature |
Type |
A1 Journal article |
| Year |
2020 |
Publication |
Growth and form |
Abbreviated Journal |
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| Volume |
1 |
Issue |
1 |
Pages |
1-8 |
| Keywords |
A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
Starting from logarithmic, sinusoidal and power spirals, it is shown how these spirals are connected directly with Chebyshev polynomials, Lamé curves, with allometry and Antonelli-metrics in Finsler geometry. Curvature is a crucial concept in geometry both for closed curves and equiangular spirals, and allowed Dillen to give a general definition of spirals. Many natural shapes can be described as a combination of one of two basic shapes in nature—circle and spiral—with Gielis transformations. Using this idea, shape description itself is used to develop a novel approach to anisotropic curvature in nature. Various examples are discussed, including fusion in flowers and its connection to the recently described pseudo-Chebyshev functions. |
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Editor |
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Wos |
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Publication Date |
2020-02-23 |
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Series Title |
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Abbreviated Series Title |
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Series Issue |
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Edition |
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ISBN |
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Additional Links |
UA library record |
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Times cited |
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Open Access |
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| Notes |
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Approved |
Most recent IF: NA |
| Call Number |
UA @ admin @ c:irua:167061 |
Serial |
6569 |
| Permanent link to this record |
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| Author |
Gielis, J.; Caratelli, D.; Tavkelidze, I.; Fougerolle, Y.; Ricci, P.E.; Gerats, T. |
| Title |
Bulky knots and links generated by cutting generalized Mobius-Listing bodies and applications in the natural sciences |
Type |
H2 Book chapter |
| Year |
2013 |
Publication |
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Abbreviated Journal |
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| Volume |
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Issue |
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Pages |
167-183
T2 - Math Art Summit : Koninklijke Vlaamse |
| Keywords |
H2 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
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Thesis |
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Place of Publication |
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Editor |
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Wos |
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Publication Date |
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| 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 |
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ISBN |
978-90-6569-119-4 |
Additional Links |
UA library record |
| Impact Factor |
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Times cited |
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Open Access |
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| Notes |
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Approved |
no |
| Call Number |
UA @ admin @ c:irua:110955 |
Serial |
7569 |
| Permanent link to this record |
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| Author |
Gielis, J.; Caratelli, D.; Tavkhelidze, I. |
| Title |
The general case of cutting GML bodies : the geometrical solution |
Type |
H1 Book chapter |
| Year |
2020 |
Publication |
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Abbreviated Journal |
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| Volume |
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Issue |
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Pages |
397-411
T2 - Differential and difference equations |
| Keywords |
H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
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| Address |
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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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Wos |
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Publication Date |
2020-10-21 |
| 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 |
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ISBN |
978-3-030-56322-6 |
Additional Links |
UA library record |
| Impact Factor |
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Times cited |
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Open Access |
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| Notes |
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Approved |
Most recent IF: NA |
| Call Number |
UA @ admin @ c:irua:174477 |
Serial |
7991 |
| Permanent link to this record |
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| Author |
Gielis, J.; Ding, Y.; Shi, P. |
| Title |
Towards a geometrical theory of morphology and morphogenesis |
Type |
P3 Proceeding |
| Year |
2016 |
Publication |
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Abbreviated Journal |
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| Volume |
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Issue |
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Pages |
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| Keywords |
P3 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
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Place of Publication |
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Editor |
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Wos |
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Publication Date |
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Series Title |
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Abbreviated Series Title |
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Series Issue |
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Edition |
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ISBN |
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Additional Links |
UA library record |
| Impact Factor |
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Times cited |
