“The general case of cutting GML bodies : the geometrical solution”. Gielis J, Caratelli D, Tavkhelidze I page 397 (2020).
Keywords: H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1007/978-3-030-56323-3_31
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“The general case of cutting of Generalized Möbius-Listing surfaces and bodies”. Gielis J, Tavkhelidze I, 4Open 3, 7 (2020). http://doi.org/10.1051/FOPEN/2020007
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.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1051/FOPEN/2020007
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“Gielis transformations for the audiovisual geometry database”. Chapman D, Gielis J, Symmetry : culture and science 32, 177 (2021). http://doi.org/10.26830/SYMMETRY_2021_2_177
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.
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.26830/SYMMETRY_2021_2_177
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“Lamé-Gielis curves in biology and geometry”. Gielis J, Shi P, Beirinckx B, Caratelli D, Ricci PE, (2021)
Keywords: P3 Proceeding; Sustainable Energy, Air and Water Technology (DuEL)
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“The Mӧbius phenomenon in Generalized Mӧbius-Listing bodies with cross sections of odd and even polygons”. Gielis J, Tavkhelidze I, Sn –, 1512-0066 34, 23 (2020)
Keywords: A3 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
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“The Möbius phenomenon in Generalized Möbius-Listing surfaces and bodies, and Arnold's Cat phenomenon”. Gielis J, Ricci PE, Tavkhelidze I, Advanced Studies : Euro-Tbilisi Mathematical Journal 14, 17 (2021). http://doi.org/10.3251/ASETMJ/1932200812
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.
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.3251/ASETMJ/1932200812
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“Phi-bonacci in Ancient Greece”. Gielis J, Symmetry : culture and science 32, 25 (2021). http://doi.org/10.26830/SYMMETRY_2021_1_025
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.
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.26830/SYMMETRY_2021_1_025
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“The apeirogon and dual numbers”. Gielis J, Brasili S, Symmetry : culture and science 32, 157 (2021). http://doi.org/10.26830/SYMMETRY_2021_2_157
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.
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.26830/SYMMETRY_2021_2_157
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Gielis J (2023) Fred Van Oystaeyen : Time hybrids: a new generic theory of reality. 347–351
Keywords: Review; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.26830/SYMMETRY_2023_3_357
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“Inequality measure of leaf area distribution for a drought-tolerant landscape plant”. Huang L, Ratkowsky DA, Hui C, Gielis J, Lian M, Shi P, Plants 12, 3143 (2023). http://doi.org/10.3390/PLANTS12173143
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.
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.3390/PLANTS12173143
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“Leaf functional traits : ecological and evolutionary implications”. Shi P, Gielis J, Niklas KJ, Niinemets Ü, Schrader J page 185 p. (2023).
Keywords: ME3 Book as editor; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.3389/978-2-83252-086-4
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“Simon Stevin as a central figure in the development of abstract algebra and generic programming”. Gielis J, Symmetry : culture and science 34, 155 (2023). http://doi.org/10.26830/SYMMETRY_2023_2_155
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.
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.26830/SYMMETRY_2023_2_155
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“Advanced particle swarm optimization methods for electromagnetics”. Mescia L, Bia P, Gielis J, Caratelli D, , 109 (2023). http://doi.org/10.55060/s.atmps.231115.010
Abstract: Electromagnetic design problems involve optimizing multiple parameters that are nonlinearly related to objective functions. Traditional optimization techniques require significant computational resources that grow exponentially as the problem size increases. Therefore, a method that can produce good results with moderate memory and computational resources is desirable. Bioinspired optimization methods, such as particle swarm optimization (PSO), are known for their computational efficiency and are commonly used in various scientific and technological fields. In this article we explore the potential of advanced PSO-based algorithms to tackle challenging electromagnetic design and analysis problems faced in real-life applications. It provides a detailed comparison between conventional PSO and its quantum-inspired version regarding accuracy and computational costs. Additionally, theoretical insights on convergence issues and sensitivity analysis on parameters influencing the stochastic process are reported. The utilization of a novel quantum PSO-based algorithm in advanced scenarios, such as reconfigurable and shaped lens antenna synthesis, is illustrated. The hybrid modeling approach, based on the unified geometrical description enabled by the Gielis Transformation, is applied in combination with a suitable quantum PSO-based algorithm, along with a geometrical tube tracing and physical optics technique for solving the inverse problem aimed at identifying the geometrical parameters that yield optimal antenna performance.
