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	Author	Gielis, J.; Natalini, P.; Ricci, P.E.
	Title	A note about generalized forms of the Gielis formula			Type	H1 Book chapter
	Year	2017	Publication		Abbreviated Journal
	Volume	2	Issue		Pages	107-116 T2 - Modeling in mathematics : proceedings
	Keywords	H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	We generalize the Gielis Superformula by extending the R. Chacon approach, but avoiding the use of Jacobi elliptic functions. The obtained results are extended to the three-dimensional case. Several new shapes are derived by using the computer algebra system Mathematica(C).
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000442076400008	Publication Date	2017-04-20
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN		ISBN	978-94-6239-260-1; 978-94-6239-261-8; 2543-0300; 978-94-6239-260-1	Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:144550			Serial	8318
Permanent link to this record



	Author	Caratelli, D.; Gielis, J.; Ricci, P.E.
	Title	Fourier-like solution of the Dirichlet problem for the Laplace Equation in k-type Gielis domains			Type	A1 Journal article
	Year	2011	Publication	Journal of pure and applied mathematics : advances and applications	Abbreviated Journal
	Volume	5	Issue	2	Pages	99-111
	Keywords	A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	The interior and exterior Dirichlet problems for the Laplace equation in k-type Gielis domains are analytically addressed by using a suitable Fourier-like technique. A dedicated numerical procedure based on the computer-aided algebra tool 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. Computed results are found to be in good agreement with theoretical findings on Fourier series expansion presented by Carleson.
	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:91090			Serial	7982
Permanent link to this record



	Author	Gielis, J.; Caratelli, D.; Fougerolle, Y.; Ricci, P.E.; Gerats, T.
	Title	A biogeometrical model for corolla fusion in Asclepiad flowers			Type	H1 Book chapter
	Year	2017	Publication		Abbreviated Journal
	Volume	2	Issue		Pages	83-105 T2 - Modeling in mathematics : proceedings
	Keywords	H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	The molecular genetics of flower development have been studied extensively for more than two decades. Fusion of organs and the tendency to oligomery, important characteristics of flower evolution, so far have remained fairly elusive. We present a geometric model for shape and fusion in the corolla of Asclepiads. Examples demonstrate how fusion of petals creates stable centers, a prerequisite for the formation of complex pollination structures via congenital and postgenital fusion events, with the formation of de novo organs, specific to Asclepiads. The development of the corolla reduces to simple inequalities from the MATHS-BOX. The formation of stable centers and of bell and tubular shapes in flowers are immediate and logical consequences of the shape. Our model shows that any study on flowers, especially in evo-devo perspective should be performed within the wider framework of polymery and oligomery and of fusion and synorganization.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000442076400007	Publication Date	2017-04-20
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN		ISBN	978-94-6239-260-1; 978-94-6239-261-8; 2543-0300; 978-94-6239-260-1	Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:144551			Serial	7561
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	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	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	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	Most recent IF: NA
	Call Number	UA @ admin @ c:irua:200773			Serial	9043
Permanent link to this record



	Author	Shi, P.; Yu, K.; Niinemets, Ü.; Gielis, J.
