Equivalence of Cables Of Mutants of Knots

1989 ◽  
Vol 41 (2) ◽  
pp. 250-273 ◽  
Author(s):  
Józef H. Przytycki
Keyword(s):  
Mirror Image ◽  
Alexander Polynomial ◽  
The Other ◽  
Homfly Polynomial ◽  
Similar Formula ◽  
Conway Polynomial ◽  
Other Hand ◽  
Limited Possibility

There is the nice formula which links the Alexander polynomial of (m, k)-cable of a link with the Alexander polynomial of the link [5] [36] [38]. H. Morton and H. Short investigated whether a similar formula holds for the Jones-Conway (Homfly) polynomial and they found that it is very unlikely. Morton and Short made many calculations of the Jones-Conway polynomial of (2, q)-cables along knots (2 was chosen because of limited possibility of computers) and they get very interesting experimental material [24], [25]. In particular they found that using their method they were able to distinguish some Birman [4] and Lozano-Morton [22] examples (all which they tried) and the 942 knot (in the Rolfsen [37] notation) from its mirror image. On the other hand they were unable to distinguish the Conway knot and the Kinoshita-Terasaka knot.

Relationship between Frames of Reference and Mirror-Image Reversals

Perception ◽  
10.1068/p5529 ◽  
2007 ◽  
Vol 36 (7) ◽  
pp. 1049-1056 ◽  
Author(s):  
Hirokazu Yoshimura ◽  
Tatsuo Tabata
Keyword(s):  
Mirror Image ◽  
Frame Of Reference ◽  
The Other ◽  
Frames Of Reference ◽  
Physical Aspect ◽  
Other Hand ◽  
Extended Problem ◽  
Left Right Asymmetry ◽  
Common Frame Of Reference ◽  
Intrinsic Frame

The mirror puzzle related to the perception of mirror images as left–right reversed can be more fully understood by considering an extended problem that includes also the perception of mirror images that are not left–right reversed. The purpose of the present study is to clarify the physical aspect of this extended problem logically and parsimoniously. Separate use of the intrinsic frame of reference that belongs to the object and one that belongs to its mirror image always leads to the perception of left–right reversal when the object has left–right asymmetry; on the other hand, the perception of left–right nonreversal is always due to the application of a common frame of reference to the object and its mirror image.

Reading The Time of Trimming under the Desk of Religious Zionism: Haim Beʾer and National-Religious Identity

Zutot ◽  
2014 ◽  
Vol 11 (1) ◽  
pp. 6-17
Author(s):  
Yael Shenker
Keyword(s):  
National Identity ◽  
Religious Identity ◽  
Mirror Image ◽  
Religious Discourse ◽  
Religious Community ◽  
National Identities ◽  
The Other ◽  
Other Hand ◽  
The One ◽  
The Relationship

This article addresses Israeli novelist Haim Beʾer’s relation to national-religious identity and the rifts and the pain it causes him, as can be discerned from his fiction and journalism, and certainly from interviews with him. His relation to national-religious identity also reflects a sort of mirror image, at times inverted, of the relationship between religious and national identities. Beʾer’s movement between religious community and nation criticizes on the one hand prevalent conceptions of secularization and national identity in Zionist discourse, and, on the other hand, conceptions of redemption in religious discourse.

scholarly journals A PARTIAL ORDER ON THE SET OF PRIME KNOTS WITH UP TO 11 CROSSINGS

2011 ◽  
Vol 20 (02) ◽  
pp. 275-303 ◽  
Author(s):  
KEIICHI HORIE ◽  
TERUAKI KITANO ◽  
MINEKO MATSUMOTO ◽  
MASAAKI SUZUKI
Keyword(s):  
Partial Order ◽  
Alexander Polynomial ◽  
Surjective Homomorphism ◽  
The Other ◽  
Other Hand ◽  
Twisted Alexander Polynomial

Let K be a prime knot in S3 and G(K) = π1(S3 - K) the knot group. We write K1 ≥ K2 if there exists a surjective homomorphism from G(K1) onto G(K2). In this paper, we determine this partial order on the set of prime knots with up to 11 crossings. There exist such 801 prime knots and then 640, 800 should be considered. The existence of a surjective homomorphism can be proved by constructing it explicitly. On the other hand, the non-existence of a surjective homomorphism can be proved by the Alexander polynomial and the twisted Alexander polynomial.