Keywords: P1 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.55060/s.atmps.231115.010
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“Conquering Mount Improbable”. Gielis J, , 153 (2023). http://doi.org/10.55060/s.atmps.231115.013
Abstract: Our scientific and technological worldviews are largely dominated by the concepts of entropy and complexity. Originating in 19th-century thermodynamics, the concept of entropy merged with information in the last century, leading to definitions of entropy and complexity by Kolmogorov, Shannon and others. In its simplest form, this worldview is an application of the normal rules of arithmetic. In this worldview, when tossing a coin, a million heads or tails in a row is theoretically possible, but impossible in practice and in real life. On this basis, the impossible (in the binary case, the outermost entries of Pascal's triangle xn and yn for large values of n) can be safely neglected, and one can concentrate fully on what is common and what conforms to the law of large numbers, in fields ranging from physics to sociology and everything in between. However, in recent decades it has been shown that what is most improbable tends to be the rule in nature. Indeed, if one combines the outermost entries xn and yn with the normal rules of arithmetic, either addition or multiplication, one obtains Lamé curves and power laws respectively. In this article, some of these correspondences are highlighted, leading to a double conclusion. First, Gabriel Lamé's geometric footprint in mathematics and the sciences is enormous. Second, conic sections are at the core once more. Whereas mathematics so far has been exclusively the language of patterns in the sciences, the door is opened for mathematics to also become the language of the individual. The probabilistic worldview and Lamé's footprint can be seen as dual methods. In this context, it is to be expected that the notions of information, complexity, simplicity and redundancy benefit from this different viewpoint.
Keywords: P1 Proceeding; Economics; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.55060/s.atmps.231115.013
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“Generalized Möbius-Listing bodies and the heart”. Gielis J, Tavkhelidze I, Ricci PE, Sn –, 2247-689x 13, 58 (2023)
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.
Keywords: A3 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
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“A note on Generalized Möbius-Listing Bodies”. Gielis J, Tavkhelidze I, , 31 (2023). http://doi.org/10.55060/s.atmps.231115.003
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
Keywords: P1 Proceeding; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.55060/s.atmps.231115.003
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“Plant morphology and function, geometric morphometrics, and modelling : decoding the mathematical secrets of plants”. Gao J, Huang W, Gielis J, Shi P, Plants 12, 3724 (2023). http://doi.org/10.3390/PLANTS12213724
Keywords: Editorial; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.3390/PLANTS12213724
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“Plant morphology and function, geometric morphometrics, and modelling : decoding the mathematical secrets of plants”. Gao J, Huang W, Gielis J, Shi P page 224 p. (2023).
Abstract: Delve into the diverse aspects of plant morphology, their responses to global climate change, and the spatiotemporal dynamics of forest productivity. Join us on a journey through the intricate web of plant characteristics and their impact on the environment.
Keywords: ME3 Book as editor; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.3390/BOOKS978-3-0365-9423-1
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“Proceedings of the 1st International Symposium on Square Bamboos and the Geometree (ISSBG 2022)”. Gielis J, Brasili S page xi, 175 p. (2023).
