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Gielis, J.; Caratelli, D.; Shi, P.; Ricci, P.E. |
![goto web page (via DOI) doi](http://nano.uantwerpen.be/nanorefs/img/doi.gif)
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Title |
A note on spirals and curvature |
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A1 Journal article |
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2020 |
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Growth and form |
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1 |
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1 |
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1-8 |
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A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
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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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2020-02-23 |
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UA @ admin @ c:irua:167061 |
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6569 |
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Author |
De Tommasi, E.; Rogato, A.; Caratelli, D.; Mescia, L.; Gielis, J. |
![find book details (via ISBN) isbn](img/isbn.gif)
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Title |
Following the photons route : mathematical models describing the interaction of diatoms with light |
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H1 Book chapter |
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Year |
2022 |
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1-53 |
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H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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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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978-1-119-74985-1 |
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Call Number |
UA @ admin @ c:irua:186731 |
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7165 |
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Ricci, P.E.; Gielis, J. |
![find book details (via ISBN) isbn](img/isbn.gif)
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Title |
From Pythagoras to Fourier and from geometry to nature |
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MA3 Book as author |
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2022 |
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146 p. |
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MA3 Book as author; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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2022-03-23 |
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978-90-832323-0-0; 978-90-832323-1-7 |
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UA @ admin @ c:irua:186730 |
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7166 |
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Gielis, J.; Grigolia, R. |
![find record details (via OpenURL) openurl](img/xref.gif)
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Title |
Lamé curves and Rvachev's R-functions |
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A3 Journal article |
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Year |
2022 |
Publication |
Sn – 1512-0066 |
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37 |
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1-4 |
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A3 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
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Gielis transformations are a generalization of Lame curves. To combine domains, we can make use of the natural alliance between Lame's work and Rvachev's R-functions. A logical next step is the extension to n-valued logic dening dierent partitions. |
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UA @ admin @ c:irua:189316 |
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7178 |
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Gielis, J.; Shi, P.; Caratelli, D. |
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Title |
Universal equations : a fresh perspective |
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A1 Journal article |
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2022 |
Publication |
Growth and Form |
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A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
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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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UA @ admin @ c:irua:189317 |
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7224 |
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Gielis, J.; Tavkelidze, I.; Ricci, P.E. |
![find record details (via OpenURL) openurl](img/xref.gif)
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Title |
About “bulky” links, generated by generalized Möbius-Listing bodies |
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H3 Book chapter |
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2011 |
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115-128
T2 - Proceedings of the International Conf |
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H3 Book chapter; Sustainable Energy, Air and Water Technology (DuEL) |
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978-9941-0-3727-6 |
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UA @ admin @ c:irua:97753 |
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7403 |
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Tavkhelidze, I.; Gielis, J.; Pinelas, S. |
![find record details (via OpenURL) openurl](img/xref.gif)
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About some methods of analytic representation and classification of a wide set of geometric figures with “complex” configuration |
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A3 Journal article |
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2020 |
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Sn – 1512-0066 |
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34 |
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81-84 |
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A3 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
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UA @ admin @ c:irua:174475 |
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7406 |
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Tavkhelidze, I.; Gielis, J.; Pinelas, S. |
![goto web page (via DOI) doi](http://nano.uantwerpen.be/nanorefs/img/doi.gif)
![find record details (via OpenURL) openurl](img/xref.gif)
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About some methods of analytic representation and classification of a wide set of geometric figures with “complex” configuration |
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H1 Book chapter |
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2020 |
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347-359
T2 - Differential and difference equations |
