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	Author	Gielis, J.
	Title	Er bestaan geen absurde, irrationele, onregelmatige of onderling niet-onmeetbare meetkundige getallen			Type	A2 Journal article
	Year	2021	Publication	Wiskunde en onderwijs	Abbreviated Journal
	Volume	47	Issue	188	Pages	23-33
	Keywords	A2 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	2032-0485	ISBN		Additional Links	UA library record
	Impact Factor		Times cited		Open Access
	Notes				Approved	Most recent IF: NA
	Call Number	UA @ admin @ c:irua:183083			Serial	7934
Permanent link to this record



	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
Permanent link to this record



	Author	Lian, M.; Shi, P.; Zhang, L.; Yao, W.; Gielis, J.; Niklas, K.J.
	Title	A generalized performance equation and its application in measuring the Gini index of leaf size inequality			Type	A1 Journal article
	Year	2023	Publication	Trees: structure and function	Abbreviated Journal
	Volume	37	Issue		Pages	1555-1565
	Keywords	A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	The goal of this study is to provide a rigorous tool to quantify the inequality of the leaf size distribution of an individual plant, thereby serving as a reference trait for quantifying plant adaptations to local environmental conditions. The tool to be presented and tested employs three components: (1) a performance equation (PE), which can produce flexible asymmetrical and symmetrical bell-shaped curves, (2) the Lorenz curve (i.e., the cumulative proportion of leaf size vs. the cumulative proportion of number of leaves), which is the basis for calculating, and (3) the Gini index, which measures the inequality of leaf size distribution. We sampled 12 individual plants of a dwarf bamboo and measured the area and dry mass of each leaf of each plant. We then developed a generalized performance equation (GPE) of which the PE is a special case and fitted the Lorenz curve to leaf size distribution using the GPE and PE. The GPE performed better than the PE in fitting the Lorenz curve. We compared the Gini index of leaf area distribution with that of leaf dry mass distribution and found that there was a significant difference between the two indices that might emerge from the scaling relationship between leaf dry mass and area. Nevertheless, there was a strong correlation between the two Gini indices (r2 = 0.9846). This study provides a promising tool based on the GPE for quantifying the inequality of leaf size distributions across individual plants and can be used to quantify plant adaptations to local environmental conditions.
	Address
	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
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	Shi, P.; Ratkowsky, D.A.; Gielis, J.
	Title	The generalized Gielis geometric equation and its application			Type	A1 Journal article
	Year	2020	Publication	Symmetry-Basel	Abbreviated Journal	Symmetry-Basel
	Volume	12	Issue	4	Pages	645-10
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Many natural shapes exhibit surprising symmetry and can be described by the Gielis equation, which has several classical geometric equations (for example, the circle, ellipse and superellipse) as special cases. However, the original Gielis equation cannot reflect some diverse shapes due to limitations of its power-law hypothesis. In the present study, we propose a generalized version by introducing a link function. Thus, the original Gielis equation can be deemed to be a special case of the generalized Gielis equation (GGE) with a power-law link function. The link function can be based on the morphological features of different objects so that the GGE is more flexible in fitting the data of the shape than its original version. The GGE is shown to be valid in depicting the shapes of some starfish and plant leaves.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000540222200156	Publication Date	2020-04-21
	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	4	Open Access
	Notes	; This research was funded by the Jiangsu Government Scholarship for Overseas Studies (grant number: JS-2018-038). ;			Approved	Most recent IF: 2.7; 2020 IF: 1.457
	Call Number	UA @ admin @ c:irua:168141			Serial	6526
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	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
Permanent link to this record



	Author	Chapman, D.; Gielis, J.
	Title	Gielis transformations for the audiovisual geometry database			Type	A1 Journal article
	Year	2021	Publication	Symmetry : culture and science	Abbreviated Journal
	Volume	32	Issue	2	Pages	177-180
	Keywords	A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	This publication introduces the audiovisual geometry database with Gielis transformations as initial records for a prototype of the database. A concise overview is given of the rationale behind the database and studying wave phenomena with Gielis transformations. First results on a form of timbral polyphony observed in Gielis curves and future work are briefly discussed.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos		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
	Impact Factor		Times cited		Open Access	Not_Open_Access
	Notes				Approved	Most recent IF: NA
	Call Number	UA @ admin @ c:irua:180965			Serial	8004
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	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	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
Permanent link to this record