Keywords: ME3 Book as editor; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.55060/s.atmps.231115.000
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Brasili S, Gielis J (2024) Legacy and innovation across symmetry's dimensions. 005–006
Keywords: L1 Letter to the editor; Antwerp engineering, PhotoElectroChemistry & Sensing (A-PECS)
DOI: 10.26830/SYMMETRY_2024_1_005
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“Editorial: leaf functional traits : ecological and evolutionary implications”. Niklas KJ, Shi P, Gielis J, Schrader J, Niinemets U, Frontiers in plant science 14, 1169558 (2023). http://doi.org/10.3389/FPLS.2023.1169558
Keywords: Editorial; Sustainable Energy, Air and Water Technology (DuEL)
Impact Factor: 5.6
DOI: 10.3389/FPLS.2023.1169558
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“A simple way to calculate the volume and surface area of avian eggs”. Shi P, Chen L, Quinn BK, Yu K, Miao Q, Guo X, Lian M, Gielis J, Niklas KJ, Annals of the New York Academy of Sciences 1524, 118 (2023). http://doi.org/10.1111/NYAS.15000
Abstract: Egg geometry can be described using Preston's equation, which has seldom been used to calculate egg volume (V) and surface area (S) to explore S versus V scaling relationships. Herein, we provide an explicit re-expression of Preston's equation (designated as EPE) to calculate V and S, assuming that an egg is a solid of revolution. The side (longitudinal) profiles of 2221 eggs of six avian species were digitized, and the EPE was used to describe each egg profile. The volumes of 486 eggs from two avian species predicted by the EPE were compared with those obtained using water displacement in graduated cylinders. There was no significant difference in V using the two methods, which verified the utility of the EPE and the hypothesis that eggs are solids of revolution. The data also indicated that V is proportional to the product of egg length (L) and maximum width (W) squared. A 2/3-power scaling relationship between S and V for each species was observed, that is, S is proportional to (LW2)(2/3). These results can be extended to describe the shapes of the eggs of other species to study the evolution of avian (and perhaps reptilian) eggs.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
Impact Factor: 5.2
DOI: 10.1111/NYAS.15000
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“‘biogeom&rsquo, : an R package for simulating and fitting natural shapes”. Shi P, Gielis J, Quinn BK, Niklas KJ, Ratkowsky DA, Schrader J, Ruan H, Wang L, Niinemets Ü, Niinennets U, Annals of the New York Academy of Sciences 1516, 123 (2022). http://doi.org/10.1111/NYAS.14862
Abstract: Many natural objects exhibit radial or axial symmetry in a single plane. However, a universal tool for simulating and fitting the shapes of such objects is lacking. Herein, we present an R package called 'biogeom' that simulates and fits many shapes found in nature. The package incorporates novel universal parametric equations that generate the profiles of bird eggs, flowers, linear and lanceolate leaves, seeds, starfish, and tree-rings, and three growth-rate equations that generate the profiles of ovate leaves and the ontogenetic growth curves of animals and plants. 'biogeom' includes several empirical datasets comprising the boundary coordinates of bird eggs, fruits, lanceolate and ovate leaves, tree rings, seeds, and sea stars. The package can also be applied to other kinds of natural shapes similar to those in the datasets. In addition, the package includes sigmoid curves derived from the three growth-rate equations, which can be used to model animal and plant growth trajectories and predict the times associated with maximum growth rate. 'biogeom' can quantify the intra- or interspecific similarity of natural outlines, and it provides quantitative information of shape and ontogenetic modification of shape with important ecological and evolutionary implications for the growth and form of the living world.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
Impact Factor: 5.2
DOI: 10.1111/NYAS.14862
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“Comparison of a universal (but complex) model for avian egg shape with a simpler model”. Shi P, Gielis J, Niklas KJ, Annals of the New York Academy of Sciences 1514, 34 (2022). http://doi.org/10.1111/NYAS.14799
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.
Keywords: Editorial; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
Impact Factor: 5.2
DOI: 10.1111/NYAS.14799
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“Comparison of two polar equations in describing the geometries of domestic pigeon (Columba livia domestica) eggs”. Wang L, Griffin DK, Romanov MN, Gielis J, Poultry science , 104196 (2024). http://doi.org/10.1016/J.PSJ.2024.104196
Abstract: Two-dimensional (2D)egg-shape equa-tions are potent mathematical tools, facilitating the description of avian egg geometries in their applied mathematical modelling and poultry science implementations. In the present study, 2 distinct polar equations,namely the Carter-Morley-Jones equation (CMJE) and simplified Gielis equation(SGE), were used to fit the profile geometries of 415 domestic pigeon (Columba livia domestica) eggs based on nonlinear least squares regression methods.
Keywords: A1 Journal article; Antwerp engineering, PhotoElectroChemistry & Sensing (A-PECS)
Impact Factor: 4.4
DOI: 10.1016/J.PSJ.2024.104196
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Gielis J (2021) Double helix of phyllotaxis : analysis of the geometric model of plant morphogenesis, by Boris Rozin. 139–140
Keywords: Review; Sustainable Energy, Air and Water Technology (DuEL)
Impact Factor: 4.25
DOI: 10.1086/714470
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“New indices to balance α-diversity against tree size inequality”. Zhang L, Quinn BK, Hui C, Lian M, Gielis J, Gao J, Shi P, Journal of forestry research 35, 31 (2024). http://doi.org/10.1007/S11676-023-01686-3
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.