	Title	Can leaf shape be represented by the ratio of leaf width to length? Evidence from nine species of Magnolia and Michelia (Magnoliaceae)			Type	A1 Journal article
	Year	2021	Publication	Forests	Abbreviated Journal	Forests
	Volume	12	Issue	1	Pages	41
	Keywords	A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Leaf shape is closely related to economics of leaf support and leaf functions, including light interception, water use, and CO2 uptake, so correct quantification of leaf shape is helpful for studies of leaf structure/function relationships. There are some extant indices for quantifying leaf shape, including the leaf width/length ratio (W/L), leaf shape fractal dimension (FD), leaf dissection index, leaf roundness index, standardized bilateral symmetrical index, etc. W/L ratio is the simplest to calculate, and recent studies have shown the importance of the W/L ratio in explaining the scaling exponent of leaf dry mass vs. leaf surface area and that of leaf surface area vs. leaf length. Nevertheless, whether the W/L ratio could reflect sufficient geometrical information of leaf shape has been not tested. The FD might be the most accurate measure for the complexity of leaf shape because it can characterize the extent of the self-similarity and other planar geometrical features of leaf shape. However, it is unknown how strongly different indices of leaf shape complexity correlate with each other, especially whether W/L ratio and FD are highly correlated. In this study, the leaves of nine Magnoliaceae species (>140 leaves for each species) were chosen for the study. We calculated the FD value for each leaf using the box-counting approach, and measured leaf fresh mass, surface area, perimeter, length, and width. We found that FD is significantly correlated to the W/L ratio and leaf length. However, the correlation between FD and the W/L ratio was far stronger than that between FD and leaf length for each of the nine species. There were no strong correlations between FD and other leaf characteristics, including leaf area, ratio of leaf perimeter to area, fresh mass, ratio of leaf fresh mass to area, and leaf roundness index. Given the strong correlation between FD and W/L, we suggest that the simpler index, W/L ratio, can provide sufficient information of leaf shape for similarly-shaped leaves. Future studies are needed to characterize the relationships among FD and W/L in leaves with strongly varying shape, e.g., in highly dissected leaves.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000611074700001	Publication Date	2020-12-31
	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	1.951	Times cited		Open Access	OpenAccess
	Notes				Approved	Most recent IF: 1.951
	Call Number	UA @ admin @ c:irua:174473			Serial	7572
Permanent link to this record



	Author	Dattoli, G.; Di Palma, E.; Gielis, J.; Licciardi, S.
	Title	Parabolic trigonometry			Type	A1 Journal article
	Year	2020	Publication	International journal of applied and computational mathematics	Abbreviated Journal
	Volume	6	Issue	2	Pages	37
	Keywords	A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos		Publication Date	2020-03-04
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2349-5103	ISBN		Additional Links	UA library record
	Impact Factor		Times cited		Open Access
	Notes				Approved	Most recent IF: NA
	Call Number	UA @ admin @ c:irua:167049			Serial	6578
Permanent link to this record



	Author	Mescia, L.; Chiapperino, M.A.; Bia, P.; Lamacchia, C.M.; Gielis, J.; Caratelli, D.
	Title	Design of electroporation process in irregularly shaped multicellular systems			Type	A1 Journal article
	Year	2019	Publication	Electronics (Basel)	Abbreviated Journal
	Volume	8	Issue	1	Pages	37
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Electroporation technique is widely used in biotechnology and medicine for the transport of various molecules through the membranes of biological cells. Different mathematical models of electroporation have been proposed in the literature to study pore formation in plasma and nuclear membranes. These studies are mainly based on models using a single isolated cell with a canonical shape. In this work, a spacetime (x,y,t) multiphysics model based on quasi-static Maxwells equations and nonlinear Smoluchowskis equation has been developed to investigate the electroporation phenomenon induced by pulsed electric field in multicellular systems having irregularly shape. The dielectric dispersion of the cell compartments such as nuclear and plasmatic membranes, cytoplasm, nucleoplasm and external medium have been incorporated into the numerical algorithm, too. Moreover, the irregular cell shapes have been modeled by using the Gielis transformations.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000457142800037	Publication Date	2019-01-03
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2079-9292	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:157203			Serial	7765
Permanent link to this record



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



	Author	Zhang, L.; Quinn, B.K.; Hui, C.; Lian, M.; Gielis, J.; Gao, J.; Shi, P.
