Records |
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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Volume |
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Issue |
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Pages |
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Keywords |
P3 Proceeding; Sustainable Energy, Air and Water Technology (DuEL) |
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UA library record |
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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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Volume |
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Issue |
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Pages |
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Keywords |
P3 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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Approved |
no |
Call Number |
UA @ admin @ c:irua:108672 |
Serial |
8555 |
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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Publication Date |
2020-02-23 |
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UA library record |
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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 |
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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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Edition |
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ISSN |
1451-4966; 2406-1077 |
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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:128660 |
Serial |
8327 |
Permanent link to this record |
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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 |
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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. |
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Wos |
000316567700002 |
Publication Date |
2013-03-13 |
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 |
1120-6357 |
ISBN |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
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Times cited |
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Open Access |
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Approved |
no |
Call Number |
UA @ admin @ c:irua:107174 |
Serial |
7405 |
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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 |
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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. |
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000774655100002 |
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UA library record; WoS full record |
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Times cited |
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Open Access |
OpenAccess |
Notes |
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Approved |
Most recent IF: NA |
Call Number |
UA @ admin @ c:irua:183081 |
Serial |
8258 |
Permanent link to this record |
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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 |
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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. |
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Wos |
http://rjm-cs.ro/2023v13i2_7.pdf#page=1 |
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Additional Links |
UA library record; http://rjm-cs.ro/2023v13i2_7.pdf#page=1 |
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:200773 |
Serial |
9043 |
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 |
|
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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Wos |
000442076400007 |
Publication Date |
2017-04-20 |
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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 |
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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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.; Natalini, P.; Ricci, P.E. |
Title |
A note about generalized forms of the Gielis formula |
Type |
H1 Book chapter |
Year |
2017 |
Publication |
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Abbreviated Journal |
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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). |
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Place of Publication |
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Wos |
000442076400008 |
Publication Date |
2017-04-20 |
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 |
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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:144550 |
Serial |
8318 |
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 |
|
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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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 |
Permanent link to this record |
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Author |
Gielis, J.; Tavkelidze, I.; Ricci, P.E. |
Title |
About “bulky” links, generated by generalized Möbius-Listing bodies |
Type |
H3 Book chapter |
Year |
2011 |
Publication |
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Abbreviated Journal |
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Volume |
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Issue |
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Pages |
115-128
T2 - Proceedings of the International Conf |
Keywords |
H3 Book chapter; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
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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 |
978-9941-0-3727-6 |
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:97753 |
Serial |
7403 |
Permanent link to this record |
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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 |
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 |
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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 |
Tavkhelidze, I.; Caratelli, D.; Gielis, J.; Ricci, P.E.; Rogava, M.; Transirico, M. |
Title |
On a geometric model of bodies with “complex” configuration and some movements |