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H1 Book chapter; Sustainable Energy, Air and Water Technology (DuEL) |
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2020-10-21 |
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978-3-030-56322-6 |
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UA @ admin @ c:irua:174479 |
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7407 |
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Gielis, J.; Caratelli, D.; Fougerolle, Y.; Ricci, P.E.; Gerats, T. |
![find book details (via ISBN) isbn](img/isbn.gif)
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Title |
A biogeometrical model for corolla fusion in Asclepiad flowers |
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H1 Book chapter |
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2017 |
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2 |
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83-105
T2 - Modeling in mathematics : proceedings |
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H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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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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000442076400007 |
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2017-04-20 |
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978-94-6239-260-1; 978-94-6239-261-8; 2543-0300; 978-94-6239-260-1 |
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UA library record; WoS full record; WoS citing articles |
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no |
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UA @ admin @ c:irua:144551 |
Serial |
7561 |
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Gielis, J.; Caratelli, D.; Tavkelidze, I.; Fougerolle, Y.; Ricci, P.E.; Gerats, T. |
![find record details (via OpenURL) openurl](img/xref.gif)
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Title |
Bulky knots and links generated by cutting generalized Mobius-Listing bodies and applications in the natural sciences |
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H2 Book chapter |
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2013 |
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167-183
T2 - Math Art Summit : Koninklijke Vlaamse |
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H2 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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978-90-6569-119-4 |
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UA @ admin @ c:irua:110955 |
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7569 |
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Gielis, J.; Caratelli, D.; de Jong van Coevorden, M.; Ricci, P.E. |
![find book details (via ISBN) isbn](img/isbn.gif)
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Title |
The common descent of biological shape description and special functions |
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H1 Book chapter |
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2018 |
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230 |
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119-131
T2 - Differential and difference equations |
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H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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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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000451375900010 |
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2018-05-08 |
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978-3-319-75646-2; 2194-1009; 978-3-319-75647-9; 978-3-319-75646-2 |
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UA library record; WoS full record; WoS citing articles |
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UA @ admin @ c:irua:150949 |
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7685 |
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Van den Akker, S.; Bormans, P.; Peeters, H.; Gielis, J.; Prinsen, E. |
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Cytokinin dynamics in cell suspension cultures of Bambusa balcooa Roxburgh using UPLC-ESI/MS/MS |
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H3 Book chapter |
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2012 |
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539-547
T2 - Proceedings of the 9th World Bamboo C |
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H3 Book chapter; Engineering sciences. Technology; Integrated Molecular Plant Physiology Research (IMPRES); Sustainable Energy, Air and Water Technology (DuEL) |
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UA @ admin @ c:irua:97754 |
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7750 |
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Author |
Bia, P.; Caratelli, D.; Mescia, L.; Gielis, J. |
![find record details (via OpenURL) openurl](img/xref.gif)
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Title |
Electromagnetic characterization of supershaped lens antennas for high-frequency applications |
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H1 Book chapter |
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2013 |
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1679-1682
T2 - Proceedings of the 43rd European Mi |
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H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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000330768700424 |
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978-2-87487-031-6 |
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UA library record; WoS full record; WoS citing articles |
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UA @ admin @ c:irua:110954 |
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7865 |
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Author |
Caratelli, D.; Gielis, J.; Ricci, P.E. |
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Title |
Fourier-like solution of the Dirichlet problem for the Laplace Equation in k-type Gielis domains |
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A1 Journal article |
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2011 |
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Journal of pure and applied mathematics : advances and applications |
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5 |
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2 |
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99-111 |
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A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
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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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no |
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Call Number |
UA @ admin @ c:irua:91090 |
Serial |
7982 |
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Author |
Gielis, J.; Caratelli, D.; Tavkhelidze, I. |
![goto web page (via DOI) doi](http://nano.uantwerpen.be/nanorefs/img/doi.gif)
![find record details (via OpenURL) openurl](img/xref.gif)
