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	Author	Tavkhelidze, I.; Caratelli, D.; Gielis, J.; Ricci, P.E.; Rogava, M.; Transirico, M.
	Title	On a geometric model of bodies with “complex” configuration and some movements			Type	H1 Book chapter
	Year	2017	Publication		Abbreviated Journal
	Volume	2	Issue		Pages	129-158 T2 - Modeling in mathematics : proceedings
	Keywords	H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Aim of this chapter is analytical representation of one wide class of geometric figures (lines, surfaces and bodies) and their complicated displacements. The accurate estimation of physical characteristics (such as volume, surface area, length, or other specific parameters) relevant to human organs is of fundamental importance in medicine. One central idea of this article is, in this respect, to provide a general methodology for the evaluation, as a function of time, of the volume and center of gravity featured by moving of one class of bodies used of describe different human organs.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000442076400010	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:144552			Serial	8326
Permanent link to this record



	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
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos		Publication Date
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		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



	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	Fougerolle, Y.; Truchetet, F.; Gielis, J.
	Title	Potential fields of self intersecting Gielis curves for modeling and generalized blending techniques			Type	P1 Proceeding
	Year	2017	Publication	Modeling In Mathematics	Abbreviated Journal
	Volume	2	Issue		Pages	67-81 T2 -
	Keywords	P1 Proceeding; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	The definition of Gielis curves allows for the representation of self intersecting curves. The analysis and the understanding of these representations is of major interest for the analytical representation of sectors bounded by multiple subsets of curves (or surfaces), as this occurs for instance in many natural objects. We present a construction scheme based on R-functions to build signed potential fields with guaranteed differential properties, such that their zero-set corresponds to the outer, the inner envelop, or combined subparts of the curve. Our framework is designed to allow for the definition of composed domains built upon Boolean operations between several distinct objects or some subpart of self-intersecting curves, but also provides a representation for soft blending techniques in which the traditional Boolean union and intersection become special cases of linear combinations between the objects' potential fields. Finally, by establishing a connection between R-functions and Lame curves, we can extend the domain of the p parameter within the R-p-function from the set of the even positive numbers to the real numbers strictly greater than 1, i.e. p is an element of]1, +infinity[.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000442076400006	Publication Date	2017-04-20
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	978-94-6239-261-8; 978-94-6239-260-1; 978-94-6239-260-1	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:153801			Serial	8395
Permanent link to this record



	Author	Gielis, J.; Potters, G.
	Title	Proceedings of the 9th World Bamboo Congress, Antwerp 2012			Type	P3 Proceeding
	Year	2012	Publication		Abbreviated Journal
	Volume		Issue		Pages
	Keywords	P3 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos		Publication Date
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN		ISBN		Additional Links	UA library record
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:97756			Serial	8413
Permanent link to this record



	Author	Tavkhelidze, I.; Gielis, J.
	Title	The process of cutting GML_mⁿ bodies with d_m-knives			Type	A3 Journal article
	Year	2018	Publication	Sn – 1512-0066	Abbreviated Journal
	Volume	32	Issue		Pages	67-70
	Keywords	A3 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos		Publication Date
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN		ISBN		Additional Links	UA library record
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:159971			Serial	8417
Permanent link to this record



	Author	Shi, P.; Liu, M.; Yu, X.; Gielis, J.; Ratkowsky, D.A.
	Title	Proportional relationship between leaf area and the product of leaf length and width of four types of special leaf shapes			Type	A1 Journal article
	Year	2019	Publication	Forests (19994907)	Abbreviated Journal
	Volume	10	Issue	2	Pages	178
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	The leaf area, as an important leaf functional trait, is thought to be related to leaf length and width. Our recent study showed that the Montgomery equation, which assumes that leaf area is proportional to the product of leaf length and width, applied to different leaf shapes, and the coefficient of proportionality (namely the Montgomery parameter) range from 1/2 to π/4. However, no relevant geometrical evidence has previously been provided to support the above findings. Here, four types of representative leaf shapes (the elliptical, sectorial, linear, and triangular shapes) were studied. We derived the range of the estimate of the Montgomery parameter for every type. For the elliptical and triangular leaf shapes, the estimates are π/4 and 1/2, respectively; for the linear leaf shape, especially for the plants of Poaceae that can be described by the simplified Gielis equation, the estimate ranges from 0.6795 to π/4; for the sectorial leaf shape, the estimate ranges from 1/2 to π/4. The estimates based on the observations of actual leaves support the above theoretical results. The results obtained here show that the coefficient of proportionality of leaf area versus the product of leaf length and width only varies in a small range, maintaining the allometric relationship for leaf area and thereby suggesting that the proportional relationship between leaf area and the product of leaf length and width broadly remains stable during leaf evolution.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000460744000102	Publication Date	2019-02-20
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	1999-4907	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:157200			Serial	8427
Permanent link to this record