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Open Access |
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| Notes |
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Approved |
no |
| Call Number |
UA @ admin @ c:irua:144548 |
Serial |
8677 |
| Permanent link to this record |
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| Author |
Gielis, J.; Grigolia, R. |
| Title |
Lamé curves and Rvachev's R-functions |
Type |
A3 Journal article |
| Year |
2022 |
Publication |
Sn – 1512-0066 |
Abbreviated Journal |
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| Volume |
37 |
Issue |
|
Pages |
1-4 |
| Keywords |
A3 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
Gielis transformations are a generalization of Lame curves. To combine domains, we can make use of the natural alliance between Lame's work and Rvachev's R-functions. A logical next step is the extension to n-valued logic dening dierent partitions. |
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Publication Date |
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Series Title |
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Abbreviated Series Title |
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Series Issue |
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Edition |
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ISBN |
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Additional Links |
UA library record |
| Impact Factor |
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Times cited |
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Open Access |
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| Notes |
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Approved |
Most recent IF: NA |
| Call Number |
UA @ admin @ c:irua:189316 |
Serial |
7178 |
| Permanent link to this record |
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| Author |
Gielis, J.; Natalini, P.; Ricci, P.E. |
| Title |
A note about generalized forms of the Gielis formula |
Type |
H1 Book chapter |
| Year |
2017 |
Publication |
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Abbreviated Journal |
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| Volume |
2 |
Issue |
|
Pages |
107-116
T2 - Modeling in mathematics : proceedings |
| Keywords |
H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
We generalize the Gielis Superformula by extending the R. Chacon approach, but avoiding the use of Jacobi elliptic functions. The obtained results are extended to the three-dimensional case. Several new shapes are derived by using the computer algebra system Mathematica(C). |
| Address |
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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 |
000442076400008 |
Publication Date |
2017-04-20 |
| 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 |
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ISBN |
978-94-6239-260-1; 978-94-6239-261-8; 2543-0300; 978-94-6239-260-1 |
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 |
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| Notes |
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Approved |
no |
| Call Number |
UA @ admin @ c:irua:144550 |
Serial |
8318 |
| Permanent link to this record |
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| Author |
Gielis, J.; Potters, G. |
| Title |
Proceedings of the 9th World Bamboo Congress, Antwerp 2012 |
Type |
P3 Proceeding |
| Year |
2012 |
Publication |
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Abbreviated Journal |
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| Volume |
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Issue |
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Pages |
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| Keywords |
P3 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
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Thesis |
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Place of Publication |
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Editor |
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Wos |
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Publication Date |
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| 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 |
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ISBN |
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Additional Links |
UA library record |
| Impact Factor |
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Times cited |
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Open Access |
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| Notes |
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Approved |
no |
| Call Number |
UA @ admin @ c:irua:97756 |
Serial |
8413 |
| Permanent link to this record |
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| Author |
Gielis, J.; Ricci, P.E.; Tavkhelidze, I. |
| Title |
The Möbius phenomenon in Generalized Möbius-Listing surfaces and bodies, and Arnold's Cat phenomenon |
Type |
A1 Journal article |
| Year |
2021 |
Publication |
Advanced Studies : Euro-Tbilisi Mathematical Journal |
Abbreviated Journal |
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| Volume |
14 |
Issue |
4 |
Pages |
17-35 |
| Keywords |
A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
Möbius bands have been studied extensively, mainly in topology. Generalized Möbius-Listing surfaces and bodies providing a full geometrical generalization, is a quite new field, motivated originally by solutions of boundary value problems. Analogous to cutting of the original Möbius band, for this class of surfaces and bodies, results have been obtained when cutting such bodies or surfaces. In general, cutting leads to interlinked and intertwined different surfaces or bodies, resulting in very complex systems. However, under certain conditions, the result of cutting can be a single surface or body, which reduces complexity considerably. Our research is motivated by this reduction of complexity. In the study of cutting Generalized Möbius-Listing bodies with polygons as cross section, the conditions under which a single body results, displaying the Möbius phenomenon of a one-sided body, have been determined for even and odd polygons. These conditions are based on congruence and rotational symmetry of the resulting cross sections after cutting, and on the knife cutting the origin. The Möbius phenomenon is important, since the process of cutting (or separation of zones in a GML body in general) then results in a single body, not in different, intertwined domains. In all previous works it was assumed that the cross section of the GML bodies is constant, but the main result of this paper is that it is sufficient that only one cross section on the whole GML structure meets the conditions for the Möbius phenomenon to occur. Several examples are given to illustrate this. |