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Title |
The general case of cutting GML bodies : the geometrical solution |
Type |
H1 Book chapter |
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Year |
2020 |
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Pages |
397-411
T2 - Differential and difference equations |
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Keywords |
H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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2020-10-21 |
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978-3-030-56322-6 |
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Most recent IF: NA |
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Call Number |
UA @ admin @ c:irua:174477 |
Serial |
7991 |
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Author |
Gielis, J. |
![find book details (via ISBN) isbn](img/isbn.gif)
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Title |
The geometrical beauty of plants |
Type |
MA3 Book as author |
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Year |
2017 |
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Pages |
229 p. |
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MA3 Book as author; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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2017-06-01 |
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978-94-6239-150-5; 978-94-6239-151-2 |
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Call Number |
UA @ admin @ c:irua:144554 |
Serial |
7997 |
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Author |
Gielis, J.; Shi, P.; Beirinckx, B.; Caratelli, D.; Ricci, P.E. |
![find record details (via OpenURL) openurl](img/xref.gif)
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Title |
Lamé-Gielis curves in biology and geometry |
Type |
P3 Proceeding |
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Year |
2021 |
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P3 Proceeding; Sustainable Energy, Air and Water Technology (DuEL) |
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Most recent IF: NA |
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Call Number |
UA @ admin @ c:irua:178828 |
Serial |
8145 |
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Author |
Gielis, J.; Tavkhelidze, I. |
![find record details (via OpenURL) openurl](img/xref.gif)
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Title |
The Mӧbius phenomenon in Generalized Mӧbius-Listing bodies with cross sections of odd and even polygons |
Type |
A3 Journal article |
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Year |
2020 |
Publication |
Sn – 1512-0066 |
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34 |
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23-26 |
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A3 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
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Most recent IF: NA |
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Call Number |
UA @ admin @ c:irua:174474 |
Serial |
8257 |
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Author |
Gielis, J.; Ricci, P.E.; Tavkhelidze, I. |
![goto web page url](http://nano.uantwerpen.be/nanorefs/img/www.gif)
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Title |
The Möbius phenomenon in Generalized Möbius-Listing surfaces and bodies, and Arnold's Cat phenomenon |
Type |
A1 Journal article |
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Year |
2021 |
Publication |
Advanced Studies : Euro-Tbilisi Mathematical Journal |
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Volume |
14 |
Issue |
4 |
Pages |
17-35 |
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Keywords |
A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
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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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OpenAccess |
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Approved |
Most recent IF: NA |
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Call Number |
UA @ admin @ c:irua:183081 |
Serial |
8258 |
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Author |
Gielis, J.; Ricci, P.E.; Tavkhelidze, I. |
![find book details (via ISBN) isbn](img/isbn.gif)
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Title |
Modeling in mathematics : proceedings of the second Tbilisi-Salerno workshop on modeling in mathematics |
Type |
ME3 Book as editor |
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Year |
2017 |
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Abbreviated Journal |
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Volume |
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Issue |
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Pages |
185 p. |
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ME3 Book as editor; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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2017-04-20 |
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978-94-6239-260-1; 978-94-6239-261-8 |
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no |
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Call Number |
UA @ admin @ c:irua:144553 |
Serial |
8263 |
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Author |
Gielis, J.; Natalini, P.; Ricci, P.E. |
![find book details (via ISBN) isbn](img/isbn.gif)
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Title |
A note about generalized forms of the Gielis formula |
Type |
H1 Book chapter |
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Year |
2017 |
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Abbreviated Journal |
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Volume |
2 |
Issue |
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Pages |
107-116
T2 - Modeling in mathematics : proceedings |
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Keywords |
H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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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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000442076400008 |
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2017-04-20 |
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978-94-6239-260-1; 978-94-6239-261-8; 2543-0300; 978-94-6239-260-1 |
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UA library record; WoS full record; WoS citing articles |
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no |
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UA @ admin @ c:irua:144550 |
Serial |
8318 |
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Author |
Tavkhelidze, I.; Caratelli, D.; Gielis, J.; Ricci, P.E.; Rogava, M.; Transirico, M. |
![find book details (via ISBN) isbn](img/isbn.gif)
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Title |
On a geometric model of bodies with “complex” configuration and some movements |
Type |
H1 Book chapter |
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2017 |
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2 |
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Pages |