	Author	Li, Y.; Quinn, B.K.; Gielis, J.; Li, Y.; Shi, P.
	Title	Evidence that supertriangles exist in nature from the vertical projections of Koelreuteria paniculata fruit			Type	A1 Journal article
	Year	2022	Publication	Symmetry	Abbreviated Journal	Symmetry-Basel
	Volume	14	Issue	1	Pages	23
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Many natural radial symmetrical shapes (e.g., sea stars) follow the Gielis equation (GE) or its twin equation (TGE). A supertriangle (three triangles arranged around a central polygon) represents such a shape, but no study has tested whether natural shapes can be represented as/are supertriangles or whether the GE or TGE can describe their shape. We collected 100 pieces of Koelreuteria paniculata fruit, which have a supertriangular shape, extracted the boundary coordinates for their vertical projections, and then fitted them with the GE and TGE. The adjusted root mean square errors (RMSEadj) of the two equations were always less than 0.08, and >70% were less than 0.05. For 57/100 fruit projections, the GE had a lower RMSEadj than the TGE, although overall differences in the goodness of fit were non-significant. However, the TGE produces more symmetrical shapes than the GE as the two parameters controlling the extent of symmetry in it are approximately equal. This work demonstrates that natural supertriangles exist, validates the use of the GE and TGE to model their shapes, and suggests that different complex radially symmetrical shapes can be generated by the same equation, implying that different types of biological symmetry may result from the same biophysical mechanisms.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000746030100001	Publication Date	2021-12-27
	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	OpenAccess
	Notes				Approved	Most recent IF: 2.7
	Call Number	UA @ admin @ c:irua:186453			Serial	7158
Permanent link to this record



	Author	Shi, P.; Wang, L.; Quinn, B.K.K.; Gielis, J.
	Title	A new program to estimate the parameters of Preston's equation, a general formula for describing the egg shape of birds			Type	A1 Journal article
	Year	2023	Publication	Symmetry	Abbreviated Journal	Symmetry-Basel
	Volume	15	Issue	1	Pages	231-10
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Preston's equation is a general model describing the egg shape of birds. The parameters of Preston's equation are usually estimated after re-expressing it as the Todd-Smart equation and scaling the egg's actual length to two. This method assumes that the straight line through the two points on an egg's profile separated by the maximum distance (i.e., the longest axis of an egg's profile) is the mid-line. It hypothesizes that the photographed egg's profile is perfectly bilaterally symmetrical, which seldom holds true because of photographic errors and placement errors. The existing parameter estimation method for Preston's equation considers an angle of deviation for the longest axis of an egg's profile from the mid-line, which decreases prediction errors to a certain degree. Nevertheless, this method cannot provide an accurate estimate of the coordinates of the egg's center, and it leads to sub-optimal parameter estimation. Thus, it is better to account for the possible asymmetry between the two sides of an egg's profile along its mid-line when fitting egg-shape data. In this paper, we propose a method based on the optimization algorithm (optimPE) to fit egg-shape data and better estimate the parameters of Preston's equation by automatically searching for the optimal mid-line of an egg's profile and testing its validity using profiles of 59 bird eggs spanning a wide range of existing egg shapes. We further compared this method with the existing one based on multiple linear regression (lmPE). This study demonstrated the ability of the optimPE method to estimate numerical values of the parameters of Preston's equation and provide the theoretical egg length (i.e., the distance between two ends of the mid-line of an egg's profile) and the egg's maximum breadth. This provides a valuable approach for comparing egg shapes among conspecifics or across different species, or even different classes (e.g., birds and reptiles), in future investigations.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000927531000001	Publication Date	2023-01-13
	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	OpenAccess
	Notes				Approved	Most recent IF: 2.7; 2023 IF: 1.457
	Call Number	UA @ admin @ c:irua:195347			Serial	7279
Permanent link to this record