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Place of Publication |
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Wos |
000774655100002 |
Publication Date |
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Series Title |
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Abbreviated Series Title |
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Series Issue |
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Edition |
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ISBN |
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Additional Links |
UA library record; WoS full record |
| 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:183081 |
Serial |
8258 |
| Permanent link to this record |
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| Author |
Gielis, J.; Ricci, P.E.; Tavkhelidze, I. |
| Title |
Modeling in mathematics : proceedings of the second Tbilisi-Salerno workshop on modeling in mathematics |
Type |
ME3 Book as editor |
| Year |
2017 |
Publication |
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Abbreviated Journal |
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| Volume |
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Issue |
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Pages |
185 p. |
| Keywords |
ME3 Book as editor; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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Thesis |
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Place of Publication |
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Editor |
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Wos |
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Publication Date |
2017-04-20 |
| 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 |
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ISBN |
978-94-6239-260-1; 978-94-6239-261-8 |
Additional Links |
UA library record |
| Impact Factor |
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Times cited |
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Open Access |
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| Notes |
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Approved |
no |
| Call Number |
UA @ admin @ c:irua:144553 |
Serial |
8263 |
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| Author |
Gielis, J.; Shi, P.; Beirinckx, B.; Caratelli, D.; Ricci, P.E. |
| Title |
Lamé-Gielis curves in biology and geometry |
Type |
P3 Proceeding |
| Year |
2021 |
Publication |
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Abbreviated Journal |
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Issue |
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Pages |
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| Keywords |
P3 Proceeding; Sustainable Energy, Air and Water Technology (DuEL) |
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Series Title |
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Abbreviated Series Title |
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Series Issue |
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Edition |
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ISBN |
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Additional Links |
UA library record |
| Impact Factor |
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Times cited |
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Open Access |
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| Notes |
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Approved |
Most recent IF: NA |
| Call Number |
UA @ admin @ c:irua:178828 |
Serial |
8145 |
| Permanent link to this record |
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| Author |
Gielis, J.; Shi, P.; Caratelli, D. |
| Title |
Universal equations : a fresh perspective |
Type |
A1 Journal article |
| Year |
2022 |
Publication |
Growth and Form |
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; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
A uniform description of natural shapes and phenomena is an important goal in science. Such description should check some basic principles, related to 1) the complexity of the model, 2) how well its fits real objects, phenomena and data, and 3) ia direct connection with optimization principles and the calculus of variations. In this article, we present nine principles, three for each group, and we compare some models with a claim to universality. It is also shown that Gielis Transformations and power laws have a common origin in conic sections |
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Additional Links |
UA library record |
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Times cited |
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Open Access |
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| Notes |
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Approved |
Most recent IF: NA |
| Call Number |
UA @ admin @ c:irua:189317 |
Serial |
7224 |
| Permanent link to this record |
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| Author |
Gielis, J.; Tavkelidze, I.; Ricci, P.E. |
| Title |
About “bulky” links, generated by generalized Möbius-Listing bodies |
Type |
H3 Book chapter |
| Year |
2011 |
Publication |
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Abbreviated Journal |
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| Volume |
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Issue |
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Pages |
115-128
T2 - Proceedings of the International Conf |
| Keywords |
H3 Book chapter; Sustainable Energy, Air and Water Technology (DuEL) |
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Place of Publication |
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Series Title |
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Abbreviated Series Title |
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Series Issue |
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Edition |
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ISBN |
978-9941-0-3727-6 |
Additional Links |
UA library record |
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Times cited |
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Open Access |
