| Records |
| Author |
Gielis, J.; Caratelli, D.; de Jong van Coevorden, M.; Ricci, P.E. |
| Title |
The common descent of biological shape description and special functions |
Type |
H1 Book chapter |
| Year |
2018 |
Publication |
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Abbreviated Journal |
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| Volume |
230 |
Issue |
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Pages  |
119-131
T2 - Differential and difference equations |
| Keywords |
H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
Gielis transformations, with their origin in botany, are used to define square waves and trigonometric functions of higher order. They are rewritten in terms of Chebyshev polynomials. The origin of both, a uniform descriptor and the origin of orthogonal polynomials, can be traced back to a letter of Guido Grandi to Leibniz in 1713 on the mathematical description of the shape of flowers. In this way geometrical description and analytical tools are seamlessly combined. |
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Wos |
000451375900010 |
Publication Date |
2018-05-08 |
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Series Title |
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Abbreviated Series Title |
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| Series Volume |
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Series Issue |
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Edition |
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| ISSN |
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ISBN |
978-3-319-75646-2; 2194-1009; 978-3-319-75647-9; 978-3-319-75646-2 |
Additional Links |
UA library record; WoS full record; WoS citing articles |
| Impact Factor |
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Times cited |
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Open Access |
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| Notes |
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Approved |
no |
| Call Number |
UA @ admin @ c:irua:150949 |
Serial |
7685 |
| Permanent link to this record |
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| Author |
Caratelli, D.; Gielis, J.; Tavkhelidze, I.; Ricci, P.E. |
| Title |
The Dirichlet problem for the Laplace equation in supershaped annuli |
Type |
A1 Journal article |
| Year |
2013 |
Publication |
Boundary value problems |
Abbreviated Journal |
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| Volume |
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Issue |
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Pages |
113-10 |
| Keywords |
A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
The Dirichlet problem for the Laplace equation in normal-polar annuli is addressed by using a suitable Fourier-like technique. Attention is in particular focused on the wide class of domains whose boundaries are defined by the so-called superformula introduced by Gielis. A dedicated numerical procedure based on the computer algebra system Mathematica© is developed in order to validate the proposed methodology. In this way, highly accurate approximations of the solution, featuring properties similar to the classical ones, are obtained. |
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Wos |
000325760900002&DestLinkType=CitingArticles&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7 |
Publication Date |
2013-05-03 |
| Series Editor |
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Series Title |
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Abbreviated Series Title |
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| Series Volume |
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Series Issue |
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Edition |
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| ISSN |
1687-2762; 1687-2770 |
ISBN |
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Additional Links |
UA library record; WoS citing articles; WoS full record |
| Impact Factor |
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Times cited |
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Open Access |
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| Notes |
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Approved |
no |
| Call Number |
UA @ admin @ c:irua:108644 |
Serial |
7812 |
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| Author |
Mescia, L.; Bia, P.; Gielis, J.; Caratelli, D. |
| Title |
Advanced particle swarm optimization methods for electromagnetics |
Type |
P1 Proceeding |
| Year |
2023 |
Publication |
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Abbreviated Journal |
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| Volume |
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Issue |
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Pages |
109-122
T2 - Proceedings of the 1st International |
| Keywords |
P1 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
Electromagnetic design problems involve optimizing multiple parameters that are nonlinearly related to objective functions. Traditional optimization techniques require significant computational resources that grow exponentially as the problem size increases. Therefore, a method that can produce good results with moderate memory and computational resources is desirable. Bioinspired optimization methods, such as particle swarm optimization (PSO), are known for their computational efficiency and are commonly used in various scientific and technological fields. In this article we explore the potential of advanced PSO-based algorithms to tackle challenging electromagnetic design and analysis problems faced in real-life applications. It provides a detailed comparison between conventional PSO and its quantum-inspired version regarding accuracy and computational costs. Additionally, theoretical insights on convergence issues and sensitivity analysis on parameters influencing the stochastic process are reported. The utilization of a novel quantum PSO-based algorithm in advanced scenarios, such as reconfigurable and shaped lens antenna synthesis, is illustrated. The hybrid modeling approach, based on the unified geometrical description enabled by the Gielis Transformation, is applied in combination with a suitable quantum PSO-based algorithm, along with a geometrical tube tracing and physical optics technique for solving the inverse problem aimed at identifying the geometrical parameters that yield optimal antenna performance. |
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Publication Date |
2023-11-29 |
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Series Title |
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Abbreviated Series Title |
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Series Issue |
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Edition |
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| ISSN |
978-90-833839-0-3 |
ISBN |
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Additional Links |
UA library record |
| Impact Factor |
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Times cited |
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Open Access |
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| Notes |
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Approved |
Most recent IF: NA |
| Call Number |
UA @ admin @ c:irua:201048 |
Serial |
9002 |
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| 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 |
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| 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. |
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Additional Links |
UA library record |
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Times cited |
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Open Access |
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| Notes |
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Approved |
no |
| Call Number |
UA @ admin @ c:irua:91090 |
Serial |
7982 |
| Permanent link to this record |
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| Author |
Gielis, J.; Caratelli, D.; Fougerolle, Y.; Ricci, P.E.; Gerats, T. |
| Title |
A biogeometrical model for corolla fusion in Asclepiad flowers |
Type |
H1 Book chapter |
| Year |
2017 |
Publication |
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Abbreviated Journal |
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| Volume |
2 |
Issue |