	Author	Wang, L.; Ratkowsky, D.A.; Gielis, J.; Ricci, P.E.; Shi, P.
	Title	Effects of the numerical values of the parameters in the Gielis equation on its geometries			Type	A1 Journal article
	Year	2022	Publication	Symmetry	Abbreviated Journal	Symmetry-Basel
	Volume	14	Issue	12	Pages	2475-12
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	The Lamé curve is an extension of an ellipse, the latter being a special case. Dr. Johan Gielis further extended the Lamé curve in the polar coordinate system by introducing additional parameters (n1, n2, n3; m): rφ=1Acosm4φn2+1Bsinm4φn3−1/n1, which can be applied to model natural geometries. Here, r is the polar radius corresponding to the polar angle φ; A, B, n1, n2 and n3 are parameters to be estimated; m is the positive real number that determines the number of angles of the Gielis curve. Most prior studies on the Gielis equation focused mainly on its applications. However, the Gielis equation can also generate a large number of shapes that are rotationally symmetric and axisymmetric when A = B and n2 = n3, interrelated with the parameter m, with the parameters n1 and n2 determining the shapes of the curves. In this paper, we prove the relationship between m and the rotational symmetry and axial symmetry of the Gielis curve from a theoretical point of view with the condition A = B, n2 = n3. We also set n1 and n2 to take negative real numbers rather than only taking positive real numbers, then classify the curves based on extremal properties of r(φ) at φ = 0, π/m when n1 and n2 are in different intervals, and analyze how n1, n2 precisely affect the shapes of Gielis curves.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000904525700001	Publication Date	2022-11-23
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2073-8994	ISBN		Additional Links	UA library record; WoS full record
	Impact Factor	2.7	Times cited		Open Access	OpenAccess
	Notes				Approved	Most recent IF: 2.7
	Call Number	UA @ admin @ c:irua:191860			Serial	7301
Permanent link to this record



	Author	Gielis, J.; Tavkhelidze, I.; Ricci, P.E.
	Title	Generalized Möbius-Listing bodies and the heart			Type	A3 Journal article
	Year	2023	Publication	Sn – 2247-689x	Abbreviated Journal
	Volume	13	Issue	2	Pages	58-70
	Keywords	A3 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Generalized Möbius-Listing surfaces and bodies generalize Möbius bands, and this research was motivated originally by solutions of boundary value problems. Analogous to cutting of the original Möbius band, for this class of surfaces and bodies, results have been obtained when cutting such bodies or surfaces. The results can be applied in a wide range of fields in the natural science, and here we propose how they can serve as a model for the heart and the circulatory system.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	http://rjm-cs.ro/2023v13i2_7.pdf#page=1	Publication Date
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN		ISBN		Additional Links	UA library record; http://rjm-cs.ro/2023v13i2_7.pdf#page=1
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:200773			Serial	9043
Permanent link to this record



	Author	Gielis, J.; Grigolia, R.
	Title	Lamé curves and Rvachev's R-functions			Type	A3 Journal article
	Year	2022	Publication	Sn – 1512-0066	Abbreviated Journal
	Volume	37	Issue		Pages	1-4
	Keywords	A3 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Gielis transformations are a generalization of Lame curves. To combine domains, we can make use of the natural alliance between Lame's work and Rvachev's R-functions. A logical next step is the extension to n-valued logic dening dierent partitions.
	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	Most recent IF: NA
	Call Number	UA @ admin @ c:irua:189316			Serial	7178
Permanent link to this record



	Author	Tavkhelidze, I.; Gielis, J.; Pinelas, S.
	Title	About some methods of analytic representation and classification of a wide set of geometric figures with “complex” configuration			Type	A3 Journal article
	Year	2020	Publication	Sn – 1512-0066	Abbreviated Journal
	Volume	34	Issue		Pages	81-84
	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	Most recent IF: NA
	Call Number	UA @ admin @ c:irua:174475			Serial	7406
Permanent link to this record