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| Notes |
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Approved |
no |
| Call Number |
UA @ admin @ c:irua:97753 |
Serial |
7403 |
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| Author |
Gielis, J.; Tavkhelidze, I. |
| Title |
The general case of cutting of Generalized Möbius-Listing surfaces and bodies |
Type |
A1 Journal article |
| Year |
2020 |
Publication |
4Open |
Abbreviated Journal |
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| Volume |
3 |
Issue |
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Pages |
7-48 |
| Keywords |
A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
The original motivation to study Generalized Möbius-Listing GML surfaces and bodies was the observation that the solution of boundary value problems greatly depends on the domains. Since around 2010 GML’s were merged with (continuous) Gielis Transformations, which provide a unifying description of geometrical shapes, as a generalization of the Pythagorean Theorem. The resulting geometrical objects can be used for modeling a wide range of natural shapes and phenomena. The cutting of GML bodies and surfaces, with the Möbius strip as one special case, is related to the field of knots and links, and classifications were obtained for GML with cross sectional symmetry of 2, 3, 4, 5 and 6. The general case of cutting GML bodies and surfaces, in particular the number of ways of cutting, could be solved by reducing the 3D problem to planar geometry. This also unveiled a range of connections with topology, combinatorics, elasticity theory and theoretical physics. |
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Place of Publication |
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Wos |
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Publication Date |
2020-08-31 |
| 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 |
2557-0250 |
ISBN |
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Additional Links |
UA library record |
| Impact Factor |
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Times cited |
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Open Access |
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| Notes |
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Approved |
Most recent IF: NA |
| Call Number |
UA @ admin @ c:irua:174471 |
Serial |
7992 |
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| Author |
Gielis, J.; Tavkhelidze, I. |
| Title |
The Mӧbius phenomenon in Generalized Mӧbius-Listing bodies with cross sections of odd and even polygons |
Type |
A3 Journal article |
| Year |
2020 |
Publication |
Sn – 1512-0066 |
Abbreviated Journal |
|
| Volume |
34 |
Issue |
|
Pages |
23-26 |
| Keywords |
A3 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
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| 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 |
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Publication Date |
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| 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 |
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ISBN |
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Additional Links |
UA library record |
| Impact Factor |
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Times cited |
|
Open Access |
|
| Notes |
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Approved |
Most recent IF: NA |
| Call Number |
UA @ admin @ c:irua:174474 |
Serial |
8257 |
| Permanent link to this record |
| |
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| |
| Author |
Gielis, J.; Tavkhelidze, I. |
| Title |
A note on Generalized Möbius-Listing Bodies |
Type |
P1 Proceeding |
| Year |
2023 |
Publication |
|
Abbreviated Journal |
|
| Volume |
|
Issue |
|
Pages |
31-39
T2 - Proceedings of the 1st International Sy |
| Keywords |
P1 Proceeding; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
Generalized Möbius-Listing surfaces and bodies generalize Möbius bands, and this research was motivated originally by solutions of boundary value problems. Analogous to cutting of the original Möbius band, for this class of surfaces and bodies, results have been obtained when cutting such bodies or surfaces. In general, cutting leads to interlinked and intertwined different surfaces or bodies, resulting in very complex systems. However, under certain conditions, the result of cutting can be a single surface or body, which reduces complexity considerably. These conditions are based on congruence and rotational symmetry of the resulting cross sections after cutting, and on the knife cutting the origin |
| 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 |
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Publication Date |
2023-11-29 |
| 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 |
|
Edition |
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| ISSN |
978-90-833839-0-3 |
ISBN |
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Additional Links |
UA library record |
| Impact Factor |
|
Times cited |
|
Open Access |
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| Notes |
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Approved |
Most recent IF: NA |
| Call Number |
UA @ admin @ c:irua:201047 |
Serial |
9063 |
| Permanent link to this record |
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| |
| Author |
Gielis, J.; Tavkhelidze, I.; Ricci, P.E. |
| Title |
About “bulky” links generated by generalized Möbius-Listing bodies GML2n |
Type |
A2 Journal article |
| Year |
2013 |
Publication |
Journal of mathematical sciences |
Abbreviated Journal |
|
| Volume |
193 |
Issue |
3 |
Pages |
449-460 |
| Keywords |
A2 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
In this paper, we consider the bulky knots and bulky links, which appear after cutting of a Generalized MöbiusListing GMLn2 body (with the radial cross section a convex plane 2-symmetric figure with two vertices) along a different Generalized MöbiusListing surfaces GMLn2 situated in it. The aim of this report is to investigate the number and geometric structure of the independent objects that appear after such a cutting process of GMLn2 bodies. In most cases we are able to count the indices of the resulting mathematical objects according to the known classification for the standard knots and links. |
| 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 |
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Publication Date |
2013-08-03 |
| 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 |
|
Edition |