Type |
H1 Book chapter |
Year |
2017 |
Publication |
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Abbreviated Journal |
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Volume |
2 |
Issue |
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Pages |
129-158
T2 - Modeling in mathematics : proceedings |
Keywords |
H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
Aim of this chapter is analytical representation of one wide class of geometric figures (lines, surfaces and bodies) and their complicated displacements. The accurate estimation of physical characteristics (such as volume, surface area, length, or other specific parameters) relevant to human organs is of fundamental importance in medicine. One central idea of this article is, in this respect, to provide a general methodology for the evaluation, as a function of time, of the volume and center of gravity featured by moving of one class of bodies used of describe different human organs. |
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Place of Publication |
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Wos |
000442076400010 |
Publication Date |
2017-04-20 |
Series Editor |
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Abbreviated Series Title |
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Series Volume |
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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:144552 |
Serial |
8326 |
Permanent link to this record |
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Author |
Ricci, P.E.; Gielis, J. |
Title |
From Pythagoras to Fourier and from geometry to nature |
Type |
MA3 Book as author |
Year |
2022 |
Publication |
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Abbreviated Journal |
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Volume |
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Issue |
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Pages |
146 p. |
Keywords |
MA3 Book as author; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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Publication Date |
2022-03-23 |
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Abbreviated Series Title |
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Series Issue |
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Edition |
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ISBN |
978-90-832323-0-0; 978-90-832323-1-7 |
Additional Links |
UA library record |
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Times cited |
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Open Access |
Not_Open_Access |
Notes |
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Approved |
Most recent IF: NA |
Call Number |
UA @ admin @ c:irua:186730 |
Serial |
7166 |
Permanent link to this record |
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Author |
Gielis, J.; Caratelli, D.; Tavkelidze, I.; Fougerolle, Y.; Ricci, P.E.; Gerats, T. |
Title |
Bulky knots and links generated by cutting generalized Mobius-Listing bodies and applications in the natural sciences |
Type |
H2 Book chapter |
Year |
2013 |
Publication |
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Abbreviated Journal |
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Volume |
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Issue |
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Pages |
167-183
T2 - Math Art Summit : Koninklijke Vlaamse |
Keywords |
H2 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
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Corporate Author |
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Publisher |
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Place of Publication |
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Publication Date |
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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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Edition |
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ISSN |
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ISBN |
978-90-6569-119-4 |
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:110955 |
Serial |
7569 |
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Author |
Gielis, J.; Ricci, P.E.; Tavkhelidze, I. |
Title |
Modeling in mathematics : proceedings of the second Tbilisi-Salerno workshop on modeling in mathematics |
Type |
ME3 Book as editor |
Year |
2017 |
Publication |
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Abbreviated Journal |
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Volume |
|
Issue |
|
Pages |
185 p. |
Keywords |
ME3 Book as editor; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
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Address |
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Corporate Author |
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Thesis |
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Publisher |
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Place of Publication |
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Editor |
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Language |
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Wos |
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Publication Date |
2017-04-20 |
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 |
|
ISSN |
|
ISBN |
978-94-6239-260-1; 978-94-6239-261-8 |
Additional Links |
UA library record |
Impact Factor |
|
Times cited |
|
Open Access |
|
Notes |
|
Approved |
no |
Call Number |
UA @ admin @ c:irua:144553 |
Serial |
8263 |
Permanent link to this record |
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|
Author |
Caratelli, D.; Gielis, J.; Tavkhelidze, I.; Ricci, P.E. |
Title |
Fourier-Hankel solution of the Robin problem for the Helmholtz equation in supershaped annular domains |
Type |
A1 Journal article |
Year |
2013 |
Publication |
Boundary value problems |
Abbreviated Journal |
|
Volume |
|
Issue |
|
Pages |
253 |
Keywords |
A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
The Robin problem for the Helmholtz equation in normal-polar annuli is addressed by using a suitable Fourier-Hankel series 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. |
Address |
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Corporate Author |
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Thesis |