	Title	New indices to balance α-diversity against tree size inequality			Type	A1 Journal article
	Year	2024	Publication	Journal of forestry research	Abbreviated Journal
	Volume	35	Issue	1	Pages	31-39
	Keywords	A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	The number and composition of species in a community can be quantified with alpha-diversity indices, including species richness (R), Simpson's index (D), and the Shannon-Wiener index (HGREEK TONOS). In forest communities, there are large variations in tree size among species and individuals of the same species, which result in differences in ecological processes and ecosystem functions. However, tree size inequality (TSI) has been largely neglected in studies using the available diversity indices. The TSI in the diameter at breast height (DBH) data for each of 999 20 m x 20 m forest census quadrats was quantified using the Gini index (GI), a measure of the inequality of size distribution. The generalized performance equation was used to describe the rotated and right-shifted Lorenz curve of the cumulative proportion of DBH and the cumulative proportion of number of trees per quadrat. We also examined the relationships of alpha-diversity indices with the GI using correlation tests. The generalized performance equation effectively described the rotated and right-shifted Lorenz curve of DBH distributions, with most root-mean-square errors (990 out of 999 quadrats) being < 0.0030. There were significant positive correlations between each of three alpha-diversity indices (i.e., R, D, and H') and the GI. Nevertheless, the total abundance of trees in each quadrat did not significantly influence the GI. This means that the TSI increased with increasing species diversity. Thus, two new indices are proposed that can balance alpha-diversity against the extent of TSI in the community: (1 – GI) x D, and (1 – GI) x H'. These new indices were significantly correlated with the original D and HGREEK TONOS, and did not increase the extent of variation within each group of indices. This study presents a useful tool for quantifying both species diversity and the variation in tree sizes in forest communities, especially in the face of cumulative species loss under global climate change.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	001131698000001	Publication Date	2023-12-28
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	1007-662x; 1993-0607	ISBN		Additional Links	UA library record; WoS full record
	Impact Factor	3	Times cited		Open Access	Not_Open_Access
	Notes				Approved	Most recent IF: 3; 2024 IF: 0.774
	Call Number	UA @ admin @ c:irua:201972			Serial	9061
Permanent link to this record



	Author	Gielis, J.; Tavkhelidze, I.
	Title	A note on Generalized Möbius-Listing Bodies			Type	P1 Proceeding
	Year	2023	Publication		Abbreviated Journal
	Volume		Issue		Pages	31-39 T2 - Proceedings of the 1st International Sy
	Keywords	P1 Proceeding; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Generalized Möbius-Listing surfaces and bodies generalize Möbius bands, and this research was motivated originally by solutions of boundary value problems. Analogous to cutting of the original Möbius band, for this class of surfaces and bodies, results have been obtained when cutting such bodies or surfaces. In general, cutting leads to interlinked and intertwined different surfaces or bodies, resulting in very complex systems. However, under certain conditions, the result of cutting can be a single surface or body, which reduces complexity considerably. These conditions are based on congruence and rotational symmetry of the resulting cross sections after cutting, and on the knife cutting the origin
	Address
	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:201047			Serial	9063
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	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	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	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
Permanent link to this record



	Author	Nicolau, F.; Gielis, J.; Simeone, A.L.; Simoes Lopes, D.
	Title	Exploring and selecting supershapes in virtual reality with line, quad, and cube shaped widgets			Type	P1 Proceeding
	Year	2022	Publication		Abbreviated Journal
	Volume		Issue		Pages	21-28
	Keywords	P1 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Supershapes are used in Parametric Design to model, literally, thou-sands of natural and man-made shapes with a single 6 parameter formula. However, users are left to probe such a rich yet dense collection of supershapes using a set of independent 1-D sliders. Some of the formula’s parameters are non-linear in nature, making them particularly difficult to grasp with conventional 1-D sliders alone. VR appears as a promising setting for Parametric Design with supershapes since it empowers users with more natural visual inspection and shape browsing techniques, with multiple solutions being displayed at once and the possibility to design more interesting forms of slider interaction. In this work, we propose VR shape widgets that allow users to probe and select supershapes from a multitude of solutions. Our designs take leverage on thumbnails, mini-maps, haptic feedback and spatial interaction, while supporting 1-D, 2-D and 3-D supershape parameter spaces. We conducted a user study (N = 18) and found that VR shape widgets are effective, more efficient, and natural than conventional VR 1-D sliders while also usable for users without prior knowledge on supershapes. We also found that the proposed VR widgets provide a quick overview of the main supershapes, and users can easily reach the desired solution without having to perform fine-grain handle manipulations.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000828657500003	Publication Date	2022-04-20
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	978-1-6654-9617-9	ISBN		Additional Links	UA library record; WoS full record
	Impact Factor		Times cited		Open Access	OpenAccess
	Notes				Approved	Most recent IF: NA
	Call Number	UA @ admin @ c:irua:188471			Serial	7161
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	Author	Gielis, J.; Ricci, P.E.; Tavkhelidze, I.