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| ISSN |
1072-3374; 1573-8795 |
ISBN |
|
Additional Links |
UA library record |
| Impact Factor |
|
Times cited |
|
Open Access |
|
| Notes |
|
Approved |
no |
| Call Number |
UA @ admin @ c:irua:110953 |
Serial |
7404 |
| Permanent link to this record |
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| |
| Author |
Gielis, J.; Tavkhelidze, I.; Ricci, P.E. |
| Title |
Generalized Möbius-Listing bodies and the heart |
Type |
A3 Journal article |
| Year |
2023 |
Publication |
Sn – 2247-689x |
Abbreviated Journal |
|
| Volume |
13 |
Issue |
2 |
Pages |
58-70 |
| Keywords |
A3 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
Generalized Möbius-Listing surfaces and bodies generalize Möbius bands, and this research was motivated originally by solutions of boundary value problems. Analogous to cutting of the original Möbius band, for this class of surfaces and bodies, results have been obtained when cutting such bodies or surfaces. The results can be applied in a wide range of fields in the natural science, and here we propose how they can serve as a model for the heart and the circulatory system. |
| 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 |
http://rjm-cs.ro/2023v13i2_7.pdf#page=1 |
Publication Date |
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| 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 |
|
ISBN |
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Additional Links |
UA library record; http://rjm-cs.ro/2023v13i2_7.pdf#page=1 |
| Impact Factor |
|
Times cited |
|
Open Access |
|
| Notes |
|
Approved |
Most recent IF: NA |
| Call Number |
UA @ admin @ c:irua:200773 |
Serial |
9043 |
| Permanent link to this record |
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| |
| Author |
Gielis, J.; Verhulst, R.; Caratelli, D.; Ricci, P.E.; Tavkhelidze, I. |
| Title |
On means, polynomials and special functions |
Type |
A1 Journal article |
| Year |
2014 |
Publication |
The teaching of mathematics |
Abbreviated Journal |
|
| Volume |
17 |
Issue |
1 |
Pages |
1-20 |
| Keywords |
A1 Journal article; Educational sciences; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
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| 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 |
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Publication Date |
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| 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 |
|
Edition |
|
| ISSN |
1451-4966; 2406-1077 |
ISBN |
|
Additional Links |
UA library record |
| Impact Factor |
|
Times cited |
|
Open Access |
|
| Notes |
|
Approved |
no |
| Call Number |
UA @ admin @ c:irua:128660 |
Serial |
8327 |
| Permanent link to this record |
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| |
| Author |
Huang, L.; Ratkowsky, D.A.; Hui, C.; Gielis, J.; Lian, M.; Shi, P. |
| Title |
Inequality measure of leaf area distribution for a drought-tolerant landscape plant |
Type |
A1 Journal article |
| Year |
2023 |
Publication |
Plants |
Abbreviated Journal |
|
| Volume |
12 |
Issue |
17 |
Pages |
3143-11 |
| Keywords |
A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
Measuring the inequality of leaf area distribution per plant (ILAD) can provide a useful tool for quantifying the influences of intra- and interspecific competition, foraging behavior of herbivores, and environmental stress on plants’ above-ground architectural structures and survival strategies. Despite its importance, there has been limited research on this issue. This paper aims to fill this gap by comparing four inequality indices to measure ILAD, using indices for quantifying household income that are commonly used in economics, including the Gini index (which is based on the Lorenz curve), the coefficient of variation, the Theil index, and the mean log deviation index. We measured the area of all leaves for 240 individual plants of the species Shibataea chinensis Nakai, a drought-tolerant landscape plant found in southern China. A three-parameter performance equation was fitted to observations of the cumulative proportion of leaf area vs. the cumulative proportion of leaves per plant to calculate the Gini index for each individual specimen of S. chinensis. The performance equation was demonstrated to be valid in describing the rotated and right shifted Lorenz curve, given that >96% of root-mean-square error values were smaller than 0.004 for 240 individual plants. By examining the correlation between any of the six possible pairs of indices among the Gini index, the coefficient of variation, the Theil index, and the mean log deviation index, the data show that these indices are closely related and can be used interchangeably to quantify ILAD. |
| 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 |
001065193100001 |
Publication Date |
2023-08-31 |
| 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 |
|
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:199564 |
Serial |
8886 |
| Permanent link to this record |
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| Author |
Huang, W.; Li, Y.; Niklas, K.J.; Gielis, J.; Ding, Y.; Cao, L.; Shi, P. |
| Title |
A superellipse with deformation and its application in describing the cross-sectional shapes of a square bamboo |
Type |
A1 Journal article |
| Year |
2020 |
Publication |
Symmetry-Basel |
Abbreviated Journal |
Symmetry-Basel |
| Volume |
12 |
Issue |
12 |
Pages |
2073 |
| Keywords |
A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
Many cross-sectional shapes of plants have been found to approximate a superellipse rather than an ellipse. Square bamboos, belonging to the genus Chimonobambusa (Poaceae), are a group of plants with round-edged square-like culm cross sections. The initial application of superellipses to model these culm cross sections has focused on Chimonobambusa quadrangularis (Franceschi) Makino. However, there is a need for large scale empirical data to confirm this hypothesis. In this study, approximately 750 cross sections from 30 culms of C. utilis were scanned to obtain cross-sectional boundary coordinates. A superellipse exhibits a centrosymmetry, but in nature the cross sections of culms usually deviate from a standard circle, ellipse, or superellipse because of the influences of the environment and terrain, resulting in different bending and torsion forces during growth. Thus, more natural cross-sectional shapes appear to have the form of a deformed superellipse. The superellipse equation with a deformation parameter (SEDP) was used to fit