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	Author	Gielis, J.
	Title	Phi-bonacci in Ancient Greece			Type	A1 Journal article
	Year	2021	Publication	Symmetry : culture and science	Abbreviated Journal
	Volume	32	Issue	1	Pages	25-40
	Keywords	A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Fibonacci numbers are a very popular subject in mathematics, culture and science. A major open question is why the ancient Greeks overlooked this series, while they were very familiar with the golden mean and division in extreme and mean ratio. Furthermore, they could compute the square root of five to a high degree of precision using Theon 's ladder. This fact is based on tables built with side and diagonal numbers, and it is a simple and incredibly efficient method to compute roots of integers, though it is little known even now among most of the experts. The biologist D 'Arcy Wentworth Thompson showed that the same method could be used to generate the Fibonacci series using a simple shift in the computation of the tables. He argues, quite convincingly, that the ancient Greeks could not have overlooked this. Actually, the same method can be used to generate all possible regular phyllotaxis patterns.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000643822700002	Publication Date	2021-03-30
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	0865-4824	ISBN		Additional Links	UA library record; WoS full record
	Impact Factor		Times cited		Open Access	OpenAccess
	Notes				Approved	Most recent IF: NA
	Call Number	UA @ admin @ c:irua:178322			Serial	8376
Permanent link to this record



	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.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000309517500001	Publication Date	2012-09-30
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	1932-6203	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:102202			Serial	8711
Permanent link to this record



	Author	Caratelli, D.; Gielis, J.; Tavkhelidze, I.; Ricci, P.E.
	Title	Fourier-Hankel solution of the Robin problem for the Helmholtz equation in supershaped annular domains			Type	A1 Journal article
	Year	2013	Publication	Boundary value problems	Abbreviated Journal
	Volume		Issue		Pages	253
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	The Robin problem for the Helmholtz equation in normal-polar annuli is addressed by using a suitable Fourier-Hankel series technique. Attention is in particular focused on the wide class of domains whose boundaries are defined by the so-called superformula introduced by Gielis. A dedicated numerical procedure based on the computer algebra system Mathematica© is developed in order to validate the proposed methodology. In this way, highly accurate approximations of the solution, featuring properties similar to the classical ones, are obtained.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000340237600004	Publication Date	2013-11-22
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	1687-2762; 1687-2770	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:111558			Serial	7981
Permanent link to this record



	Author	Caratelli, D.; Gielis, J.; Tavkhelidze, I.; Ricci, P.E.
	Title	The Dirichlet problem for the Laplace equation in supershaped annuli			Type	A1 Journal article
	Year	2013	Publication	Boundary value problems	Abbreviated Journal
	Volume		Issue		Pages	113-10
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	The Dirichlet problem for the Laplace equation in normal-polar annuli is addressed by using a suitable Fourier-like technique. Attention is in particular focused on the wide class of domains whose boundaries are defined by the so-called superformula introduced by Gielis. A dedicated numerical procedure based on the computer algebra system Mathematica© is developed in order to validate the proposed methodology. In this way, highly accurate approximations of the solution, featuring properties similar to the classical ones, are obtained.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000325760900002&DestLinkType=CitingArticles&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7	Publication Date	2013-05-03
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	1687-2762; 1687-2770	ISBN		Additional Links	UA library record; WoS citing articles; WoS full record
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:108644			Serial	7812
Permanent link to this record



	Author	Mescia, L.; Bia, P.; Caratelli, D.; Chiapperino, M.A.; Stukach, O.; Gielis, J.
	Title	Electromagnetic mathematical modeling of 3D supershaped dielectric lens antennas			Type	A1 Journal article
	Year	2016	Publication	Mathematical problems in engineering: theory, methods, and applications	Abbreviated Journal
	Volume		Issue		Pages	8130160-10
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	The electromagnetic analysis of a special class of 3D dielectric lens antennas is described in detail. This new class of lens antennas has a geometrical shape defined by the three-dimensional extension of Gielis formula. The analytical description of the lens shape allows the development of a dedicated semianalytical hybrid modeling approach based on geometrical tube tracing and physical optic. In order to increase the accuracy of the model, the multiple reflections occurring within the lens are also taken into account.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000372246600001	Publication Date	2016-02-29
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	1024-123x; 1563-5147	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:131516			Serial	7866
Permanent link to this record