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Publisher |
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Place of Publication |
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Editor |
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Language |
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Wos |
000340237600004 |
Publication Date |
2013-11-22 |
Series Editor |
|
Series Title |
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Abbreviated Series Title |
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Series Volume |
|
Series Issue |
|
Edition |
|
ISSN |
1687-2762; 1687-2770 |
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:111558 |
Serial |
7981 |
Permanent link to this record |
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|
|
Author |
Caratelli, D.; Gielis, J.; Tavkhelidze, I.; Ricci, P.E. |
Title |
Spherical harmonic solution of the Robin problem for the Helmholtz equation in a supershaped shell |
Type |
A1 Journal article |
Year |
2013 |
Publication |
Applied mathematics |
Abbreviated Journal |
|
Volume |
4 |
Issue |
1a |
Pages |
263-270 |
Keywords |
A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
The Robin problem for the Helmholtz equation in normal-polar shells is addressed by using a suitable spherical harmonic expansion technique. Attention is in particular focused on the wide class of domains whose boundaries are defined by a generalized version of the so-called superformula introduced by Gielis. A dedicated numerical procedure based on the computer algebra system Mathematica? is developed in order to validate the proposed methodology. In this way, highly accurate approximations of the solution, featuring properties similar to the classical ones, are obtained. |
Address |
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Corporate Author |
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Thesis |
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Publisher |
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Place of Publication |
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Editor |
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Language |
|
Wos |
|
Publication Date |
2013-01-30 |
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
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Series Volume |
|
Series Issue |
|
Edition |
|
ISSN |
2152-7385 |
ISBN |
|
Additional Links |
UA library record |
Impact Factor |
|
Times cited |
|
Open Access |
|
Notes |
|
Approved |
no |
Call Number |
UA @ admin @ c:irua:107177 |
Serial |
8576 |
Permanent link to this record |
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Author |
Gielis, J.; Tavkhelidze, I.; Ricci, P.E. |
Title |
About “bulky” links generated by generalized Möbius-Listing bodies GML2n |
Type |
A2 Journal article |
Year |
2013 |
Publication |
Journal of mathematical sciences |
Abbreviated Journal |
|
Volume |
193 |
Issue |
3 |
Pages |
449-460 |
Keywords |
A2 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
In this paper, we consider the bulky knots and bulky links, which appear after cutting of a Generalized MöbiusListing GMLn2 body (with the radial cross section a convex plane 2-symmetric figure with two vertices) along a different Generalized MöbiusListing surfaces GMLn2 situated in it. The aim of this report is to investigate the number and geometric structure of the independent objects that appear after such a cutting process of GMLn2 bodies. In most cases we are able to count the indices of the resulting mathematical objects according to the known classification for the standard knots and links. |
Address |
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Corporate Author |
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Thesis |
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Publisher |
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Place of Publication |
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Editor |
|
Language |
|
Wos |
|
Publication Date |
2013-08-03 |
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
Series Volume |
|
Series Issue |
|
Edition |
|
ISSN |
1072-3374; 1573-8795 |
ISBN |
|
Additional Links |
UA library record |
Impact Factor |
|
Times cited |
|
Open Access |
|
Notes |
|
Approved |
no |
Call Number |
UA @ admin @ c:irua:110953 |
Serial |
7404 |
Permanent link to this record |
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Author |
Caratelli, D.; Gielis, J.; Natalini, P.; Ricci, P.E.; Tavkhelidze, I. |
Title |
The Robin problem for the Helmholtz equation in a starlike planar domain |
Type |
A1 Journal article |
Year |
2011 |
Publication |
Georgian mathematical journal |
Abbreviated Journal |
|
Volume |
18 |
Issue |
3 |
Pages |
465-479 |
Keywords |
A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
The interior and exterior Robin problems for the Helmholtz equation in starlike planar domains are addressed by using a suitable Fourier-like technique. Attention is in particular focused on normal-polar domains whose boundaries are defined by the so-called superformula introduced by J. Gielis. A dedicated numerical procedure based on the computer algebra system Mathematica© is developed in order to validate the proposed approach. In this way, highly accurate approximations of the solution, featuring properties similar to the classical ones, are obtained. The computed results are found to be in good agreement with the theoretical findings on Fourier series expansion presented by L. Carleson. |
Address |
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Corporate Author |
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Thesis |
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Publisher |
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Place of Publication |
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Editor |
|
Language |
|
Wos |
000296166100004 |
Publication Date |
2021-02-28 |
Series Editor |
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Series Title |
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Abbreviated Series Title |
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Series Volume |
|
Series Issue |
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Edition |
|
ISSN |
1072-947x |
ISBN |
|
Additional Links |
UA library record; WoS full record; WoS citing articles |
Impact Factor |
|
Times cited |
|
Open Access |
|
Notes |
|
Approved |