boundary data. We find that the cross-sectional shapes (including outer and inner rings) of C. utilis can be well described by SEDP. The adjusted root-mean-square error of SEDP is smaller than that of the superellipse equation without a deformation parameter. A major finding is that the cross-sectional shapes can be divided into two types of superellipse curves: hyperellipses and hypoellipses, even for cross sections from the same culm. There are two proportional relationships between ring area and the product of ring length and width for both the outer and inner rings. The proportionality coefficients are significantly different, as a consequence of the two different superellipse types (i.e., hyperellipses and hypoellipses). The difference in the proportionality coefficients between hyperellipses and hypoellipses for outer rings is greater than that for inner rings. This work informs our understanding and quantifying of the longitudinal deformation of plant stems for future studies to assess the influences of the environment on stem development. This work is also informative for understanding the deviation of natural shapes from a strict rotational symmetry. |
| 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 |
000602546300001 |
Publication Date |
2020-12-15 |
| 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 |
|
Edition |
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| ISSN |
2073-8994 |
ISBN |
|
Additional Links |
UA library record; WoS full record; WoS citing articles |
| Impact Factor |
2.7 |
Times cited |
|
Open Access |
|
| Notes |
|
Approved |
Most recent IF: 2.7; 2020 IF: 1.457 |
| Call Number |
UA @ admin @ c:irua:174472 |
Serial |
8622 |
| Permanent link to this record |
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| |
| Author |
Huang, W.; Su, X.; Ratkowsky, D.A.; Niklas, K.J.; Gielis, J.; Shi, P. |
| Title |
The scaling relationships of leaf biomass vs. leaf surface area of 12 bamboo species |
Type |
A1 Journal article |
| Year |
2019 |
Publication |
Global ecology and conservation |
Abbreviated Journal |
|
| Volume |
20 |
Issue |
|
Pages |
e00793 |
| Keywords |
A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
There is convincing evidence for a scaling relationship between leaf dry weight (DW) and leaf surface area (A) for broad-leaved plants, and most estimates of the scaling exponent of DW vs. A are greater than unity. However, the scaling relationship of leaf fresh weight (FW) vs. A has been largely neglected. In the present study, we examined whether there is a statistically strong scaling relationship between FW and A and compared the goodness of fit to that of DW vs. A. Between 250 and 520 leaves from each of 12 bamboo species within 2 genera (Phyllostachys and Pleioblastus) were investigated. The reduced major axis regression protocols were used to determine scaling relationships. The fit for the linearized scaling relationship of FW vs. A was compared with that of DW vs. A using the coefficient of determination (i.e., r2). A stronger scaling relationship between FW and A than that between DW and A was observed for each of the 12 bamboo species investigated. Among the 12 species examined, five had significantly smaller scaling exponents of FW vs. A compared to those of DW vs. A; only one species had a scaling exponent of FW vs. A greater than that of DW vs. A. No significant difference between the two scaling exponents was observed for the remaining 6 species. Researchers conducting future studies might be well advised to consider the influence of leaf fresh weight when exploring the scaling relationships of foliar biomass allocation patterns. |
| 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 |
000498226800095 |
Publication Date |
2019-09-19 |
| 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 |
2351-9894; 2351-9894 |
ISBN |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
| Impact Factor |
|
Times cited |
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Open Access |
|
| Notes |
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Approved |
no |
| Call Number |
UA @ admin @ c:irua:162954 |
Serial |
8497 |
| Permanent link to this record |
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| Author |
Li, Q.; Niklas, K.J.J.; Niinemets, U.; Zhang, L.; Yu, K.; Gielis, J.; Gao, J.; Shi, P. |
| Title |
Stomatal shape described by a superellipse in four Magnoliaceae species |
Type |
A1 Journal article |
| Year |
2023 |
Publication |
Botany letters |
Abbreviated Journal |
|
| Volume |
|
Issue |
|
Pages |
1-9 |
| Keywords |
A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
Stomata are essential for the exchange of water vapour and atmospheric gases between vascular plants and their external environments. The stomatal geometries of many plants appear to be elliptical. However, prior studies have not tested whether this is a mathematical reality, particularly since many natural shapes that appear to be ellipses are superellipses with greater or smaller edge curvature than predicted for an ellipse. Compared with the ellipse equation, the superellipse equation includes an additional parameter that allows generation of a larger range of shapes. We randomly selected 240 stomata from each of four Magnoliaceae species to test whether the stomatal geometries are superellipses or ellipses. The stomatal geometries for most stomata (943/960) were found to be described better using the superellipse equation. The traditional “elliptical stomata hypothesis” resulted in an underestimation of the area of stomata, whereas the superellipse equation accurately predicted stomatal area. This finding has important implications for the estimation of stomatal area in studies looking at stomatal shape, geometry, and function. |
| 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 |
001024190300001 |
Publication Date |
2023-07-12 |
| Series Editor |
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Series Title |
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Abbreviated Series Title |
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| Series Volume |
|
Series Issue |
|
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 |
|
Open Access |
Not_Open_Access: Available from 12.01.2024 |
| Notes |
|
Approved |
Most recent IF: 1.5; 2023 IF: NA |
| Call Number |
UA @ admin @ c:irua:197847 |
Serial |
8935 |
| Permanent link to this record |
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| Author |
Li, Y.; Niklas, K.J.; Gielis, J.; Niinemets, Ü.; Schrader, J.; Wang, R.; Shi, P. |
| Title |