	Author	Shi, P.; Chen, L.; Quinn, B.K.; Yu, K.; Miao, Q.; Guo, X.; Lian, M.; Gielis, J.; Niklas, K.J.
	Title	A simple way to calculate the volume and surface area of avian eggs			Type	A1 Journal article
	Year	2023	Publication	Annals of the New York Academy of Sciences	Abbreviated Journal
	Volume	1524	Issue	1	Pages	118-131
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Egg geometry can be described using Preston's equation, which has seldom been used to calculate egg volume (V) and surface area (S) to explore S versus V scaling relationships. Herein, we provide an explicit re-expression of Preston's equation (designated as EPE) to calculate V and S, assuming that an egg is a solid of revolution. The side (longitudinal) profiles of 2221 eggs of six avian species were digitized, and the EPE was used to describe each egg profile. The volumes of 486 eggs from two avian species predicted by the EPE were compared with those obtained using water displacement in graduated cylinders. There was no significant difference in V using the two methods, which verified the utility of the EPE and the hypothesis that eggs are solids of revolution. The data also indicated that V is proportional to the product of egg length (L) and maximum width (W) squared. A 2/3-power scaling relationship between S and V for each species was observed, that is, S is proportional to (LW2)(2/3). These results can be extended to describe the shapes of the eggs of other species to study the evolution of avian (and perhaps reptilian) eggs.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000975679400001	Publication Date	2023-04-28
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	0077-8923; 1749-6632	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor	5.2	Times cited		Open Access	OpenAccess
	Notes				Approved	Most recent IF: 5.2; 2023 IF: 4.706
	Call Number	UA @ admin @ c:irua:196724			Serial	8827
Permanent link to this record



	Author	Shi, P.; Gielis, J.; Quinn, B.K.; Niklas, K.J.; Ratkowsky, D.A.; Schrader, J.; Ruan, H.; Wang, L.; Niinemets, Ü.; Niinennets, U.
	Title	‘biogeom’ : an R package for simulating and fitting natural shapes			Type	A1 Journal article
	Year	2022	Publication	Annals of the New York Academy of Sciences	Abbreviated Journal	Ann Ny Acad Sci
	Volume	1516	Issue	1	Pages	123-134
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Many natural objects exhibit radial or axial symmetry in a single plane. However, a universal tool for simulating and fitting the shapes of such objects is lacking. Herein, we present an R package called 'biogeom' that simulates and fits many shapes found in nature. The package incorporates novel universal parametric equations that generate the profiles of bird eggs, flowers, linear and lanceolate leaves, seeds, starfish, and tree-rings, and three growth-rate equations that generate the profiles of ovate leaves and the ontogenetic growth curves of animals and plants. 'biogeom' includes several empirical datasets comprising the boundary coordinates of bird eggs, fruits, lanceolate and ovate leaves, tree rings, seeds, and sea stars. The package can also be applied to other kinds of natural shapes similar to those in the datasets. In addition, the package includes sigmoid curves derived from the three growth-rate equations, which can be used to model animal and plant growth trajectories and predict the times associated with maximum growth rate. 'biogeom' can quantify the intra- or interspecific similarity of natural outlines, and it provides quantitative information of shape and ontogenetic modification of shape with important ecological and evolutionary implications for the growth and form of the living world.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000829772300001	Publication Date	2022-07-26
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	0077-8923; 1749-6632	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor	5.2	Times cited		Open Access	OpenAccess
	Notes				Approved	Most recent IF: 5.2
	Call Number	UA @ admin @ c:irua:189314			Serial	7131
Permanent link to this record