	Author	Mescia, L.; Chiapperino, M.A.; Bia, P.; Lamacchia, C.M.; Gielis, J.; Caratelli, D.
	Title	Relevance of the cell membrane modelling for accurate analysis of the pulsed electric field-induced electroporation			Type	P1 Proceeding
	Year	2019	Publication	Progress in Electromagnetic Research Symposium (PIERS) T2 – 2019 PhotonIcs & Electromagnetics Research Symposium – Spring (PIERS-Spring), 17-20 June 2019, Rome, Italy	Abbreviated Journal
	Volume		Issue		Pages	2985-2991
	Keywords	P1 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	In this work, a nonlinear dispersive multiphysic model based on Maxwell and asymptotic Smoluchowsky equations has been developed to analyze the electroporation phenomenon induced by pulsed electric field on biological cells. The irregular plasma membrane geometry has been modeled by incorporating in the numerical algorithm the Gielis superformula as well as the dielectric dispersion of the plasma membrane has been modeled using the multi-relaxation Debye-based relationship. The study has been carried out with the aim to compare our model implementing a thin plasma membrane with the simplified model in which the plasma membrane is modeled as a distributed impedance boundary condition. The numerical analysis has been performed exposing the cell to external electric pulses having rectangular shapes. By an inspection of the obtained results, significant differences can be highlighted between the two models confirming the need to incorporate the effective thin membrane into the numerical algorithm to well predict the cell response to the pulsed electric fields in terms of transmembrane voltages and pore densities, especially when the cell is exposed to external nanosecond pulses.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000550769302158	Publication Date	2020-03-03
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	978-1-72813-404-8; 978-1-72813-403-1	ISBN		Additional Links	UA library record; WoS full record
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:169171			Serial	8469
Permanent link to this record



	Author	Fougerolle, Y.D.; Truchetet, F.; Demonceaux, C.; Gielis, J.
	Title	A robust evolutionary algorithm for the recovery of rational Gielis curves			Type	A1 Journal article
	Year	2013	Publication	Pattern recognition	Abbreviated Journal
	Volume	46	Issue	8	Pages	2078-2091
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Gielis curves (GC) can represent a wide range of shapes and patterns ranging from star shapes to symmetric and asymmetric polygons, and even self intersecting curves. Such patterns appear in natural objects or phenomena, such as flowers, crystals, pollen structures, animals, or even wave propagation. Gielis curves and surfaces are an extension of Lamé curves and surfaces (superquadrics) which have benefited in the last two decades of extensive researches to retrieve their parameters from various data types, such as range images, 2D and 3D point clouds, etc. Unfortunately, the most efficient techniques for superquadrics recovery, based on deterministic methods, cannot directly be adapted to Gielis curves. Indeed, the different nature of their parameters forbids the use of a unified gradient descent approach, which requires initial pre-processings, such as the symmetry detection, and a reliable pose and scale estimation. Furthermore, even the most recent algorithms in the literature remain extremely sensitive to initialization and often fall into local minima in the presence of large missing data. We present a simple evolutionary algorithm which overcomes most of these issues and unifies all of the required operations into a single though efficient approach. The key ideas in this paper are the replacement of the potential fields used for the cost function (closed form) by the shortest Euclidean distance (SED, iterative approach), the construction of cost functions which minimize the shortest distance as well as the curve length using R-functions, and slight modifications of the evolutionary operators. We show that the proposed cost function based on SED and R-function offers the best compromise in terms of accuracy, robustness to noise, and missing data.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000317944800002	Publication Date	2013-01-29
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	0031-3203	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:107181			Serial	8485
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
Permanent link to this record



	Author	Caratelli, D.; Gielis, J.; Ricci, P.E.; Tavkhelidze, I.
	Title	Some properties of “bulky” links, generated by Generalized Möbius Listing's bodies GML₄ⁿ			Type	A2 Journal article
	Year	2016	Publication	Journal of mathematical sciences	Abbreviated Journal
	Volume	216	Issue	4	Pages	509-518
	Keywords	A2 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 that appear after cutting of generalized MöbiusListing GML 4 n bodies (with corresponding radial cross sections square) along different generalized MöbiusListing surfaces GML 2 n situated in it. The aim of this article is to examine the number and geometric structure of independent objects that appear after such a cutting process of GML 4 n 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		Publication Date	2016-06-10
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	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:133948			Serial	8554
Permanent link to this record



