scholarly journals A diagrammatic approach to link invariants of finite degree

2004 ◽  
Vol 94 (2) ◽  
pp. 295 ◽  
Author(s):  
Olof-Petter Östlund
Keyword(s):  
Finite Degree ◽  
Explicit Formulas ◽  
Connected Sum ◽  
Knot Invariants ◽  
Graphical Calculus ◽  
Link Invariants ◽  
Low Degree ◽  
Coalgebra Structure ◽  
Arrow Diagrams

In [5] M. Polyak and O. Viro developed a graphical calculus of diagrammatic formulas for Vassiliev link invariants, and presented several explicit formulas for low degree invariants. M. Goussarov [2] proved that this arrow diagram calculus provides formulas for all Vassiliev knot invariants. The original note [5] contained no proofs, and it also contained some minor inaccuracies. This paper fills the gap in literature by presenting the material of [5] with all proofs and details, in a self-contained form. Furthermore, a compatible coalgebra structure, related to the connected sum of knots, is introduced on the algebra of based arrow diagrams with one circle.

scholarly journals Characterization of finite type string link invariants of degree <5

2010 ◽  
Vol 148 (3) ◽  
pp. 439-472 ◽  
Author(s):  
JEAN-BAPTISTE MEILHAN ◽  
AKIRA YASUHARA
Keyword(s):  
Finite Type ◽  
Knot Invariants ◽  
Link Invariants ◽  
Finite Type Invariants ◽  
Low Degree ◽  
String Links ◽  
Complete Set ◽  
Milnor Invariants

AbstractWe give a complete set of finite type string link invariants of degree <5. In addition to Milnor invariants, these include several string link invariants constructed by evaluating knot invariants on certain closures of (cabled) string links. We show that finite type invariants classify string links up toCk-moves fork≤ 5, which proves, at low degree, a conjecture due to Goussarov and Habiro. We also give a similar classification of string links up toCk-moves and concordance fork≤ 6.

FINITE-DEGREE LINK INVARIANTS AND CONNECTIVITY

1996 ◽  
Vol 05 (01) ◽  
pp. 117-136
Author(s):  
STEVE SAWIN
Keyword(s):  
Finite Degree ◽  
Polynomial Invariant ◽  
Link Invariants ◽  
Finite Sum

Finite-degree invariants of links are defined following [Sta92] and Kontsevich’s integral is shown to generalize to this situation. The notion of connectivity is introduced, and finite-degree invariants are shown to decompose into a finite sum of invariants of finite degree and connectivity. Given an invariant of finite connectivity, a polynomial invariant of finite connectivity is given encoding its value of the invariant on cabled links. Invariants of finite degree and connectivity are constructed from the linking matrix and shown to classify finite-degree invariants of large connectivity.

Braids, chain of Yang–Baxter like operations, and (transverse) knot invariants

2018 ◽  
Vol 27 (11) ◽  
pp. 1843009
Author(s):  
Tetsuya Ito
Keyword(s):  
Baxter Equation ◽  
Knot Invariants ◽  
Link Invariants ◽  
Potential Applications ◽  
A Chain

We introduce a notion of a chain of Yang–Baxter like operations. This is a sequence of solutions of an asymmetric variant of the Yang–Baxter equation and is a multi-operator generalization of (bi)rack/quandles. We discuss knot and link invariants coming from a chain of Yang–Baxter like operations, and give potential applications. Among them, we define a cocycle invariant for transverse links.

scholarly journals FINITE-TYPE KNOT INVARIANTS BASED ON THE BAND-PASS AND DOUBLED-DELTA MOVES

2010 ◽  
Vol 19 (03) ◽  
pp. 355-384 ◽  
Author(s):  
JAMES CONANT ◽  
JACOB MOSTOVOY ◽  
TED STANFORD
Keyword(s):  
Abelian Group ◽  
Large Class ◽  
Finite Type ◽  
Equivalence Classes ◽  
Connected Sum ◽  
Knot Invariants ◽  
Vassiliev Invariants ◽  
Finite Type Invariants ◽  
Conway Polynomial ◽  
Band Pass