	Author	Shi, P.; Gielis, J.; Niklas, K.J.
	Title	Comparison of a universal (but complex) model for avian egg shape with a simpler model			Type	Editorial
	Year	2022	Publication	Annals of the New York Academy of Sciences	Abbreviated Journal	Ann Ny Acad Sci
	Volume	1514	Issue	1	Pages	34-42
	Keywords	Editorial; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Recently, a universal equation by Narushin, Romanov, and Griffin (hereafter, the NRGE) was proposed to describe the shape of avian eggs. While NRGE can simulate the shape of spherical, ellipsoidal, ovoidal, and pyriform eggs, its predictions were not tested against actual data. Here, we tested the validity of the NRGE by fitting actual data of egg shapes and compared this with the predictions of our simpler model for egg shape (hereafter, the SGE). The eggs of nine bird species were sampled for this purpose. NRGE was found to fit the empirical data of egg shape well, but it did not define the egg length axis (i.e., the rotational symmetric axis), which significantly affected the prediction accuracy. The egg length axis under the NRGE is defined as the maximum distance between two points on the scanned perimeter of the egg's shape. In contrast, the SGE fitted the empirical data better, and had a smaller root-mean-square error than the NRGE for each of the nine eggs. Based on its mathematical simplicity and goodness-of-fit, the SGE appears to be a reliable and useful model for describing egg shape.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000803394100001	Publication Date	2022-06-01
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	0077-8923; 1749-6632	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor	5.2	Times cited		Open Access	OpenAccess
	Notes				Approved	Most recent IF: 5.2
	Call Number	UA @ admin @ c:irua:188470			Serial	7139
Permanent link to this record



	Author	Nicolau, F.; Gielis, J.; Simeone, A.L.; Simoes Lopes, D.
	Title	Exploring and selecting supershapes in virtual reality with line, quad, and cube shaped widgets			Type	P1 Proceeding
	Year	2022	Publication		Abbreviated Journal
	Volume		Issue		Pages	21-28
	Keywords	P1 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Supershapes are used in Parametric Design to model, literally, thou-sands of natural and man-made shapes with a single 6 parameter formula. However, users are left to probe such a rich yet dense collection of supershapes using a set of independent 1-D sliders. Some of the formula’s parameters are non-linear in nature, making them particularly difficult to grasp with conventional 1-D sliders alone. VR appears as a promising setting for Parametric Design with supershapes since it empowers users with more natural visual inspection and shape browsing techniques, with multiple solutions being displayed at once and the possibility to design more interesting forms of slider interaction. In this work, we propose VR shape widgets that allow users to probe and select supershapes from a multitude of solutions. Our designs take leverage on thumbnails, mini-maps, haptic feedback and spatial interaction, while supporting 1-D, 2-D and 3-D supershape parameter spaces. We conducted a user study (N = 18) and found that VR shape widgets are effective, more efficient, and natural than conventional VR 1-D sliders while also usable for users without prior knowledge on supershapes. We also found that the proposed VR widgets provide a quick overview of the main supershapes, and users can easily reach the desired solution without having to perform fine-grain handle manipulations.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000828657500003	Publication Date	2022-04-20
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	978-1-6654-9617-9	ISBN		Additional Links	UA library record; WoS full record
	Impact Factor		Times cited		Open Access	OpenAccess
	Notes				Approved	Most recent IF: NA
	Call Number	UA @ admin @ c:irua:188471			Serial	7161
Permanent link to this record



	Author	de Jong van Coevorden, C.M.; Gielis, J.; Caratelli, D.
	Title	Application of Gielis transformation to the design of metamaterial structures			Type	A1 Journal article
	Year	2018	Publication	Journal of physics : conference series	Abbreviated Journal
	Volume	963	Issue		Pages	Unsp 012008
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	In this communication, the use of Gielis transformation to design more compact metamaterial unit cells is explored. For this purpose, transformed complementary split ring resonators and spiral resonators are coupled to micro-strip lines and theirbehaviour is investigated. The obtained results confirm that the useof the considered class of supershaped geometries enables the synthesis of very compact scalable microwave components.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000435022800008	Publication Date	2018-02-20
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	1742-6588; 1742-6596	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:150947			Serial	7475
Permanent link to this record