	Title	The Möbius phenomenon in Generalized Möbius-Listing surfaces and bodies, and Arnold's Cat phenomenon			Type	A1 Journal article
	Year	2021	Publication	Advanced Studies : Euro-Tbilisi Mathematical Journal	Abbreviated Journal
	Volume	14	Issue	4	Pages	17-35
	Keywords	A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Möbius bands have been studied extensively, mainly in topology. Generalized Möbius-Listing surfaces and bodies providing a full geometrical generalization, is a quite new field, motivated originally by solutions of boundary value problems. Analogous to cutting of the original Möbius band, for this class of surfaces and bodies, results have been obtained when cutting such bodies or surfaces. In general, cutting leads to interlinked and intertwined different surfaces or bodies, resulting in very complex systems. However, under certain conditions, the result of cutting can be a single surface or body, which reduces complexity considerably. Our research is motivated by this reduction of complexity. In the study of cutting Generalized Möbius-Listing bodies with polygons as cross section, the conditions under which a single body results, displaying the Möbius phenomenon of a one-sided body, have been determined for even and odd polygons. These conditions are based on congruence and rotational symmetry of the resulting cross sections after cutting, and on the knife cutting the origin. The Möbius phenomenon is important, since the process of cutting (or separation of zones in a GML body in general) then results in a single body, not in different, intertwined domains. In all previous works it was assumed that the cross section of the GML bodies is constant, but the main result of this paper is that it is sufficient that only one cross section on the whole GML structure meets the conditions for the Möbius phenomenon to occur. Several examples are given to illustrate this.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000774655100002	Publication Date
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN		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:183081			Serial	8258
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	Author	Vermander, C.; De Wael, J.; Gielis, J.
	Title	De kleine boerderij : twee bijzondere tuinkamers			Type	A2 Journal article
	Year	2019	Publication	Groencontact	Abbreviated Journal
	Volume	45	Issue	5	Pages	14-19
	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	1374-4631	ISBN		Additional Links	UA library record
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:164895			Serial	8142
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	Author	Tavkhelidze, I.; Cassisa, C.; Gielis, J.; Ricci, P.E.
	Title	About “bulky” links, generated by generalized Möbius Listing's bodies GML₃ⁿ			Type	A1 Journal article
	Year	2013	Publication	Matematica e applicazioni : atti della Accademia nazionale dei Lincei	Abbreviated Journal
	Volume	24	Issue	1	Pages	11-38
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	In the present paper we consider the “bulky knots'' and ”bulky links'', which appear after cutting a Generalized Möbius Listing's GMLn3 body (whose radial cross section is a plane 3-symmetric figure with three vertices) along different Generalized Möbius Listing's surfaces GMLn2 situated in it. This article is aimed to investigate the number and geometric structure of the independent objects appearing after such a cutting process of GMLn3 bodies. In most cases we are able to count the indices of the resulting mathematical objects according to the known tabulation for Knots and Links of small complexity.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000316567700002	Publication Date	2013-03-13
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	1120-6357	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:107174			Serial	7405
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	Author	Gielis, J.; Tavkhelidze, I.