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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. |
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Thesis |
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Place of Publication |
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Wos |
000442076400007 |
Publication Date |
2017-04-20 |
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Series Title |
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Abbreviated Series Title |
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| Series Volume |
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Series Issue |
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Edition |
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| ISSN |
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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 |
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Times cited |
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Open Access |
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| Notes |
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Approved |
no |
| Call Number |
UA @ admin @ c:irua:144551 |
Serial |
7561 |
| Permanent link to this record |
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| 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 |
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| 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. |
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Wos |
000457142800037 |
Publication Date |
2019-01-03 |
| Series Editor |
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Series Title |
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Abbreviated Series Title |
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| Series Volume |
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Series Issue |
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Edition |
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| ISSN |
2079-9292 |
ISBN |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
| Impact Factor |
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Times cited |
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Open Access |
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| Notes |
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Approved |
no |
| Call Number |
UA @ admin @ c:irua:157203 |
Serial |
7765 |
| Permanent link to this record |
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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 |
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| 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. |
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Wos |
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Publication Date |
2020-02-23 |
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Additional Links |
UA library record |
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Times cited |
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Open Access |
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| Notes |
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Approved |
Most recent IF: NA |
| Call Number |
UA @ admin @ c:irua:167061 |
Serial |
6569 |
| Permanent link to this record |
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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 |
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Abbreviated Journal |
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| Volume |
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Issue |
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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. |
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Edition |
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ISBN |
978-1-119-74985-1 |
Additional Links |
UA library record |
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Times cited |
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Open Access |
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| Notes |
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Approved |
Most recent IF: NA |
| Call Number |
UA @ admin @ c:irua:186731 |
Serial |
7165 |
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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 |
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| Volume |
17 |
Issue |
1 |
Pages |
1-20 |
| Keywords |
A1 Journal article; Educational sciences; Sustainable Energy, Air and Water Technology (DuEL) |
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Abbreviated Series Title |
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Series Issue |
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Edition |
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| ISSN |
1451-4966; 2406-1077 |
ISBN |
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Additional Links |
UA library record |
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Times cited |
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Open Access |
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Approved |
no |
| Call Number |
UA @ admin @ c:irua:128660 |
Serial |
8327 |
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| Author |
Gielis, J.; Shi, P.; Caratelli, D. |
| Title |
Universal equations : a fresh perspective |
Type |
A1 Journal article |
| Year |
2022 |
Publication |
Growth and Form |
Abbreviated Journal |
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| Volume |
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Issue |
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Pages |
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| Keywords |
A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
A uniform description of natural shapes and phenomena is an important goal in science. Such description should check some basic principles, related to 1) the complexity of the model, 2) how well its fits real objects, phenomena and data, and 3) ia direct connection with optimization principles and the calculus of variations. In this article, we present nine principles, three for each group, and we compare some models with a claim to universality. It is also shown that Gielis Transformations and power laws have a common origin in conic sections |
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Additional Links |
UA library record |
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Times cited |
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Open Access |
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| Notes |
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Approved |
Most recent IF: NA |
| Call Number |
UA @ admin @ c:irua:189317 |
Serial |
7224 |
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| Author |
Gielis, J.; Shi, P.; Beirinckx, B.; Caratelli, D.; Ricci, P.E. |
| Title |
Lamé-Gielis curves in biology and geometry |
Type |
P3 Proceeding |
| Year |
2021 |
Publication |
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Abbreviated Journal |
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Issue |
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Pages |
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P3 Proceeding; Sustainable Energy, Air and Water Technology (DuEL) |
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UA library record |
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Times cited |
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Open Access |
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Approved |
Most recent IF: NA |
| Call Number |
UA @ admin @ c:irua:178828 |
Serial |
8145 |
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| Author |
Caratelli, D.; Gielis, J.; Ricci, P.E.; Tavkhelidze, I. |
| Title |
Some properties of “bulky” links, generated by Generalized Möbius Listing's bodies GML4n |
Type |
P3 Proceeding |
| Year |
2013 |
Publication |
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Abbreviated Journal |
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Issue |
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Pages |
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P3 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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Additional Links |
UA library record |
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Times cited |
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Open Access |
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Approved |
no |
| Call Number |
UA @ admin @ c:irua:108672 |
Serial |
8555 |
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