	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
	Volume		Issue		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
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	001033135400001	Publication Date	2023-07-25
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2381-8107; 2381-8115	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor	1.5	Times cited		Open Access	Not_Open_Access: Available from 24.01.2024
	Notes				Approved	Most recent IF: 1.5; 2023 IF: NA
	Call Number	UA @ admin @ c:irua:198001			Serial	8864
Permanent link to this record



	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
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	001024190300001	Publication Date	2023-07-12
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2381-8107; 2381-8115	ISBN		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



	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
	Volume	3	Issue		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.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos		Publication Date	2020-08-31
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2557-0250	ISBN		Additional Links	UA library record
	Impact Factor		Times cited		Open Access
	Notes				Approved	Most recent IF: NA
	Call Number	UA @ admin @ c:irua:174471			Serial	7992
Permanent link to this record



	Author	Bia, P.; Caratelli, D.; Mescia, L.; Gielis, J.
	Title	Analysis and synthesis of supershaped dielectric lens antennas			Type	A1 Journal article
	Year	2015	Publication	IET microwaves, antennas and propagation	Abbreviated Journal
	Volume	9	Issue	14	Pages	1497-1504
	Keywords	A1 Journal article; Engineering sciences. Technology; Mass communications; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	A novel class of supershaped dielectric lens antennas, whose geometry is described by the three-dimensional (3D) Gielis formula, is introduced and analysed. To this end, a hybrid modelling approach based on geometrical and physical optics is adopted in order to efficiently analyse the multiple wave reflections occurring within the lens and to evaluate the relevant impact on the radiation properties of the antenna under analysis. The developed modelling procedure has been validated by comparison with numerical results already reported in the literature and, afterwards, applied to the electromagnetic characterisation of Gielis dielectric lens antennas with shaped radiation pattern. Furthermore, a dedicated optimisation algorithm based on quantum particle swarm optimisation has been developed for the synthesis of 3D supershaped lens antennas with single feed, as well as with beamforming capabilities.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000364491200002	Publication Date	2015-08-14
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	1751-8725	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:128659			Serial	7441
Permanent link to this record



	Author	De Tommasi, E.; Gielis, J.; Rogato, A.
	Title	Diatom frustule morphogenesis and function : a multidisciplinary survey			Type	A1 Journal article
	Year	2017	Publication	Marine Genomics	Abbreviated Journal
	Volume	35	Issue		Pages	1-18
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Diatoms represent the major component of phytoplankton and are responsible for about 2025% of global primary production. Hundreds of millions of years of evolution led to tens of thousands of species differing in dimensions and morphologies. In particular, diatom porous silica cell walls, the frustules, are characterized by an extraordinary, species-specific diversity. It is of great interest, among the marine biologists and geneticists community, to shed light on the origin and evolutionary advantage of this variability of dimensions, geometries and pore distributions. In the present article the main reported data related to frustule morphogenesis and functionalities with contributions from fundamental biology, genetics, mathematics, geometry and physics are reviewed.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000412957700001	Publication Date	2017-07-20
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	1874-7787	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:144546			Serial	7807
Permanent link to this record



