1,182 research outputs found
Pseudo links and singular links in the Solid Torus
Get PDFIn this paper we introduce and study the theories of pseudo links and
singular links in the Solid Torus, ST. Pseudo links are links with some missing
crossing information that naturally generalize the notion of knot diagrams, and
that have potential use in molecular biology, while singular links are links
that contain a finite number of self-intersections. We consider pseudo links
and singular links in ST and we set up the appropriate topological theory in
order to construct invariants for these types of links in ST. In particular, we
formulate and prove the analogue of the Alexander theorem for pseudo links and
for singular links in ST. We then introduce the mixed pseudo braid monoid and
the mixed singular braid monoid, with the use of which, we formulate and prove
the analogue of the Markov theorem for pseudo links and for singular links in
ST. \smallbreak Moreover, we introduce the pseudo Hecke algebra of type A,
, the cyclotomic and generalized pseudo Hecke algebras of type
B, , and discuss how the pseudo braid monoid (cor. the
mixed pseudo braid monoid) can be represented by (cor. by
). This is the first step toward the construction of
HOMFLYPT-type invariants for pseudo links in and in ST. We also introduce
the cyclotomic and generalized singular Hecke algebras of type B,
, and we present two sets that we conjecture that they
form linear bases for . Finally, we generalize the bracket
polynomial for pseudo links in ST.Comment: 25 pages, 16 figure
The Braid Approach to the HOMFLYPT Skein Module of the Lens Spaces L(p, 1)
No full textIn this paper we present recent results toward the computation of the HOMFLYPT skein module of the lens spaces L(p, 1), S (L(p, 1)), via braids. Our starting point is the knot theory of the solid torus ST and the Lambropoulou invariant, X, for knots and links in ST, the universal analogue of the HOMFLYPT polynomial in ST. The relation between S (L(p, 1)) and S(ST) is established in Diamantis et al. (J Knot Theory Ramif, 25: 13, 2016, [5]) and it is shown that in order to compute S (L(p, 1)), it suffices to solve an infinite system of equations obtained by performing all possible braid band moves on elements in the basis of S(ST),., presented in Diamantis and Lambropoulou (J Pure Appl Algebra, 220(2): 577-605, 2016, [4]). The solution of this infinite system of equations is very technical and is the subject of a sequel work (Diamantis and Lambropoulou, The HOMFLYPT skein module of the lens spaces L(p, 1) via braids, in preparation
A Modular Logic Approach for Expressing Web Services in XML Applying Dynamic Rules in XML
Get PDFRuleML is considered to be a markup language for the semantic web. It allows the enrichment of web ontologies by adding definitions of derived concepts and it enhances interoperability among different systems and tools by publishing rules in an XML format. Moreover the in-creasing demand for interfaces that enhance information sharing has given rise to XML doc-uments that include embedded calls to web services. In this paper we propose a variation of RuleML that is based on modular logic programming. Our approach is based in a two level architecture. In the first level a modular logic language, called M-log, is presented. This lan-guage encompasses several mechanisms for invoking web services. In the second level we ex-ploit the semantics of M-log to present a variation of RuleML with rich modeling capabilities. Formal foundations for this variation are given through direct translation to M-log semantics.Knowledge Management, XML, Modular Logic Programming, E-Services
Topological steps toward the Homflypt skein module of the lens spaces L(p,1) via braids
No full textIn this paper, we work toward the Homflypt skein module of the lens spaces L(p, 1), S(L(p, 1)) using braids. In particular, we establish the connection between S(ST), the Homflypt skein module of the solid torus ST, and S(L(p, 1)) and arrive at an infinite system, whose solution corresponds to the computation of S(L(p, 1)). We start from the Lambropoulou invariant X for knots and links in ST, the universal analog of the Homflypt polynomial in ST, and a new basis,., of S(ST) presented in [I. Diamantis and S. Lambropoulou, A new basis for the Homflypt skein module of the solid torus, J. Pure Appl. Algebra 220(2) (2016) 577-605, http://dx.doi.org/10.1016/j.jpaa.2015.06.014, arXiv: 1412.3642[math. GT]]. We show that S(L(p, 1)) is obtained from S(ST) by considering relations coming from the performance of braid band move(s) [bbm] on elements in the basis., where the bbm are performed on any moving strand of each element in.. We do that by proving that the system of equations obtained from diagrams in ST by performing bbm on any moving strand is equivalent to the system obtained if we only consider elements in the basic set.. The importance of our approach is that it can shed light on the problem of computing skein modules of arbitrary c.c.o. 3-manifolds, since any 3-manifold can be obtained by surgery on S-3 along unknotted closed curves. The main difficulty of the problem lies in selecting from the infinitum of band moves some basic ones and solving the infinite system of equations
The braid approach to the HOMFLYPT skein module of the lens spaces
No full textIn this paper we present recent results toward the computation of the HOMFLYPT skein module of the lens spaces L(p, 1), S (L(p, 1)), via braids. Our starting point is the knot theory of the solid torus ST and the Lambropoulou invariant, X, for knots and links in ST, the universal analogue of the HOMFLYPT polynomial in ST. The relation between S (L(p, 1)) and S(ST) is established in Diamantis et al. (J Knot Theory Ramif, 25: 13, 2016, [5]) and it is shown that in order to compute S (L(p, 1)), it suffices to solve an infinite system of equations obtained by performing all possible braid band moves on elements in the basis of S(ST),., presented in Diamantis and Lambropoulou (J Pure Appl Algebra, 220(2): 577-605, 2016, [4]). The solution of this infinite system of equations is very technical and is the subject of a sequel work (Diamantis and Lambropoulou, The HOMFLYPT skein module of the lens spaces L(p, 1) via braids, in preparation
Ioannis Dallaei De imaginibus libri IV.
