國立虎尾科技大學 |

Helices

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Helices/ by Angel Ferrandez Izquierdo.
作者:	Ferrandez Izquierdo, Angel.
出版者:	Cham :Springer Nature Switzerland : : 2025.,
面頁冊數:	xix, 230 p. :ill., digital ; : 24 cm.;
Contained By:	Springer Nature eBook
標題:	Helices (Algebraic topology) -
電子資源:	https://doi.org/10.1007/978-3-032-09663-0
ISBN:	9783032096630

Helices
Ferrandez Izquierdo, Angel.

Helices[electronic resource] /by Angel Ferrandez Izquierdo. - Cham :Springer Nature Switzerland :2025. - xix, 230 p. :ill., digital ;24 cm. - RSME Springer series,v. 162509-8896 ;. - RSME Springer series ;v.1..

Chapter 1. Lancret helices in R3 -- Chapter 2. Lancret helices in S3 and H3 -- Chapter 3. The conformal extension and protein chains -- Chapter 4. Lancret helices in homogeneous 3-spaces -- Chapter 5. Lancret helices in the Minkowski space L3 -- Chapter 6. Lancret helices in the de Sitter S31 and anti de Sitter H31 spaces -- Chapter 7. Lightlike helices in Ln, Sn1 and Hn1 -- Chapter 8. Lightlike Lancret helices in Ln -- Chapter 9. The Hasimoto transformation -- Chapter 10. Variational models -- Chapter 11. Bosons in spaces forms.

This book provides an overview of generalised helices, or Lancret helices, in both Riemannian and Lorentzian backgrounds. We would like to highlight, if that were possible, this mathematical structure with great preponderance in nature and even in our daily lives. Moreover, we intend to collect many somewhat scattered results and put them in a unique context using helices as leitmotiv. Everybody is aware of the ubiquity of helices in nature and admires their intrinsic beauty, but it seems that people are not interested in knowing the omnipresence of helices in the real world. Without getting into great speculations, we soon realize that nature is governed by a principle of minimum energy, that is, any natural process occurs at minimum cost. With that idea in mind, and thinking in a supercoiled DNA molecule, we are predisposed to think that this phenomenon reflects the need to place the greatest amount of matter in the least possible space. Or even that the arrangement in a double supercoiled helix is the optimal organization to facilitate the mechanism of replication. That said, we should think of some kind of energy functional, defined on a suitable space of curves, and determine its critical points. Furthermore, the theory of helices falls into place in a broader scenario. For instance, helicoids or surfaces with helicoidal symmetry basically inherit all their properties from their generating curves, the helices, and also arise in many contexts. The level of work has been structured so that it is suitable for a Master of Science, links with the expertise of a Bachelor in Mathematics or Physics, and leaves an open door to the research world. In addition, we have tried to make a self-contained book, for which we have included several appendices. And, wishing that our eyes see beyond, we have deployed a wide and unsuspected series of helices in geometries where light-like vectors play a key role.

ISBN: 9783032096630

Standard No.: 10.1007/978-3-032-09663-0doiSubjects--Topical Terms:

1462201
Helices (Algebraic topology)

LC Class. No.: QA612

Dewey Class. No.: 514.2

Helices
LDR:03452nam a22003375a 4500 001 1171838
003 DE-He213
005 20251120120400.0
006 m d
007 cr nn 008maaau
008 260504s2025 sz s 0 eng d
020 $a 9783032096630 $q (electronic bk.)
020 $a 9783032096623 $q (paper)
024 7 $a 10.1007/978-3-032-09663-0 $2 doi
035 $a 978-3-032-09663-0
040 $a GP $c GP
041 0 $a eng
050 4 $a QA612
072 7 $a PBP $2 bicssc
072 7 $a MAT038000 $2 bisacsh
072 7 $a PBP $2 thema
082 0 4 $a 514.2 $2 23
090 $a QA612 $b .F372 2025
100 1 $a Ferrandez Izquierdo, Angel. $3 1502509
245 1 0 $a Helices $h [electronic resource] / $c by Angel Ferrandez Izquierdo.
260 $a Cham : $c 2025. $b Springer Nature Switzerland : $b Imprint: Springer,
300 $a xix, 230 p. : $b ill., digital ; $c 24 cm.
490 1 $a RSME Springer series, $x 2509-8896 ; $v v. 16
505 0 $a Chapter 1. Lancret helices in R3 -- Chapter 2. Lancret helices in S3 and H3 -- Chapter 3. The conformal extension and protein chains -- Chapter 4. Lancret helices in homogeneous 3-spaces -- Chapter 5. Lancret helices in the Minkowski space L3 -- Chapter 6. Lancret helices in the de Sitter S31 and anti de Sitter H31 spaces -- Chapter 7. Lightlike helices in Ln, Sn1 and Hn1 -- Chapter 8. Lightlike Lancret helices in Ln -- Chapter 9. The Hasimoto transformation -- Chapter 10. Variational models -- Chapter 11. Bosons in spaces forms.
520 $a This book provides an overview of generalised helices, or Lancret helices, in both Riemannian and Lorentzian backgrounds. We would like to highlight, if that were possible, this mathematical structure with great preponderance in nature and even in our daily lives. Moreover, we intend to collect many somewhat scattered results and put them in a unique context using helices as leitmotiv. Everybody is aware of the ubiquity of helices in nature and admires their intrinsic beauty, but it seems that people are not interested in knowing the omnipresence of helices in the real world. Without getting into great speculations, we soon realize that nature is governed by a principle of minimum energy, that is, any natural process occurs at minimum cost. With that idea in mind, and thinking in a supercoiled DNA molecule, we are predisposed to think that this phenomenon reflects the need to place the greatest amount of matter in the least possible space. Or even that the arrangement in a double supercoiled helix is the optimal organization to facilitate the mechanism of replication. That said, we should think of some kind of energy functional, defined on a suitable space of curves, and determine its critical points. Furthermore, the theory of helices falls into place in a broader scenario. For instance, helicoids or surfaces with helicoidal symmetry basically inherit all their properties from their generating curves, the helices, and also arise in many contexts. The level of work has been structured so that it is suitable for a Master of Science, links with the expertise of a Bachelor in Mathematics or Physics, and leaves an open door to the research world. In addition, we have tried to make a self-contained book, for which we have included several appendices. And, wishing that our eyes see beyond, we have deployed a wide and unsuspected series of helices in geometries where light-like vectors play a key role.
650 0 $a Helices (Algebraic topology) $3 1462201
650 1 4 $a Topology. $3 633483
650 2 4 $a Geometry. $3 579899
650 2 4 $a Applications of Mathematics. $3 669175
650 2 4 $a Mathematical Applications in Environmental Science. $3 1366053
650 2 4 $a Mathematical and Computational Biology. $3 786706
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
830 0 $a RSME Springer series ; $v v.1. $3 1112854
856 4 0 $u https://doi.org/10.1007/978-3-032-09663-0
950 $a Mathematics and Statistics (SpringerNature-11649)