Neurotransmitter plasticity of cultured sympathetic neurones. Are the effects of muscle-conditioned medium reversible?

Development ◽  
1987 ◽  
Vol 101 (3) ◽  
pp. 617-625
Author(s):  
S. Vidal ◽  
B. Raynaud ◽  
D. Clarous ◽  
M.J. Weber
Keyword(s):  
Conditioned Medium ◽  
Primary Cultures ◽  
Mirror Image ◽  
The Other ◽  
High Rate ◽  
Lower State ◽  
Other Hand ◽  
Subsequent Exposure ◽  
Sympathetic Neurones ◽  
Neurotransmitter Plasticity

Muscle-conditioned medium (CM) induces choline acetyltransferase (CAT) activity in primary cultures of new-born rat sympathetic neurones and depresses the development of tyrosine hydroxylase (TOH). By following these two enzymes, we have determined whether (1) the effects of CM are reversible and (2) the neurones progressively lose their sensitivity to CM with time in culture. When neurones were cultured in the presence of 50% CM (CM+ medium), TOH activity developed slowly but CAT activity developed at a high rate. When the cultures were then switched to unconditioned medium (CM- medium), CAT activity remained elevated and continued to develop at higher rate than in cultures that were never exposed to CM. On the other hand, the switch to CM- medium was accompanied by a transition from a low to a high rate of TOH development. CAT induction by CM was thus essentially irreversible, whereas the impairment of TOH development was fully reversible. Conversely, we studied the effects of altering CM- to CM+ medium at progressively later culture days. CAT remained fully inducible for at least 2 to 3 weeks. On the other hand, TOH activity, which initially developed rapidly in CM- medium, first decreased to low levels after a switch to CM+ medium and then increased again, but at a slower rate. Neuronal depolarization by elevated K+ and exposure to CM have mirror-image, and antagonistic, effects on both CAT and TOH developments (Raynaud et al. 1987a). Walicke, Campenot & Patterson (1977) showed that a previous depolarization reduced the induction of cholinergic traits by a subsequent exposure to CM. We found that (1) such a depolarization only delayed the induction of CAT by several days and did not prevent the transition to a state of low TOH expression caused by CM and (2) an exposure of the cultures to elevated K+ after exposure to CM did not cause a decline in CAT activity. These data thus suggest that a state of high TOH expression can superimpose on a previously induced state of elevated CAT expression, but that the induction of CAT caused by a delayed exposure to CM is accompanied by a transition from a high to a lower state of TOH expression. In addition, neuronal depolarization does not stabilize the noradrenergic phenotype in a permanent manner and can not reverse cholinergic expression of sympathetic neurones to a purely noradrenergic phenotype.

How to see a cube moving into its mirror image

2012 ◽  
Vol 96 (537) ◽  
pp. 471-479
Author(s):  
Ester Dalvit ◽  
Domenico Luminati
Keyword(s):  
Euclidean Space ◽  
Dimensional Space ◽  
Rigid Motion ◽  
Mirror Image ◽  
The Other ◽  
Dimensional Euclidean Space ◽  
Other Hand ◽  
Rigid Motions

In n-dimensional Euclidean space no reflection with respect to a hyperplane can be realised by a rigid motion. But this is possible if we allow rigid motions in (n + 1)-dimensional space. These notes show a way to visualise a rigid motion of a cube in 4-dimensional space that flips the cube ‘as the page of a book’.The two terms rigid motion and isometry are sometimes used as synonyms. Yet they do refer to different concepts. The first one has a purely kinematic connotation: the swing of a door or the movement of a piece of furniture pushed over the floor are described by rigid motions. On the other hand to ensure that two figures are isometric it is enough that there exists a correspondence between their points that maintains the relative distances.