129-158
T2 - Modeling in mathematics : proceedings |
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Keywords |
H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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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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000442076400010 |
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2017-04-20 |
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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 |
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no |
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Call Number |
UA @ admin @ c:irua:144552 |
Serial |
8326 |
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Author |
Gielis, J.; Potters, G. |
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Title |
Proceedings of the 9th World Bamboo Congress, Antwerp 2012 |
Type |
P3 Proceeding |
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2012 |
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P3 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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no |
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Call Number |
UA @ admin @ c:irua:97756 |
Serial |
8413 |
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Author |
Tavkhelidze, I.; Gielis, J. |
![find record details (via OpenURL) openurl](img/xref.gif)
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Title |
The process of cutting GMLmn bodies with dm-knives |
Type |
A3 Journal article |
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Year |
2018 |
Publication |
Sn – 1512-0066 |
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32 |
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67-70 |
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A3 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
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no |
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Call Number |
UA @ admin @ c:irua:159971 |
Serial |
8417 |
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Author |
Caratelli, D.; Gielis, J.; Ricci, P.E.; Tavkhelidze, I. |
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Title |
Some properties of “bulky” links, generated by Generalized Möbius Listing's bodies GML4n |
Type |
P3 Proceeding |
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2013 |
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P3 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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Call Number |
UA @ admin @ c:irua:108672 |
Serial |
8555 |
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Author |
Tavkhelidze, I.; Gielis, J. |
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Title |
Structure of the dm knives and process of cutting of GML(man) or GRT(man) bodies |
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A3 Journal article |
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Year |
2019 |
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Sn – 1512-0066 |
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33 |
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A3 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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no |
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Call Number |
UA @ admin @ c:irua:164897 |
Serial |
8588 |
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Author |
Gielis, J. |
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Title |
Temperate bamboos in ornamental horticulture: differentiators and spillover effects into the 21st century |
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H3 Book chapter |
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2012 |
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603-623
T2 - Proceedings of the 9th World Bamboo C |
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H3 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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no |
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Call Number |
UA @ admin @ c:irua:97755 |
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8644 |
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Author |
Gielis, J.; Ding, Y.; Shi, P. |
![find record details (via OpenURL) openurl](img/xref.gif)
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Title |
Towards a geometrical theory of morphology and morphogenesis |
Type |
P3 Proceeding |
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2016 |
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P3 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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no |
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Call Number |
UA @ admin @ c:irua:144548 |
Serial |
8677 |
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Author |
Gielis, J. |
![goto web page (via DOI) doi](http://nano.uantwerpen.be/nanorefs/img/doi.gif)
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Title |
Fred Van Oystaeyen : Time hybrids: a new generic theory of reality |
Type |
Review |
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Year |
2023 |
Publication |
Symmetry, Culture and Science |
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Volume |
34 |
Issue |
3 |
Pages |
347-351 |
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Keywords |
Review; Sustainable Energy, Air and Water Technology (DuEL) |
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Open Access |
OpenAccess |
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Approved |
Most recent IF: NA |
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Call Number |
UA @ admin @ c:irua:199538 |
Serial |
8871 |
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Author |
Shi, P.; Gielis, J.; Niklas, K.J.; Niinemets, Ü.; Schrader, J. |
![goto web page (via DOI) doi](http://nano.uantwerpen.be/nanorefs/img/doi.gif)
![find record details (via OpenURL) openurl](img/xref.gif)
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Title |
Leaf functional traits : ecological and evolutionary implications |
Type |
ME3 Book as editor |
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Year |
2023 |
Publication |
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Abbreviated Journal |
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Volume |
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Issue |
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Pages |
185 p. |
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Keywords |
ME3 Book as editor; Sustainable Energy, Air and Water Technology (DuEL) |
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2023-04-14 |
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ISBN |
978-2-8325-2086-4; 1664-8714 |
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Open Access |
OpenAccess |
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Approved |
Most recent IF: NA |
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Call Number |
UA @ admin @ c:irua:198002 |
Serial |
8894 |
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Permanent link to this record |