	Author	Gielis, J.; Tavkhelidze, I.
	Title	The Mӧbius phenomenon in Generalized Mӧbius-Listing bodies with cross sections of odd and even polygons			Type	A3 Journal article
	Year	2020	Publication	Sn – 1512-0066	Abbreviated Journal
	Volume	34	Issue		Pages	23-26
	Keywords	A3 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract
	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	Most recent IF: NA
	Call Number	UA @ admin @ c:irua:174474			Serial	8257
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	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
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	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
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	Author	Gielis, J.
	Title	Double helix of phyllotaxis : analysis of the geometric model of plant morphogenesis, by Boris Rozin			Type	Review
	Year	2021	Publication	Quarterly Review Of Biology	Abbreviated Journal	Q Rev Biol
	Volume	96	Issue	2	Pages	139-140
	Keywords	Review; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos		Publication Date	2021-05-19
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	0033-5770; 1539-7718	ISBN		Additional Links	UA library record
	Impact Factor	4.25	Times cited		Open Access	Not_Open_Access
	Notes				Approved	Most recent IF: 4.25
	Call Number	UA @ admin @ c:irua:178829			Serial	7824
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	Author	Mescia, L.; Lamacchia, C.M.; Chiapperino, M.A.; Bia, P.; Gielis, J.; Caratelli, D.
	Title	Design of irregularly shaped lens antennas including supershaped feed			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	169-173
	Keywords	P1 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	A new class of irregularly shaped dielectric lens antennas with a supershaped microstrip antenna feeder is presented and detailed in this work. The surface of the lens antenna and the feeder shape have been modelled by using the three and two-dimensional Gielis formula, respectively. The antenna design has been carried out by integrating an home-made software tool with the CST Microwave Studio®. The radiation properties of the whole antenna system have been evaluated using a dedicated high-frequency technique based on the tube tracing approximation. Moreover, the effects due to the multiple internal reflections have been properly modeled. The proposed model was applied to study unusual and complex lens antenna systems with the aim to design special radiation characteristics.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000550769300021	Publication Date	2020-03-03
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	978-1-72813-403-1; 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:169169			Serial	7766
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	Author	Mescia, L.; Chiapperino, M.A.; Bia, P.; Lamacchia, C.M.; Gielis, J.; Caratelli, D.
	Title	Multiphysics modelling of membrane electroporation in irregularly shaped cells			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	2992-2998
	Keywords	P1 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Electroporation is a non-thermal electromagnetic phenomenon widely used in medical diseases treatment. Different mathematical models of electroporation have been proposed in literature to study pore evolution in biological membranes. This paper presents a nonlinear dispersive multiphysic model of electroporation in irregular shaped biological cells in which the spatial and temporal evolution of the pores size is taken into account. The model solves Maxwell and asymptotic Smoluchowski equations and it describes the dielectric dispersion of cell media using a Debye-based relationship. Furthermore, the irregular cell shape has been modeled using the Gielis superformula. Taking into account the cell in mitosis phase, the electroporation process has been studied comparing the numerical results pertaining the model with variable pore radius with those in which the pore radius is supposed constant. The numerical analysis has been performed exposing the biological cell to a rectangular electric pulse having duration of 10 μs. The obtained numerical results highlight considerable differences between the two different models underling the need to include into the numerical algorithm the differential equation modeling the spatial and time evolution of the pores size.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000550769302159	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; WoS citing articles
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:169170			Serial	8288
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	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
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	Author	Gielis, J.; Caratelli, D.; Fougerolle, Y.; Ricci, P.E.; Tavkelidze, I.; Gerats, T.
	Title	Universal natural shapes : from unifying shape description to simple methods for shape analysis and boundary value problems			Type	A1 Journal article
	Year	2012	Publication	PLoS ONE	Abbreviated Journal
	Volume	7	Issue	9	Pages	e29324-11
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Gielis curves and surfaces can describe a wide range of natural shapes and they have been used in various studies in biology and physics as descriptive tool. This has stimulated the generalization of widely used computational methods. Here we show that proper normalization of the Levenberg-Marquardt algorithm allows for efficient and robust reconstruction of Gielis curves, including self-intersecting and asymmetric curves, without increasing the overall complexity of the algorithm. Then, we show how complex curves of k-type can be constructed and how solutions to the Dirichlet problem for the Laplace equation on these complex domains can be derived using a semi-Fourier method. In all three methods, descriptive and computational power and efficiency is obtained in a surprisingly simple way.