We study generalizations of finite-type knot invariants obtained by replacing the crossing change in the Vassiliev skein relation by some other local move, analyzing in detail the band-pass and doubled-delta moves. Using braid-theoretic techniques, we show that, for a large class of local moves, generalized Goussarov's n-equivalence classes of knots form groups under connected sum. (Similar results, but with a different approach, have been obtained before by Taniyama and Yasuhara.) It turns out that primitive band-pass finite-type invariants essentially coincide with standard primitive finite-type invariants, but things are more interesting for the doubled-delta move. The complete degree 0 doubled-delta invariant is the S-equivalence class of the knot. In this context, we generalize a result of Murakami and Ohtsuki to show that the only primitive Vassiliev invariants of S-equivalence taking values in an abelian group with no 2-torsion arise from the Alexander–Conway polynomial. We start analyzing degree one doubled-delta invariants by considering which Vassiliev invariants are of doubled-delta degree one, finding that there is exactly one such invariant in each odd Vassiliev degree, and at most one (which is ℤ2-valued) in each even Vassiliev degree. Analyzing higher doubled-delta degrees, we observe that the Euler degree n + 1 part of Garoufalidis and Kricker's rational lift of the Kontsevich integral is a doubled-delta degree 2n invariant.

Knot invariants with multiple skein relations

2018 ◽  
Vol 27 (02) ◽  
pp. 1850017 ◽  
Author(s):  
Zhiqing Yang
Keyword(s):  
Link Diagram ◽  
Oriented Link ◽  
Knot Invariants ◽  
Link Invariants ◽  
Kauffman Polynomial ◽  
Skein Relation

Given any oriented link diagram, one can construct knot invariants using skein relations. Usually such a skein relation contains three or four terms. In this paper, the author introduces several new ways to smooth a crossings, and uses a system of skein equations to construct link invariants. This invariant can also be modified by writhe to get a more powerful invariant. The modified invariant is a generalization of both the HOMFLYPT polynomial and the two-variable Kauffman polynomial. Using the diamond lemma, a simplified version of the modified invariant is given. It is easy to compute and is a generalization of the two-variable Kauffman polynomial.

Assessment of Damage to Human Platelets after Aggregation and Other Injuries by Microscopic Observation and Estimation of Serotonin Uptake

1970 ◽  
Vol 23 (02) ◽  
pp. 261-275 ◽  
Author(s):  
G Zbinden ◽  
J. N Mehrishi ◽  
S Tomlin
Keyword(s):  
Platelet Aggregation ◽  
Electrophoretic Mobility ◽  
Human Platelets ◽  
Freezing And Thawing ◽  
Low Degree ◽  
Microscopic Evaluation ◽  
Negative Surface ◽  
Negative Surface Charge ◽  
Charged Macromolecules ◽  
5 Ht Uptake

SummaryThe severity of platelet damage induced by hyper- and hypotonic NaCl solutions and freezing and thawing was assessed by microscopic evaluation and measuring inhibition of 5-HT uptake. The same techniques were used to quantitate the effects of aggregating agents. The positively charged macromolecules PS, Poly-L und Poly-O reduced the net negative surface charge as determined by microelectrophoresis, caused platelet aggregation and inhibited 5-HT uptake. The damaging effects of Poly-L and Poly-O were more severe and more closely related to concentration than that of PS. The negatively charged macromolecules Poly-IC and NaPS increased the anodic electrophoretic mobility. Poly-IC and heparin caused a low degree of platelet clumping and no inhibition of 5-HT uptake. NaPS produced severe platelet damage with extensive clumping and complete inhibition of 5-HT uptake. Na laurate had the same effect, but did not alter electrophoretic mobility. ADP caused concentration-dependent platelet aggregation and inhibition of 5-HT uptake. The effects of ADP and NaPS were compared in agitated and non-agitated platelet samples containing identical concentrations of the 2 compounds. Agitation was found to increase the degree of platelet clumping and to reduce 5-HT uptake.

SOLOS FRÁGEIS DO PARQUE NACIONAL DA SERRA DA CAPIVARA, PIAUÍ

GEOgraphia ◽  
2018 ◽  
Vol 19 (41) ◽  
pp. 123
Author(s):  
Gustavo Souza Valladares ◽  
Cláudia Maria Sabóia de Aquino ◽  
Renê Pedro de Aquino ◽  
Raphael Moreira Beirigo
Keyword(s):  
Soil Conservation ◽  
National Park ◽  
Soil Classification ◽  
Degradation Process ◽  
Archaeological Sites ◽  
Small Depth ◽  
Palabras Clave ◽  
Low Degree ◽  
Chemical Attributes ◽  
Pelitic Rocks