	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
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000498226800095	Publication Date	2019-09-19
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2351-9894; 2351-9894	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:162954			Serial	8497
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	Author	Dattoli, G.; Di Palma, E.; Gielis, J.; Licciardi, S.
	Title	Parabolic trigonometry			Type	A1 Journal article
	Year	2020	Publication	International journal of applied and computational mathematics	Abbreviated Journal
	Volume	6	Issue	2	Pages	37
	Keywords	A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos		Publication Date	2020-03-04
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2349-5103	ISBN		Additional Links	UA library record
	Impact Factor		Times cited		Open Access
	Notes				Approved	Most recent IF: NA
	Call Number	UA @ admin @ c:irua:167049			Serial	6578
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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
	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
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	001131698000001	Publication Date	2023-12-28
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	1007-662x; 1993-0607	ISBN		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
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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
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000695118600001	Publication Date	2021-09-12
	Series Editor		Series Title		Abbreviated Series Title
	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
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	Author	Tian, F.; Wang, Y.; Sandhu, H.S.; Gielis, J.; Shi, P.
	Title	Comparison of seed morphology of two ginkgo cultivars			Type	A1 Journal article
	Year	2020	Publication	Journal Of Forestry Research	Abbreviated Journal	J Forestry Res
	Volume	31	Issue	3	Pages	751-758
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Ginkgo biloba L. is a precious relic tree species with important economic value. Seeds, as a vital reproductive organ of plants, can be used to distinguish cultivars of the species. We chose 400 seeds from two cultivars of ginkgo (Fozhi and Maling; 200 seeds for each cultivar) as the study material and used the Gielis equation to fit the projected shape of these seeds. The coefficients of variation (CV) in root mean squared errors (RMSE) obtained from the fitted data were used to compare the level of inter-cultivar variations in seed shape. We also used the covariance analysis to compare the allometric relationships between seed weights and projected areas of these two cultivars. The Gielis equation fitted well the seed shapes of two ginkgo cultivars. The lower CV in RMSE of cultivar Fozhi than Maling indicated a less symmetrical seed shape in the latter than the former. The bootstrap percentile method showed that the seed shape differences between the two cultivars were significant. However, there was no significant difference in the exponents between the seed weights and the projected areas of these two cultivars. Overall, the significant differences in shapes between the seeds of two ginkgo cultivars were well explained by the Gielis equation; this model can be further extended to compare morphological differences in other ginkgo cultivars, and even for plant seeds or animal eggs that have similar oval shapes.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000529367600005	Publication Date	2018-07-28
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	1007-662x	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor	3	Times cited	3	Open Access
	Notes	; ;			Approved	Most recent IF: 3; 2020 IF: 0.774
	Call Number	UA @ admin @ c:irua:154987			Serial	6474
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	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
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	001069570200001	Publication Date	2023-08-26
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	0931-1890; 1432-2285	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor	2.3	Times cited		Open Access	Not_Open_Access: Available from 26.02.2024
	Notes				Approved	Most recent IF: 2.3; 2023 IF: 1.842
	Call Number	UA @ admin @ c:irua:199562			Serial	8874
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	Author	Shi, P.; Liu, M.; Ratkowsky, D.A.; Gielis, J.; Su, J.; Yu, X.; Wang, P.; Zhang, L.; Lin, Z.; Schrader, J.
	Title	Leaf area-length allometry and its implications in leaf shape evolution			Type	A1 Journal article
	Year	2019	Publication	Trees: structure and function	Abbreviated Journal
	Volume	33	Issue	4	Pages	1073-1085