	Title	The general case of cutting of Generalized Möbius-Listing surfaces and bodies			Type	A1 Journal article
	Year	2020	Publication	4Open	Abbreviated Journal
	Volume	3	Issue		Pages	7-48
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	The original motivation to study Generalized Möbius-Listing GML surfaces and bodies was the observation that the solution of boundary value problems greatly depends on the domains. Since around 2010 GML’s were merged with (continuous) Gielis Transformations, which provide a unifying description of geometrical shapes, as a generalization of the Pythagorean Theorem. The resulting geometrical objects can be used for modeling a wide range of natural shapes and phenomena. The cutting of GML bodies and surfaces, with the Möbius strip as one special case, is related to the field of knots and links, and classifications were obtained for GML with cross sectional symmetry of 2, 3, 4, 5 and 6. The general case of cutting GML bodies and surfaces, in particular the number of ways of cutting, could be solved by reducing the 3D problem to planar geometry. This also unveiled a range of connections with topology, combinatorics, elasticity theory and theoretical physics.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos		Publication Date	2020-08-31
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2557-0250	ISBN		Additional Links	UA library record
	Impact Factor		Times cited		Open Access
	Notes				Approved	Most recent IF: NA
	Call Number	UA @ admin @ c:irua:174471			Serial	7992
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	Author	Gielis, J.; Caratelli, D.; Shi, P.; Ricci, P.E.
	Title	A note on spirals and curvature			Type	A1 Journal article
	Year	2020	Publication	Growth and form	Abbreviated Journal
	Volume	1	Issue	1	Pages	1-8
	Keywords	A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Starting from logarithmic, sinusoidal and power spirals, it is shown how these spirals are connected directly with Chebyshev polynomials, Lamé curves, with allometry and Antonelli-metrics in Finsler geometry. Curvature is a crucial concept in geometry both for closed curves and equiangular spirals, and allowed Dillen to give a general definition of spirals. Many natural shapes can be described as a combination of one of two basic shapes in nature—circle and spiral—with Gielis transformations. Using this idea, shape description itself is used to develop a novel approach to anisotropic curvature in nature. Various examples are discussed, including fusion in flowers and its connection to the recently described pseudo-Chebyshev functions.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos		Publication Date	2020-02-23
	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:167061			Serial	6569
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	Author	Li, Y.; Quinn, B.K.; Niinemets, Ü.; Schrader, J.; Gielis, J.; Liu, M.; Shi, P.
	Title	Ellipticalness index : a simple measure of the complexity of oval leaf shape			Type	A1 Journal article
	Year	2022	Publication	Pakistan journal of botany : An official publication of pakistan botanical society	Abbreviated Journal	Pak J Bot
	Volume	54	Issue	6	Pages	1-8
	Keywords	A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Plants have diverse leaf shapes that have evolved to adapt to the environments they have experienced over their evolutionary history. Leaf shape and leaf size can greatly influence the growth rate, competitive ability, and productivity of plants. However, researchers have long struggled to decide how to properly quantify the complexity of leaf shape. Prior studies recommended the leaf roundness index (RI = 4πA/P2) or dissection index (DI = ), where P is leaf perimeter and A is leaf area. However, these two indices merely measure the extent of the deviation of leaf shape from a circle, which is usually invalid as leaves are seldom circular. In this study, we proposed a simple measure, named the ellipticalness index (EI), for quantifying the complexity of leaf shape based on the hypothesis that the shape of any oval leaf can be regarded as a variation from a standard ellipse. 2220 leaves from nine species of Magnoliaceae were sampled to check the validity of the EI. We also tested the validity of the Montgomery equation (ME), which assumes a proportional relationship between leaf area and the product of leaf length and width, because the EI actually comes from the proportionality coefficient of the ME. We also compared the ME with five other models of leaf area. The ME was found to be the best model for calculating leaf area based on consideration of the trade-off between model fit vs. complexity, which strongly supported the robustness of the EI for describing oval leaf shape. The new index can account for both leaf shape and size, and we conclude that it is a promising method for quantifying and comparing oval leaf shapes across species in future studies.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000814279700028	Publication Date	2022-05-23
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	0556-3321	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor	1.2	Times cited		Open Access	OpenAccess
	Notes				Approved	Most recent IF: 1.2
	Call Number	UA @ admin @ c:irua:188469			Serial	7153
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	Author	De Tommasi, E.; Rogato, A.; Caratelli, D.; Mescia, L.; Gielis, J.