	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	Wang, L.; Miao, Q.; Niinemets, Ü.; Gielis, J.; Shi, P.
	Title	Quantifying the variation in the geometries of the outer rims of corolla tubes of Vinca major L			Type	A1 Journal article
	Year	2022	Publication	Plants	Abbreviated Journal
	Volume	11	Issue	15	Pages	1987-12
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Many geometries of plant organs can be described by the Gielis equation, a polar coordinate equation extended from the superellipse equation, . Here, r is the polar radius corresponding to the polar angle φ; m is a positive integer that determines the number of angles of the Gielis curve when φ ∈ [0 to 2π); and the rest of the symbols are parameters to be estimated. The pentagonal radial symmetry of calyxes and corolla tubes in top view is a common feature in the flowers of many eudicots. However, prior studies have not tested whether the Gielis equation can depict the shapes of corolla tubes. We sampled randomly 366 flowers of Vinca major L., among which 360 had five petals and pentagonal corolla tubes, and six had four petals and quadrangular corolla tubes. We extracted the planar coordinates of the outer rims of corolla tubes (in top view) (ORCTs), and then fitted the data with two simplified versions of the Gielis equation with k = 1 and m = 5: (Model 1), and (Model 2). The adjusted root mean square error (RMSEadj) was used to evaluate the goodness of fit of each model. In addition, to test whether ORCTs are radially symmetrical, we correlated the estimates of n2 and n3 in Model 1 on a log-log scale. The results validated the two simplified Gielis equations. The RMSEadj values for all corolla tubes were smaller than 0.05 for both models. The numerical values of n2 and n3 were demonstrated to be statistically equal based on the regression analysis, which suggested that the ORCTs of V. major are radially symmetrical. It suggests that Model 1 can be replaced by the simpler Model 2 for fitting the ORCT in this species. This work indicates that the pentagonal or quadrangular corolla tubes (in top view) can both be modeled by the Gielis equation and demonstrates that the pentagonal or quadrangular corolla tubes of plants tend to form radial symmetrical geometries during their development and growth.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000839115100001	Publication Date	2022-08-01
	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:189315			Serial	7200
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	Author	Yao, W.; Niinemets, Ü.; Yao, W.; Gielis, J.; Schrader, J.; Yu, K.; Shi, P.
	Title	Comparison of two simplified versions of the Gielis equation for describing the shape of bamboo leaves			Type	A1 Journal article
	Year	2022	Publication	Plants	Abbreviated Journal
	Volume	11	Issue	22	Pages	3058-11
	Keywords	A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Bamboo is an important component in subtropical and tropical forest communities. The plant has characteristic long lanceolate leaves with parallel venation. Prior studies have shown that the leaf shapes of this plant group can be well described by a simplified version (referred to as SGE-1) of the Gielis equation, a polar coordinate equation extended from the superellipse equation. SGE-1 with only two model parameters is less complex than the original Gielis equation with six parameters. Previous studies have seldom tested whether other simplified versions of the Gielis equation are superior to SGE-1 in fitting empirical leaf shape data. In the present study, we compared a three-parameter Gielis equation (referred to as SGE-2) with the two-parameter SGE-1 using the leaf boundary coordinate data of six bamboo species within the same genus that have representative long lanceolate leaves, with >300 leaves for each species. We sampled 2000 data points at approximately equidistant locations on the boundary of each leaf, and estimated the parameters for the two models. The root–mean–square error (RMSE) between the observed and predicted radii from the polar point to data points on the boundary of each leaf was used as a measure of the model goodness of fit, and the mean percent error between the RMSEs from fitting SGE-1 and SGE-2 was used to examine whether the introduction of an additional parameter in SGE-1 remarkably improves the model’s fitting. We found that the RMSE value of SGE-2 was always smaller than that of SGE-1. The mean percent errors among the two models ranged from 7.5% to 20% across the six species. These results indicate that SGE-2 is superior to SGE-1 and should be used in fitting leaf shapes. We argue that the results of the current study can be potentially extended to other lanceolate leaf shapes.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000887783400001	Publication Date	2022-11-14
	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:191859			Serial	7289
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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	Gao, J.; Huang, W.; Gielis, J.; Shi, P.
	Title	Plant morphology and function, geometric morphometrics, and modelling : decoding the mathematical secrets of plants			Type	Editorial
	Year	2023	Publication	Plants	Abbreviated Journal
	Volume	12	Issue	21	Pages	3724-2
	Keywords	Editorial; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	001103336500001	Publication Date	2023-10-30
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2223-7747	ISBN		Additional Links	UA library record; WoS full record
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:201173			Serial	9072
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	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
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