	Keywords	A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	According to Thompson’s principle of similarity, the area of an object should be proportional to its length squared. However, leaf area–length data of some plants have been demonstrated not to follow the principle of similarity. We explore the reasons why the leaf area–length allometry deviates from the principle of similarity and examine whether there is a general model describing the relationship among leaf area, width and length. We sampled more than 11,800 leaves from six classes of woody and herbaceous plants and tested the leaf area–length allometry. We compared six mathematical models based on root-mean-square error as the measure of goodness-of-fit. The best supported model described a proportional relationship between leaf area and the product of leaf width and length (i.e., the Montgomery model). We found that the extent to which the leaf area–length allometry deviates from the principle of similarity depends upon the extent of variation of the ratio of leaf width to length. Estimates of the parameter of the Montgomery model ranged between 1/2, which corresponds to a triangular leaf with leaf length as its height and leaf width as its base, and π/4, which corresponds to an elliptical leaf with leaf length as its major axis and leaf width as its minor axis, for the six classes of plants. The narrow range in practice of the Montgomery parameter implies an evolutionary stability for the leaf area of large-leaved plants despite the fact that leaf shapes of these plants are rather different.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000475992600010	Publication Date	2019-04-04
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	0931-1890; 1432-2285	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:159970			Serial	8170
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	Author	Martínez-Dueñas, E.J.R.; de Jong van Coevorden, C.M.; Stukach, O.V.; Panokin, N.V.; Gielis, J.; Caratelli, D.
	Title	Electromagnetic modeling and design of a novel class of complementary split‐ring resonators			Type	A1 Journal article
	Year	2019	Publication	International journal of RF and microwave computer-aided engineering	Abbreviated Journal
	Volume	29	Issue	4	Pages	e21582
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	This research study reports the assessment of complementary split ring resonators based on Gielis transformation as basic elements for the design of high‐performance microwave components in printed technology. From the electromagnetic simulation of said structures, suitable equivalent circuit models are extracted and analyzed. Physical prototypes are fabricated and tested for design validation. The obtained results confirm that the adoption of supershaped geometries enables the synthesis of very compact scalable microwave filters.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000460308500020	Publication Date	2018-11-19
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	1096-4290	ISBN		Additional Links	UA library record; WoS full record
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:155021			Serial	7867
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	Author	Lin, S.; Zhang, L.; Reddy, G.V.P.; Hui, C.; Gielis, J.; Ding, Y.; Shi, P.
	Title	A geometrical model for testing bilateral symmetry of bamboo leaf with a simplified Gielis equation			Type	A1 Journal article
	Year	2016	Publication	Ecology and evolution	Abbreviated Journal
	Volume	6	Issue	19	Pages	6798-6806
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	The size and shape of plant leaves change with growth, and an accurate description of leaf shape is crucial for describing plant morphogenesis and development. Bilateral symmetry, which has been widely observed but poorly examined, occurs in both dicot and monocot leaves, including all nominated bamboo species (approximately 1,300 species), of which at least 500 are found in China. Although there are apparent differences in leaf size among bamboo species due to genetic and environmental profiles, bamboo leaves have bilateral symmetry with parallel venation and appear similar across species. Here, we investigate whether the shape of bamboo leaves can be accurately described by a simplified Gielis equation, which consists of only two parameters (leaf length and shape) and produces a perfect bilateral shape. To test the applicability of this equation and the occurrence of bilateral symmetry, we first measured the leaf length of 42 bamboo species, examining >500 leaves per species. We then scanned 30 leaves per species that had approximately the same length as the median leaf length for that species. The leaf-shape data from scanned profiles were fitted to the simplified Gielis equation. Results confirmed that the equation fits the leaf-shape data extremely well, with the coefficients of determination being 0.995 on average. We further demonstrated the bilateral symmetry of bamboo leaves, with a clearly defined leaf-shape parameter of all 42 bamboo species investigated ranging from 0.02 to 0.1. This results in a simple and reliable tool for precise determination of bamboo species, with applications in forestry, ecology, and taxonomy.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000385626100003	Publication Date	2016-09-02
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2045-7758	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:144547			Serial	7998
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	Author	Shi, P.-J.; Xu, Q.; Sandhu, H.S.; Gielis, J.; Ding, Y.-L.; Li, H.-R.; Dong, X.-B.
	Title	Comparison of dwarf bamboos (Indocalamus sp.) leaf parameters to determine relationship between spatial density of plants and total leaf area per plant			Type	A1 Journal article
	Year	2015	Publication	Ecology and evolution	Abbreviated Journal
	Volume	5	Issue	20	Pages	4578-4589