An elliptical blade is not a true ellipse, but a superellipse : evidence from two Michelia species |
Type |
A1 Journal article |
| Year |
2022 |
Publication |
Journal of forestry research |
Abbreviated Journal |
J Forestry Res |
| Volume |
33 |
Issue |
4 |
Pages |
1341-1348 |
| Keywords |
A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
The shape of leaf laminae exhibits considerable diversity and complexity that reflects adaptations to environmental factors such as ambient light and precipitation as well as phyletic legacy. Many leaves appear to be elliptical which may represent a ‘default’ developmental condition. However, whether their geometry truly conforms to the ellipse equation (EE), i.e., (x/a)2 + (y/b)2 = 1, remains conjectural. One alternative is described by the superellipse equation (SE), a generalized version of EE, i.e., |x/a|n +|y/b|n = 1. To test the efficacy of EE versus SE to describe leaf geometry, the leaf shapes of two Michelia species (i.e., M. cavaleriei var. platypetala, and M. maudiae), were investigated using 60 leaves from each species. Analysis shows that the majority of leaves (118 out of 120) had adjusted root-mean-square errors of < 0.05 for the nonlinear fitting of SE to leaf geometry, i.e., the mean absolute deviation from the polar point to leaf marginal points was smaller than 5% of the radius of a hypothesized circle with its area equaling leaf area. The estimates of n for the two species were ˂ 2, indicating that all sampled leaves conformed to SE and not to EE. This study confirms the existence of SE in leaves, linking this to its potential functional advantages, particularly the possible influence of leaf shape on hydraulic conductance. |
| 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 |
000695118600001 |
Publication Date |
2021-09-12 |
| Series Editor |
|
Series Title |
|
Abbreviated Series Title |
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| Series Volume |
|
Series Issue |
|
Edition |
|
| ISSN |
1007-662x; 1993-0607 |
ISBN |
|
Additional Links |
UA library record; WoS full record; WoS citing articles |
| Impact Factor |
3 |
Times cited |
|
Open Access |
OpenAccess |
| Notes |
|
Approved |
Most recent IF: 3 |
| Call Number |
UA @ admin @ c:irua:180967 |
Serial |
7152 |
| Permanent link to this record |
| |
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| |
| Author |
Li, Y.; Quinn, B.K.; Gielis, J.; Li, Y.; Shi, P. |
| Title |
Evidence that supertriangles exist in nature from the vertical projections of Koelreuteria paniculata fruit |
Type |
A1 Journal article |
| Year |
2022 |
Publication |
Symmetry |
Abbreviated Journal |
Symmetry-Basel |
| Volume |
14 |
Issue |
1 |
Pages |
23 |
| Keywords |
A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
Many natural radial symmetrical shapes (e.g., sea stars) follow the Gielis equation (GE) or its twin equation (TGE). A supertriangle (three triangles arranged around a central polygon) represents such a shape, but no study has tested whether natural shapes can be represented as/are supertriangles or whether the GE or TGE can describe their shape. We collected 100 pieces of Koelreuteria paniculata fruit, which have a supertriangular shape, extracted the boundary coordinates for their vertical projections, and then fitted them with the GE and TGE. The adjusted root mean square errors (RMSEadj) of the two equations were always less than 0.08, and >70% were less than 0.05. For 57/100 fruit projections, the GE had a lower RMSEadj than the TGE, although overall differences in the goodness of fit were non-significant. However, the TGE produces more symmetrical shapes than the GE as the two parameters controlling the extent of symmetry in it are approximately equal. This work demonstrates that natural supertriangles exist, validates the use of the GE and TGE to model their shapes, and suggests that different complex radially symmetrical shapes can be generated by the same equation, implying that different types of biological symmetry may result from the same biophysical mechanisms. |
| 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 |
000746030100001 |
Publication Date |
2021-12-27 |
| Series Editor |
|
Series Title |
|
Abbreviated Series Title |
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| Series Volume |
|
Series Issue |
|
Edition |
|
| ISSN |
2073-8994 |
ISBN |
|
Additional Links |
UA library record; WoS full record; WoS citing articles |
| Impact Factor |
2.7 |
Times cited |
|
Open Access |
OpenAccess |
| Notes |
|
Approved |
Most recent IF: 2.7 |
| Call Number |
UA @ admin @ c:irua:186453 |
Serial |
7158 |
| Permanent link to this record |
| |
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| |
| Author |
Li, Y.; Quinn, B.K.; Niinemets, Ü.; Schrader, J.; Gielis, J.; Liu, M.; Shi, P. |
| Title |
Ellipticalness index : a simple measure of the complexity of oval leaf shape |
Type |
A1 Journal article |
| Year |
2022 |
Publication |
Pakistan journal of botany : An official publication of pakistan botanical society |
Abbreviated Journal |
Pak J Bot |
| Volume |
54 |
Issue |
6 |
Pages |
1-8 |
| Keywords |
A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
Plants have diverse leaf shapes that have evolved to adapt to the environments they have experienced over their evolutionary history. Leaf shape and leaf size can greatly influence the growth rate, competitive ability, and productivity of plants. However, researchers have long struggled to decide how to properly quantify the complexity of leaf shape. Prior studies recommended the leaf roundness index (RI = 4πA/P2) or dissection index (DI = ), where P is leaf perimeter and A is leaf area. However, these two indices merely measure the extent of the deviation of leaf shape from a circle, which is usually invalid as leaves are seldom circular. In this study, we proposed a simple measure, named the ellipticalness index (EI), for quantifying the complexity of leaf shape based on the hypothesis that the shape of any oval leaf can be regarded as a variation from a standard ellipse. 2220 leaves from nine species of Magnoliaceae were sampled to check the validity of the EI. We also tested the validity of the Montgomery equation (ME), which assumes a proportional relationship between leaf area and the product of leaf length and width, because the EI actually comes from the proportionality coefficient of the ME. We also compared the ME with five other models of leaf area. The ME was found to be the best model for calculating leaf area based on consideration of the trade-off between model fit vs. complexity, which strongly supported the robustness of the EI for describing oval leaf shape. The new index can account for both leaf shape and size, and we conclude that it is a promising method for quantifying and comparing oval leaf shapes across species in future studies. |