	Title	Following the photons route : mathematical models describing the interaction of diatoms with light			Type	H1 Book chapter
	Year	2022	Publication		Abbreviated Journal
	Volume		Issue		Pages	1-53
	Keywords	H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	The interaction of diatoms with sunlight is fundamental in order to deeply understand their role in terrestrial ecology and biogeochemistry, essentially due to their massive contribution to global primary production through photosynthesis and its e↵ect on carbon, oxygen and silicon cycles. Following the journey of light through natural waters, its propagation through the intricate frustule micro- and nano-structure and, finally, its fate inside the photosynthetic machinery of the living cell requires several mathematical and computational models in order to accurately describe all the involved phenomena taking place at di↵erent space scales and physical regimes. In this chapter, we review the main analytical models describing the underwater optical field, the essential numerical algorithms for the study of photonic properties of the diatom frustule seen as a natural metamaterial, as well as the principal models describing photon harvesting in diatom plastids and methods for complex EM propagation problems and wave propagation in dispersive materials with multiple relaxation times. These mathematical methods will be integrated in a unifying geometric perspective.
	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	978-1-119-74985-1	Additional Links	UA library record
	Impact Factor		Times cited		Open Access
	Notes				Approved	Most recent IF: NA
	Call Number	UA @ admin @ c:irua:186731			Serial	7165
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	Author	Gielis, J.; Grigolia, R.
	Title	Lamé curves and Rvachev's R-functions			Type	A3 Journal article
	Year	2022	Publication	Sn – 1512-0066	Abbreviated Journal
	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
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	Author	Düking, R.; Gielis, J.; Liese, W.
	Title	Carbon flux and carbon stock in a bamboo stand and their relevance for mitigating climate change			Type	A3 Journal article
	Year	2011	Publication	Bamboo Science & Culture	Abbreviated Journal
	Volume	24	Issue	1	Pages	1-6
	Keywords	A3 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	In this report we describe the basics of biological carbon fixation in bamboo forests. Confusing carbon stock with carbon flux has led to false expectations on the significance of bamboo forests as carbon sinks. Furthermore, misunderstandings about the growth of bamboo culms can lead to highly exaggerated expectations on the productivity of bamboo.
	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	1535-7635	ISBN		Additional Links	UA library record
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:91091			Serial	7578
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	Author	De Tommasi, E.; Gielis, J.; Rogato, A.
	Title	Diatom frustule morphogenesis and function : a multidisciplinary survey			Type	A1 Journal article
	Year	2017	Publication	Marine Genomics	Abbreviated Journal
	Volume	35	Issue		Pages	1-18
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Diatoms represent the major component of phytoplankton and are responsible for about 2025% of global primary production. Hundreds of millions of years of evolution led to tens of thousands of species differing in dimensions and morphologies. In particular, diatom porous silica cell walls, the frustules, are characterized by an extraordinary, species-specific diversity. It is of great interest, among the marine biologists and geneticists community, to shed light on the origin and evolutionary advantage of this variability of dimensions, geometries and pore distributions. In the present article the main reported data related to frustule morphogenesis and functionalities with contributions from fundamental biology, genetics, mathematics, geometry and physics are reviewed.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000412957700001	Publication Date	2017-07-20
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	1874-7787	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:144546			Serial	7807
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	Author	Gielis, J.; Verhulst, R.; Caratelli, D.; Ricci, P.E.; Tavkhelidze, I.
	Title	On means, polynomials and special functions			Type	A1 Journal article
	Year	2014	Publication	The teaching of mathematics	Abbreviated Journal
	Volume	17	Issue	1	Pages	1-20
	Keywords	A1 Journal article; Educational sciences; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract
	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
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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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