article 63 of islamic penal law defines adultery as: “copulation of a man with a woman who is essentially unlawful (ḥarām) to him, although in dubur (back), in cases other than misapprehended consummation.” clause 1 of article 1-221 of the new suggested bill, confirming the content of the above article, has also mentioned: “copulation is effected by the insertion of a male’s sex organ into a fe...

A special type of representation for knots and for local knot manipulations is described and used in a software tool called TOK to implement a number of algorithms on knots. Two algorithms for knot simplification are described: simulated annealing applied to the knot representation, and a “divide-simplify-join” algorithm. Both of these algorithms make use of the compact knot representation and ...

For any knot, the following are equivalent. (1) The infinite cyclic cover has uncountably many finite covers; (2) there exists a finite-image representation of the knot group for which the twisted Alexander polynomial vanishes; (3) the knot group admits a finite-image representation such that the image of the fundamental group of an incompressible Seifert surface is a proper subgroup of the ima...

Given a knot presented in a grid diagram, we construct a CW complex which has one cell for each generator of the grid chain complex, and whose homology is the grid homology. This space is welldefined, and its stable homotopy type is a knot invariant. Thus to each knot, we can associate an invariant spectrum, whose F2 homology is the knot Floer homology over F2. 1991 Mathematics Subject Classifi...

Every tame, prime and alternating knot is equivalent to a tame, prime and alternating knot in regular position, with a common projection. In this work, we show that the Dehn presentation of the knot group of a tame, prime, alternating knot, with a regular and common projection has a finite and complete rewriting system. Although there are rules in the rewriting system with lefthand side a gener...

We show that there exist infinitely many pairs of distinct knots in the 3-sphere such that each pair can yield homeomorphic lens spaces by the same Dehn surgery. Moreover, each knot of the pair can be chosen to be a torus knot, a satellite knot or a hyperbolic knot, except that both cannot be satellite knots simultaneously. This exception is shown to be unavoidable by the classical theory of bi...

We study the 2-loop part of the rational Kontsevich integral of a knot in an integer homology sphere. We give a general formula which explains how the 2-loop part of the Kontsevich integral of a knot changes after surgery on a single clasper whose leaves are not linked to the knot. As an application, we relate this formula with a conjecture of L. Rozansky about integrality of the 2-loop polynom...

We show a relationship between the non-acyclic Reidemeister torsion and a zero of the acyclic Reidemeister torsion for a λ-regular SU(2) or SL(2,C)-representation of a knot group. Then we give a method to calculate the non-acyclic Reidemeister torsion of a knot exterior. We calculate a new example and investigate the behavior of the non-acyclic Reidemeister torsion associated to a 2-bridge knot...

In this paper we investigate the descriptional complexity of knot theoretic problems and show upper bounds for planarity problem of signed and unsigned knot diagrams represented by Gauss words. Since a topological equivalence of knots can involve knot diagrams with arbitrarily many crossings then Gauss words will be considered as strings over an infinite (unbounded) alphabet. For establishing t...

Letters Laparoscopic removal of abdominal cervical suture Editor, Cervical incompetence is diagnosed in 0.1-1% of all pregnancies and in 8% of women with repeated (two or more) mid-trimester pregnancy loss. 1 Cervical cerclage should be offered to patients with three or more pregnancies ending before 37 weeks gestation 2 as there is a strong body of clinical evidence suggesting that cervical ce...