	Author	Caratelli, D.; Gielis, J.; Ricci, P.E.; Tavkhelidze, I.
	Title	Some properties of “bulky” links, generated by Generalized Möbius Listing's bodies GML₄ⁿ			Type	P3 Proceeding
	Year	2013	Publication		Abbreviated Journal
	Volume		Issue		Pages
	Keywords	P3 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos		Publication Date
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN		ISBN		Additional Links	UA library record
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:108672			Serial	8555
Permanent link to this record



	Author	Caratelli, D.; Gielis, J.; Tavkhelidze, I.; Ricci, P.E.
	Title	Spherical harmonic solution of the Robin problem for the Helmholtz equation in a supershaped shell			Type	A1 Journal article
	Year	2013	Publication	Applied mathematics	Abbreviated Journal
	Volume	4	Issue	1a	Pages	263-270
	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 shells is addressed by using a suitable spherical harmonic expansion technique. Attention is in particular focused on the wide class of domains whose boundaries are defined by a generalized version of 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		Publication Date	2013-01-30
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2152-7385	ISBN		Additional Links	UA library record
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:107177			Serial	8576
Permanent link to this record



	Author	Tavkhelidze, I.; Gielis, J.
	Title	Structure of the dm knives and process of cutting of GML(man) or GRT(man) bodies			Type	A3 Journal article
	Year	2019	Publication	Sn – 1512-0066	Abbreviated Journal
	Volume	33	Issue		Pages
	Keywords	A3 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos		Publication Date
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN		ISBN		Additional Links	UA library record
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:164897			Serial	8588
Permanent link to this record



	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
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000602546300001	Publication Date	2020-12-15
	Series Editor		Series Title		Abbreviated Series Title
	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
	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



	Author	Gielis, J.
	Title	Temperate bamboos in ornamental horticulture: differentiators and spillover effects into the 21st century			Type	H3 Book chapter
	Year	2012	Publication		Abbreviated Journal
	Volume		Issue		Pages	603-623 T2 - Proceedings of the 9th World Bamboo C
	Keywords	H3 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos		Publication Date
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN		ISBN		Additional Links	UA library record
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:97755			Serial	8644
Permanent link to this record



	Author	Gielis, J.; Brasili, S.
	Title	The apeirogon and dual numbers			Type	A1 Journal article
	Year	2021	Publication	Symmetry : culture and science	Abbreviated Journal
	Volume	32	Issue	2	Pages	157-160
	Keywords	A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	The richness, diversity, connection, depth and pleasure of studying symmetry continue to open doors. Here we report a connection between Coxeter's Apeirogon and the geometry associated with pictorial space, parabolic rotation and dual numbers.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000670122100011	Publication Date	2021-07-02
	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	Not_Open_Access
	Notes				Approved	Most recent IF: NA
	Call Number	UA @ admin @ c:irua:179759			Serial	8652
Permanent link to this record



	Author	Caratelli, D.; Gielis, J.; Natalini, P.; Ricci, P.E.; Tavkhelidze, I.
	Title	The Robin problem for the Helmholtz equation in a starlike planar domain			Type	A1 Journal article
	Year	2011	Publication	Georgian mathematical journal	Abbreviated Journal
	Volume	18	Issue	3	Pages	465-479
	Keywords	A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	The interior and exterior Robin problems for the Helmholtz equation in starlike planar domains are addressed by using a suitable Fourier-like technique. Attention is in particular focused on normal-polar domains whose boundaries are defined by the so-called superformula introduced by J. Gielis. A dedicated numerical procedure based on the computer algebra system Mathematica© is developed in order to validate the proposed approach. In this way, highly accurate approximations of the solution, featuring properties similar to the classical ones, are obtained. The computed results are found to be in good agreement with the theoretical findings on Fourier series expansion presented by L. Carleson.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000296166100004	Publication Date	2021-02-28
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	1072-947x	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:91086			Serial	8658
Permanent link to this record