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	The relationship between spatial density and size of plants is an important topic in plant ecology. The self-thinning rule suggests a −3/2 power between average biomass and density or a −1/2 power between stand yield and density. However, the self-thinning rule based on total leaf area per plant and density of plants has been neglected presumably because of the lack of a method that can accurately estimate the total leaf area per plant. We aimed to find the relationship between spatial density of plants and total leaf area per plant. We also attempted to provide a novel model for accurately describing the leaf shape of bamboos. We proposed a simplified Gielis equation with only two parameters to describe the leaf shape of bamboos one model parameter represented the overall ratio of leaf width to leaf length. Using this method, we compared some leaf parameters (leaf shape, number of leaves per plant, ratio of total leaf weight to aboveground weight per plant, and total leaf area per plant) of four bamboo species of genus Indocalamus Nakai (I. pedalis (Keng) P.C. Keng, I. pumilus Q.H. Dai and C.F. Keng, I. barbatus McClure, and I. victorialis P.C. Keng). We also explored the possible correlation between spatial density and total leaf area per plant using log-linear regression. We found that the simplified Gielis equation fit the leaf shape of four bamboo species very well. Although all these four species belonged to the same genus, there were still significant differences in leaf shape. Significant differences also existed in leaf area per plant, ratio of leaf weight to aboveground weight per plant, and leaf length. In addition, we found that the total leaf area per plant decreased with increased spatial density. Therefore, we directly demonstrated the self-thinning rule to improve light interception.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000363731500008	Publication Date	2015-09-30
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2045-7758	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:128662			Serial	7691
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	Author	Gielis, J.; Brasili, S.
	Title	Proceedings of the 1st International Symposium on Square Bamboos and the Geometree (ISSBG 2022)			Type	ME3 Book as editor
	Year	2023	Publication		Abbreviated Journal
	Volume		Issue		Pages	xi, 175 p.
	Keywords	ME3 Book as editor; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos		Publication Date	2023-11-29
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN		ISBN	978-90-833839-0-3	Additional Links	UA library record
	Impact Factor		Times cited		Open Access
	Notes				Approved	Most recent IF: NA
	Call Number	UA @ admin @ c:irua:201049			Serial	9077
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	Author	Ricci, P.E.; Gielis, J.
	Title	From Pythagoras to Fourier and from geometry to nature			Type	MA3 Book as author
	Year	2022	Publication		Abbreviated Journal
	Volume		Issue		Pages	146 p.
	Keywords	MA3 Book as author; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos		Publication Date	2022-03-23
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN		ISBN	978-90-832323-0-0; 978-90-832323-1-7	Additional Links	UA library record
	Impact Factor		Times cited		Open Access	Not_Open_Access
	Notes				Approved	Most recent IF: NA
	Call Number	UA @ admin @ c:irua:186730			Serial	7166
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	Author	Tavkhelidze, I.; Cassisa, C.; Gielis, J.; Ricci, P.E.
	Title	About “bulky” links, generated by generalized Möbius Listing's bodies GML₃ⁿ			Type	A1 Journal article
	Year	2013	Publication	Matematica e applicazioni : atti della Accademia nazionale dei Lincei	Abbreviated Journal
	Volume	24	Issue	1	Pages	11-38
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	In the present paper we consider the “bulky knots'' and ”bulky links'', which appear after cutting a Generalized Möbius Listing's GMLn3 body (whose radial cross section is a plane 3-symmetric figure with three vertices) along different Generalized Möbius Listing's surfaces GMLn2 situated in it. This article is aimed to investigate the number and geometric structure of the independent objects appearing after such a cutting process of GMLn3 bodies. In most cases we are able to count the indices of the resulting mathematical objects according to the known tabulation for Knots and Links of small complexity.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000316567700002	Publication Date	2013-03-13
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	1120-6357	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:107174			Serial	7405
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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		Abbreviated Journal
	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
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000442076400008	Publication Date	2017-04-20
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN		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		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:144550			Serial	8318
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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		Abbreviated Journal
	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.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000442076400007	Publication Date	2017-04-20
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN		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		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:144551			Serial	7561
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