no |
Call Number |
UA @ admin @ c:irua:91086 |
Serial |
8658 |
Permanent link to this record |
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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 |
A2 Journal article |
Year |
2016 |
Publication |
Journal of mathematical sciences |
Abbreviated Journal |
|
Volume |
216 |
Issue |
4 |
Pages |
509-518 |
Keywords |
A2 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
In the present paper, we consider the bulky knots and bulky links that appear after cutting of generalized MöbiusListing GML 4 n bodies (with corresponding radial cross sections square) along different generalized MöbiusListing surfaces GML 2 n situated in it. The aim of this article is to examine the number and geometric structure of independent objects that appear after such a cutting process of GML 4 n bodies. In most cases, we are able to count the indices of the resulting mathematical objects according to the known tabulation for knots and links of small complexity. |
Address |
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Corporate Author |
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Thesis |
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Publisher |
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Place of Publication |
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Editor |
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Language |
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Wos |
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Publication Date |
2016-06-10 |
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 |
1072-3374; 1573-8795 |
ISBN |
|
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 |
no |
Call Number |
UA @ admin @ c:irua:133948 |
Serial |
8554 |
Permanent link to this record |
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Author |
Wang, L.; Ratkowsky, D.A.; Gielis, J.; Ricci, P.E.; Shi, P. |
Title |
Effects of the numerical values of the parameters in the Gielis equation on its geometries |
Type |
A1 Journal article |
Year |
2022 |
Publication |
Symmetry |
Abbreviated Journal |
Symmetry-Basel |
Volume |
14 |
Issue |
12 |
Pages |
2475-12 |
Keywords |
A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
The Lamé curve is an extension of an ellipse, the latter being a special case. Dr. Johan Gielis further extended the Lamé curve in the polar coordinate system by introducing additional parameters (n1, n2, n3; m): rφ=1Acosm4φn2+1Bsinm4φn3−1/n1, which can be applied to model natural geometries. Here, r is the polar radius corresponding to the polar angle φ; A, B, n1, n2 and n3 are parameters to be estimated; m is the positive real number that determines the number of angles of the Gielis curve. Most prior studies on the Gielis equation focused mainly on its applications. However, the Gielis equation can also generate a large number of shapes that are rotationally symmetric and axisymmetric when A = B and n2 = n3, interrelated with the parameter m, with the parameters n1 and n2 determining the shapes of the curves. In this paper, we prove the relationship between m and the rotational symmetry and axial symmetry of the Gielis curve from a theoretical point of view with the condition A = B, n2 = n3. We also set n1 and n2 to take negative real numbers rather than only taking positive real numbers, then classify the curves based on extremal properties of r(φ) at φ = 0, π/m when n1 and n2 are in different intervals, and analyze how n1, n2 precisely affect the shapes of Gielis curves. |
Address |
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Corporate Author |
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Thesis |
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Publisher |
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Place of Publication |
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Editor |
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Language |
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Wos |
000904525700001 |
Publication Date |
2022-11-23 |
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 |
2073-8994 |
ISBN |
|
Additional Links |
UA library record; WoS full record |
Impact Factor |
2.7 |
Times cited |
|
Open Access |
OpenAccess |
Notes |
|
Approved |
Most recent IF: 2.7 |
Call Number |
UA @ admin @ c:irua:191860 |
Serial |
7301 |
Permanent link to this record |
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Author |
Gielis, J.; Caratelli, D.; Fougerolle, Y.; Ricci, P.E.; Tavkelidze, I.; Gerats, T. |
Title |
Universal natural shapes : from unifying shape description to simple methods for shape analysis and boundary value problems |
Type |
A1 Journal article |
Year |
2012 |
Publication |
PLoS ONE |
Abbreviated Journal |
|
Volume |
7 |
Issue |
9 |
Pages |
e29324-11 |
Keywords |
A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
Gielis curves and surfaces can describe a wide range of natural shapes and they have been used in various studies in biology and physics as descriptive tool. This has stimulated the generalization of widely used computational methods. Here we show that proper normalization of the Levenberg-Marquardt algorithm allows for efficient and robust reconstruction of Gielis curves, including self-intersecting and asymmetric curves, without increasing the overall complexity of the algorithm. Then, we show how complex curves of k-type can be constructed and how solutions to the Dirichlet problem for the Laplace equation on these complex domains can be derived using a semi-Fourier method. In all three methods, descriptive and computational power and efficiency is obtained in a surprisingly simple way. |
Address |
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Corporate Author |
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Thesis |
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Publisher |
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Place of Publication |
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Editor |
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Language |
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Wos |
000309517500001 |
Publication Date |
2012-09-30 |
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 |
1932-6203 |
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 |
|
Approved |
no |
Call Number |
UA @ admin @ c:irua:102202 |
Serial |
8711 |
Permanent link to this record |