Resumo: O Parque Nacional da Serra da Capivara (PNSC) tem alguns dos sítios arqueológicos mais importantes das Américas. A área onde os solos foram amostrados corresponde ao Parque Nacional da Serra da Capivara (PNSC) e uma área tampão de 10km no entorno de seus limites oficiais, no sudeste do Piauí. Para a elaboração do presente trabalho foram selecionados solos considerados frágeis, devido ao alto risco de degradação por erosão, formados de diferentes materiais geológicos representativos do PNSC. Todos os solos estudados são pouco evoluídos, com desenvolvimento pedogenético ainda incipiente, e enquadram-se nas ordens dos Neossolos ou Cambissolos. O bioma representativo da área de estudo é a caatinga, que pela vegetação com pouca biomassa e características decíduas confere pouca cobertura aos solos, aumentando a susceptibilidade dos mesmos à erosão. Foram coletados sete perfis de solos, em diferentes posições na paisagem e formados de materiais de origem. As amostras foram secas ao ar e analisados atributos químicos e granulométricos. Os solos estudados apresentam grandes variações em seus atributos morfológicos, químicos e granulométricos, reflexo dos diferentes materiais de origem. A fragilidade em quase todos os perfis é reflexo da incipiência dos solos, representada pelo baixo grau de agregação e coesão entre as partículas, pequena profundidade e o fator de formação relevo induz na maior erosão de cinco dos sete perfis estudados. Os solos frágeis do PNSC necessitam de cuidados especiais quanto ao manejo, pois alguns deles, principalmente os originários de rochas pelíticas da Formação Pimenteiras, encontram-se em forte processo de degradação, em muitas áreas com as rochas expostas. Palavras-chave: Conservação do solo. Classificação de solos. Degradação ambiental. Semiárido tropical. FRAGILE SOILS OF SERRA DA CAPIVARA NATIONAL PARK, PIAUÍ Abstract: The Serra da Capivara National Park (PNSC) are some of the most important archaeological sites in the Americas. The area where the soils were sampled corresponds to the PNSC and a buffer area of 10km around of its official limits in southeastern of Piauí. For this work were considered fragile soils, due to the high risk of degradation by erosion, formed in different geological materials representative of PNSC. All soils are poorly evolved, with pedogenic development incipient fall in orders of Entisols or Inceptisols. The representative of the study area biome is the caatinga, which vegetation with little biomass and deciduous characteristics, gives little coverage to the soil, increasing susceptibility to erosion. Seven soil profiles were collected at different positions and mother rocks. The soils were classified according to the Brazilian System of Soil Classification (SiBCS). The samples were air dried and analyzed the chemical attributes and texture. The soils vary widely in their morphological, chemical and grain size, reflecting the different source material attributes. The weakness in nearly all profiles reflects the incipient soil, represented by a low degree of aggregation and cohesion between the particles of soil and small depth of relief factor induces the formation of further erosion profiles 5 of the 7 studied. Fragile soils of PNSC require special care in the mangement, because some soils, especially those originating from pelitic rocks by Pimenteiras Formation, are in strong degradation process in many areas with exposed rocks. Keywords: Soil conservation. Soil classification. Environmental degradation. Tropical semiarid. SUELOS FRÁGILES DEL PARQUE NACIONAL DE LA SIERRA DE CAPYBARA, PIAUÍ Resumen: El Parque Nacional de la Sierra de Capybara (PNSC) tiene algunos de los sitios arqueológicos más importantes de las Américas. El área donde los suelos fueron muestreados corresponde al PNSC y un área tampón de 10km en el entorno de sus límites oficiales, en el sureste del Piauí. Para la elaboración del presente trabajo se seleccionaron suelos considerados frágiles, debido al alto riesgo de degradación por erosión, formados de diferentes materiales geológicos representativos del PNSC. Todos los suelos estudiados son poco evolucionados, con desarrollo pedogenético aún incipiente, y se encuadran en las órdenes de los Neossolos o Cambissolos (en portugués). El bioma representativo del área de estudio es la caatinga, que por la vegetación con poca biomasa y características deciduas, confiere poca cobertura a los suelos, aumentando la susceptibilidad de los mismos a la erosión. Se recogieron muestras de siete perfiles de suelos, en diferentes posiciones en el paisaje y formados de materiales geológicos distintos. Las muestras fueron secas al aire y analizados los atributos químicos y granulométricos. Los suelos estudiados presentan grandes variaciones en sus atributos morfológicos, químicos y granulométricos, reflejo de los diferentes materiales de origen. La fragilidad en casi todos los perfiles es reflejo de la incipiente de los suelos, representada por el bajo grado de agregación y cohesión entre las partículas, pequeña profundidad y el factor de formación relieve induce en la mayor erosión de cinco de los siete perfiles estudiados. Los suelos frágiles del PNSC necesitan cuidados especiales en cuanto al manejo, pues algunos de ellos, principalmente los originarios de rocas pelíticas de la Formación Pimenteiras, se encuentran en fuerte proceso de degradación, en muchas áreas con las rocas expuestas. Palabras clave: Conservación del suelo. Clasificación de suelos. Degradación ambiental. Semiárido tropical.

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