| 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 |
000814279700028 |
Publication Date |
2022-05-23 |
| Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
| Series Volume |
|
Series Issue |
|
Edition |
|
| ISSN |
0556-3321 |
ISBN |
|
Additional Links |
UA library record; WoS full record; WoS citing articles |
| Impact Factor |
1.2 |
Times cited |
|
Open Access |
OpenAccess |
| Notes |
|
Approved |
Most recent IF: 1.2 |
| Call Number |
UA @ admin @ c:irua:188469 |
Serial |
7153 |
| Permanent link to this record |
| |
|
| |
| Author |
Lian, M.; Shi, P.; Zhang, L.; Yao, W.; Gielis, J.; Niklas, K.J. |
| Title |
A generalized performance equation and its application in measuring the Gini index of leaf size inequality |
Type |
A1 Journal article |
| Year |
2023 |
Publication |
Trees: structure and function |
Abbreviated Journal |
|
| Volume |
37 |
Issue |
|
Pages |
1555-1565 |
| Keywords |
A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
The goal of this study is to provide a rigorous tool to quantify the inequality of the leaf size distribution of an individual plant, thereby serving as a reference trait for quantifying plant adaptations to local environmental conditions. The tool to be presented and tested employs three components: (1) a performance equation (PE), which can produce flexible asymmetrical and symmetrical bell-shaped curves, (2) the Lorenz curve (i.e., the cumulative proportion of leaf size vs. the cumulative proportion of number of leaves), which is the basis for calculating, and (3) the Gini index, which measures the inequality of leaf size distribution. We sampled 12 individual plants of a dwarf bamboo and measured the area and dry mass of each leaf of each plant. We then developed a generalized performance equation (GPE) of which the PE is a special case and fitted the Lorenz curve to leaf size distribution using the GPE and PE. The GPE performed better than the PE in fitting the Lorenz curve. We compared the Gini index of leaf area distribution with that of leaf dry mass distribution and found that there was a significant difference between the two indices that might emerge from the scaling relationship between leaf dry mass and area. Nevertheless, there was a strong correlation between the two Gini indices (r2 = 0.9846). This study provides a promising tool based on the GPE for quantifying the inequality of leaf size distributions across individual plants and can be used to quantify plant adaptations to local environmental conditions. |
| Address |
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Thesis |
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Place of Publication |
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Editor |
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| Language |
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Wos |
001069570200001 |
Publication Date |
2023-08-26 |
| 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 |
0931-1890; 1432-2285 |
ISBN |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
| Impact Factor |
2.3 |
Times cited |
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Open Access |
Not_Open_Access: Available from 26.02.2024 |
| Notes |
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Approved |
Most recent IF: 2.3; 2023 IF: 1.842 |
| Call Number |
UA @ admin @ c:irua:199562 |
Serial |
8874 |
| Permanent link to this record |
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| Author |
Lin, S.; Shao, L.; Hui, C.; Song, Y.; Reddy, G.V.P.; Gielis, J.; Li, F.; Ding, Y.; Wei, Q.; Shi, P.; Reddy, G.V.P. |
| Title |
Why does not the leaf weight-area allometry of bamboos follow the 3/2-power law? |
Type |
A1 Journal article |
| Year |
2018 |
Publication |
Frontiers in plant science |
Abbreviated Journal |
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| Volume |
9 |
Issue |
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Pages |
583 |
| Keywords |
A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
The principle of similarity (Thompson, 1917) states that the weight of an organism follows the 3/2-power law of its surface area and is proportional to its volume on the condition that the density is constant. However, the allometric relationship between leaf weight and leaf area has been reported to greatly deviate from the 3/2-power law, with the irregularity of leaf density largely ignored for explaining this deviation. Here, we choose 11 bamboo species to explore the allometric relationships among leaf area (A), density (ρ), length (L), thickness (T), and weight (W). Because the edge of a bamboo leaf follows a simplified two-parameter Gielis equation, we could show that A ∝ L2 and that A ∝ T2. This then allowed us to derive the density-thickness allometry ρ ∝ Tb and the weight-area allometry W ∝ A(b+3)/2 ≈ A9/8, where b approximates −3/4. Leaf density is strikingly negatively associated with leaf thickness, and it is this inverse relationship that results in the weight-area allometry to deviate from the 3/2-power law. In conclusion, although plants are prone to invest less dry mass and thus produce thinner leaves when the leaf area is sufficient for photosynthesis, such leaf thinning needs to be accompanied with elevated density to ensure structural stability. The findings provide the insights on the evolutionary clue about the biomass investment and output of photosynthetic organs of plants. Because of the importance of leaves, plants could have enhanced the ratio of dry material per unit area of leaf in order to increase the efficiency of photosynthesis, relative the other parts of plants. Although the conclusion is drawn only based on 11 bamboo species, it should also be applicable to the other plants, especially considering previous works on the exponent of the weight-area relationship being less than 3/2 in plants. |
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Wos |
000431415100001 |
Publication Date |
2018-05-04 |
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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 |
1664-462x |
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 |
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| Notes |
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Approved |
no |
| Call Number |
UA @ admin @ c:irua:150948 |
Serial |
8758 |
| Permanent link to this record |