No full textIncludes errata at end.Signatures: *⁸ A-2L⁸ 2M⁴ chi².Woodcut printer's device on t.p. Head- and tail-pieces, initials.Scanned copy bound with: Joannis Dallaei Apologia pro ecclesiis reformatis. Amstelodami : Apud Jodocum Jansonium, 1652.Mode of access: Internet.Binding: vellum. Author & titles written at head of spine.With his: Apologia pro ecclesiis reformatis (Amsterdam : J. Janson, 1652)
Usuardi Martyrologium
No full textOperâ Ioannis Molani Louaniensis, Louanij sacræ Theologiæ Regij ProfessorisVorlageform des Erscheinungsvermerks: Lovanii, Apud Hieronymum VVellæum, sub signo Diamantis, Anno 1573. - Im Kolophon des Hauptwerkes: Lovanii, Anno LXXIII, Mense Maio, apud Hieronymum VVellæum Typographum iuratum, Typis Iacobi Heybergij, è regione Gymnasij Lilij.NUC 626NU 030252
The Kauffman bracket skein module of the complement of (2,2p + 1)-torus knots via braids
No full textIn this paper we compute the Kauffman bracket skein module of the complement of (2, 2p + 1)-torus knots, KBSM(Tc(2,2p+1)), via braids. We start by considering geometric mixed braids in S3, the closure of which are mixed links in S3 that represent links in the complement of (2, 2p + 1)-torus knots, Tc(2,2p+1). Using the technique of parting and combing geometric mixed braids, we obtain algebraic mixed braids, that is, mixed braids that belong to the mixed braid group B2,n and that are followed by their "coset" part, that represents Tc(2,2p+1). In that way we show that links in Tc (2,2p+1) may be pushed to the genus 2 handlebody, H2, and we establish a relation between KBSM(Tc(2,2p+1)) and KBSM(H2). In particular, we show that in order to compute KBSM(Tc(2,2p+1)) it suffices to consider a basis of KBSM(H2) and study the effect of combing on elements in this basis. We consider the standard basis of KBSM(H2) and we show how to treat its elements in KBSM(Tc(2,2p+1)), passing through many different spanning sets for KBSM(Tc(2,2p+1)). These spanning sets form the intermediate steps in order to reach at the set BTc(2,2p+1), which, using an ordering relation and the notion of total winding, we prove that it forms a basis for KBSM(Tc(2,2p+1)). Note that elements in BTc(2,2p+1) have no crossings on the level of braids, and in that sense, BTc(2,2p+1) forms a more natural basis of KBSM(Tc(2,2p+1)) in our setting. We finally consider c.c.o. 3-manifolds M obtained from S3 by surgery along the trefoil knot and we discuss steps needed in order to compute the Kauffman bracket skein module of M. We first demonstrate the process described before for computing the Kauffman bracket skein module of the complement of the trefoil, KBSM(Trc), and we study the effect of braid band moves on elements in the basis of KBSM(Trc). These moves reflect isotopy in M and are similar to the second Kirby moves.The "braid" method that we propose for computing Kauffman bracket skein modules seem promising in computing KBSM of arbitrary c.c.o. 3-manifolds M. The only difficulty lies in finding the sufficient relations that reduce elements in the basis of our underlying genus g-handlebody, Hg. These relations come from combing in the case of knot complements and from combing and braid band moves for 3-manifolds obtained by surgery along a knot in S3. Our aim is to set the necessary background of this "braid" approach in order to compute Kauffman bracket skein modules of arbitrary 3-manifolds.(c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/)
Ioannis Metaxas: Speech on the occasion of the inauguration of public works
No full textTitle: Λόγος κατά τα εγκαίνια των έργων του Σελινούντος Αιγιαλείας (Speech on the occasion of the inauguration of the public works at Selinous, Egialia) Originally published: Delivered at Selinous on 31 October 1937. Language: Greek The excerpts used are from Ioannis Metaxas, Λόγοι και Ομιλίες (Athens: Ερμής, 1992), pp. 247–255. About the author Ioannis Metaxas [1871, Ithaca (Ionian Islands)–1941, Athens]: military officer and politician. He was born into a well-known aristocratic family. In ..
Knotoids, pseudo knotoids, Braidoids and pseudo braidoids on the Torus
Get PDFIn this paper we study the theory of knotoids and braidoids and the theory of pseudo knotoids and pseudo braidoids on the torus T. In particular, we introduce the notion of {\it mixed knotoids} in S2, that generalize the notion of mixed links in S3, and we present an isotopy theorem for mixed knotoids. We then generalize the Kauffman bracket polynomial, <;>, for mixed knotoids and we present a state sum formula for <;>. We also introduce the notion of {\it mixed pseudo knotoids}, that is, multi-knotoids on two components with some missing crossing information. More precisely, we present an isotopy theorem for mixed pseudo knotoids and we extend the Kauffman bracket polynomial for pseudo mixed knotoids. Finally, we introduce the theories of {\it mixed braidoids} and {\it mixed pseudo braidoids} as counterpart theories of mixed knotoids and mixed pseudo knotoids respectively. With the use of the L-moves, that we also introduce here for mixed braidoid equivalence, we formulate and prove the analogue of the Alexander and the Markov theorems for mixed knotoids. We also formulate and prove the analogue of the Alexander theorem for mixed pseudo knotoids
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