	Author	Gielis, J.; Ding, Y.; Shi, P.
	Title	Towards a geometrical theory of morphology and morphogenesis			Type	P3 Proceeding
	Year	2016	Publication		Abbreviated Journal
	Volume		Issue		Pages
	Keywords	P3 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos		Publication Date
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN		ISBN		Additional Links	UA library record
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:144548			Serial	8677
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
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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
	Volume	9	Issue		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.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000431415100001	Publication Date	2018-05-04
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	1664-462x	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:150948			Serial	8758
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	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
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	Author	Wang, L.; Shi, P.; Chen, L.; Gielis, J.; Niklas, K.J.
	Title	Evidence that Chinese white olive (Canarium album(Lour.) DC.) fruits are solids of revolution			Type	A1 Journal article
	Year	2023	Publication	Botany letters	Abbreviated Journal
	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
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	Author	Gielis, J.
	Title	Fred Van Oystaeyen : Time hybrids: a new generic theory of reality			Type	Review
	Year	2023	Publication	Symmetry, Culture and Science	Abbreviated Journal
	Volume	34	Issue	3	Pages	347-351
	Keywords	Review; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos		Publication Date
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN		ISBN		Additional Links	UA library record
	Impact Factor		Times cited		Open Access	OpenAccess
	Notes				Approved	Most recent IF: NA
	Call Number	UA @ admin @ c:irua:199538			Serial	8871
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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	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
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	001065193100001	Publication Date	2023-08-31
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2223-7747	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor		Times cited		Open Access	OpenAccess
	Notes				Approved	Most recent IF: NA
	Call Number	UA @ admin @ c:irua:199564			Serial	8886
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	Author	Shi, P.; Gielis, J.; Niklas, K.J.; Niinemets, Ü.; Schrader, J.
	Title	Leaf functional traits : ecological and evolutionary implications			Type	ME3 Book as editor
	Year	2023	Publication		Abbreviated Journal
	Volume		Issue		Pages	185 p.
	Keywords	ME3 Book as editor; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos		Publication Date	2023-04-14
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN		ISBN	978-2-8325-2086-4; 1664-8714	Additional Links	UA library record
	Impact Factor		Times cited		Open Access	OpenAccess
	Notes				Approved	Most recent IF: NA
	Call Number	UA @ admin @ c:irua:198002			Serial	8894
Permanent link to this record



	Author	Gielis, J.
	Title	Simon Stevin as a central figure in the development of abstract algebra and generic programming			Type	A1 Journal article
	Year	2023	Publication	Symmetry : culture and science	Abbreviated Journal
	Volume	34	Issue	2	Pages	155-168
	Keywords	A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Simon Stevin (1548-1620) is mainly known for the decimal system and his Clootkrans proof. His influence is also profound in infinitesimal calculus, mechanics, and even in abstract algebra and today’s conception of polynomials, algorithms, and generic programming. Here we review his influence as assessed in generic programming. According to Dr. Stepanov, one of the most influential researchers in generic programming, Stevin’s work on polynomials can be regarded as the essence of generic programming: an algorithm from one domain can be applied in another similar domain.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	001068714100003	Publication Date	2023-07-11
	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	Not_Open_Access: Available from 08.02.2024
	Notes				Approved	Most recent IF: NA
	Call Number	UA @ admin @ c:irua:198000			Serial	8929
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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
	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
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	Author	Mescia, L.; Bia, P.; Gielis, J.; Caratelli, D.
	Title	Advanced particle swarm optimization methods for electromagnetics			Type	P1 Proceeding
	Year	2023	Publication		Abbreviated Journal
	Volume		Issue		Pages	109-122 T2 - Proceedings of the 1st International
	Keywords	P1 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Electromagnetic design problems involve optimizing multiple parameters that are nonlinearly related to objective functions. Traditional optimization techniques require significant computational resources that grow exponentially as the problem size increases. Therefore, a method that can produce good results with moderate memory and computational resources is desirable. Bioinspired optimization methods, such as particle swarm optimization (PSO), are known for their computational efficiency and are commonly used in various scientific and technological fields. In this article we explore the potential of advanced PSO-based algorithms to tackle challenging electromagnetic design and analysis problems faced in real-life applications. It provides a detailed comparison between conventional PSO and its quantum-inspired version regarding accuracy and computational costs. Additionally, theoretical insights on convergence issues and sensitivity analysis on parameters influencing the stochastic process are reported. The utilization of a novel quantum PSO-based algorithm in advanced scenarios, such as reconfigurable and shaped lens antenna synthesis, is illustrated. The hybrid modeling approach, based on the unified geometrical description enabled by the Gielis Transformation, is applied in combination with a suitable quantum PSO-based algorithm, along with a geometrical tube tracing and physical optics technique for solving the inverse problem aimed at identifying the geometrical parameters that yield optimal antenna performance.
	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	978-90-833839-0-3	ISBN		Additional Links	UA library record
	Impact Factor		Times cited		Open Access
	Notes				Approved	Most recent IF: NA
	Call Number	UA @ admin @ c:irua:201048			Serial	9002
Permanent link to this record