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
Impact Factor: 3
DOI: 10.1007/S11676-023-01686-3
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“Comparison of seed morphology of two ginkgo cultivars”. Tian F, Wang Y, Sandhu HS, Gielis J, Shi P, Journal Of Forestry Research 31, 751 (2020). http://doi.org/10.1007/S11676-018-0770-Y
Abstract: Ginkgo biloba L. is a precious relic tree species with important economic value. Seeds, as a vital reproductive organ of plants, can be used to distinguish cultivars of the species. We chose 400 seeds from two cultivars of ginkgo (Fozhi and Maling; 200 seeds for each cultivar) as the study material and used the Gielis equation to fit the projected shape of these seeds. The coefficients of variation (CV) in root mean squared errors (RMSE) obtained from the fitted data were used to compare the level of inter-cultivar variations in seed shape. We also used the covariance analysis to compare the allometric relationships between seed weights and projected areas of these two cultivars. The Gielis equation fitted well the seed shapes of two ginkgo cultivars. The lower CV in RMSE of cultivar Fozhi than Maling indicated a less symmetrical seed shape in the latter than the former. The bootstrap percentile method showed that the seed shape differences between the two cultivars were significant. However, there was no significant difference in the exponents between the seed weights and the projected areas of these two cultivars. Overall, the significant differences in shapes between the seeds of two ginkgo cultivars were well explained by the Gielis equation; this model can be further extended to compare morphological differences in other ginkgo cultivars, and even for plant seeds or animal eggs that have similar oval shapes.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
Impact Factor: 3
Times cited: 3
DOI: 10.1007/S11676-018-0770-Y
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“An elliptical blade is not a true ellipse, but a superellipse : evidence from two Michelia species”. Li Y, Niklas KJ, Gielis J, Niinemets Ü, Schrader J, Wang R, Shi P, Journal of forestry research 33, 1341 (2022). http://doi.org/10.1007/S11676-021-01385-X
Abstract: The shape of leaf laminae exhibits considerable diversity and complexity that reflects adaptations to environmental factors such as ambient light and precipitation as well as phyletic legacy. Many leaves appear to be elliptical which may represent a ‘default’ developmental condition. However, whether their geometry truly conforms to the ellipse equation (EE), i.e., (x/a)2 + (y/b)2 = 1, remains conjectural. One alternative is described by the superellipse equation (SE), a generalized version of EE, i.e., |x/a|n +|y/b|n = 1. To test the efficacy of EE versus SE to describe leaf geometry, the leaf shapes of two Michelia species (i.e., M. cavaleriei var. platypetala, and M. maudiae), were investigated using 60 leaves from each species. Analysis shows that the majority of leaves (118 out of 120) had adjusted root-mean-square errors of < 0.05 for the nonlinear fitting of SE to leaf geometry, i.e., the mean absolute deviation from the polar point to leaf marginal points was smaller than 5% of the radius of a hypothesized circle with its area equaling leaf area. The estimates of n for the two species were ˂ 2, indicating that all sampled leaves conformed to SE and not to EE. This study confirms the existence of SE in leaves, linking this to its potential functional advantages, particularly the possible influence of leaf shape on hydraulic conductance.
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
Impact Factor: 3
DOI: 10.1007/S11676-021-01385-X
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“A new approach to circular inversion in l₁-normed spaces”. Ermiş, T, Şen AO, Gielis J, Symmetry 16, 874 (2024). http://doi.org/10.3390/SYM16070874
Abstract: While there are well-known synthetic methods in the literature for finding the image of a point under circular inversion in l2-normed geometry (Euclidean geometry), there is no similar synthetic method in Minkowski geometry, also known as the geometry of finite-dimensional Banach spaces. In this study, we have succeeded in creating a synthetic construction of the circular inversion in l1-normed spaces, which is one of the most fundamental examples of Minkowski geometry. Moreover, this synthetic construction has been given using the Euclidean circle, independently of the l1-norm.
Keywords: A1 Journal article; Engineering sciences. Technology; Antwerp engineering, PhotoElectroChemistry & Sensing (A-PECS)
Impact Factor: 2.7
DOI: 10.3390/SYM16070874
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