scholarly journals The Conway polynomial and amphicheiral knots

2017 ◽  
Vol 26 (05) ◽  
pp. 1750027
Author(s):  
J. Conant ◽  
V. A. Manathunga
Keyword(s):  
The Other ◽  
Conway Polynomial ◽  
Other Hand

According to work of Hartley and Kawauchi in 1979 and 1980, the Conway Polynomial of all negative amphicheiral knots and strongly positive amphicheiral knots factors as [Formula: see text] for some [Formula: see text]. Moreover, a 2012 example due to Ermotti, Hongler and Weber shows that this is not true for general amphicheiral knots. On the other hand, in 2006, the first author made a conjecture equivalent to saying that the Conway polynomial of all amphicheiral knots splits as [Formula: see text] in the ring [Formula: see text]. In this paper, we establish this conjecture for all periodically amphicheiral knots built from braids, where the period preserves the braid structure. We also give counterexamples to conjectures on the leading coefficient of the Conway polynomial of an amphicheiral knot due to Stoimenow.

scholarly journals ASYMPTOTIC BEHAVIORS OF THE COLORED JONES POLYNOMIALS OF A TORUS KNOT

2004 ◽  
Vol 15 (06) ◽  
pp. 547-555 ◽  
Author(s):  
HITOSHI MURAKAMI
Keyword(s):  
Alexander Polynomial ◽  
The Other ◽  
Torus Knots ◽  
Asymptotic Behaviors ◽  
Torus Knot ◽  
Other Hand ◽  
Jones Polynomials ◽  
Colored Jones Polynomials ◽  
Chern Simons

We study the asymptotic behaviors of the colored Jones polynomials of torus knots. Contrary to the works by R. Kashaev, O. Tirkkonen, Y. Yokota, and the author, they do not seem to give the volumes or the Chern–Simons invariants of the three-manifolds obtained by Dehn surgeries. On the other hand it is proved that in some cases the limits give the inverse of the Alexander polynomial.

A study of cometary eruptions through OH radio-lines

1999 ◽  
Vol 173 ◽  
pp. 249-254
Author(s):  
A.M. Silva ◽  
R.D. Miró
Keyword(s):  
Short Duration ◽  
Growth Curves ◽  
The Other ◽  
Initial Mass ◽  
Radio Lines ◽  
Other Hand ◽  
Sudden Rise

AbstractWe have developed a model for theH2OandOHevolution in a comet outburst, assuming that together with the gas, a distribution of icy grains is ejected. With an initial mass of icy grains of 108kg released, theH2OandOHproductions are increased up to a factor two, and the growth curves change drastically in the first two days. The model is applied to eruptions detected in theOHradio monitorings and fits well with the slow variations in the flux. On the other hand, several events of short duration appear, consisting of a sudden rise ofOHflux, followed by a sudden decay on the second day. These apparent short bursts are frequently found as precursors of a more durable eruption. We suggest that both of them are part of a unique eruption, and that the sudden decay is due to collisions that de-excite theOHmaser, when it reaches the Cometopause region located at 1.35 × 105kmfrom the nucleus.

Closing the GAP—A 5Å Scanning Microscope

1969 ◽  
Vol 27 ◽  
pp. 6-7
Author(s):  
A. V. Crewe
Keyword(s):  
Normal Form ◽  
The Other ◽  
Resolving Power ◽  
Scanning Microscope ◽  
Conventional Microscope ◽  
Other Hand ◽  
Closing The Gap ◽  
Thermal Sources ◽  
Better Than ◽  
Transmission Microscope

We have become accustomed to differentiating between the scanning microscope and the conventional transmission microscope according to the resolving power which the two instruments offer. The conventional microscope is capable of a point resolution of a few angstroms and line resolutions of periodic objects of about 1Å. On the other hand, the scanning microscope, in its normal form, is not ordinarily capable of a point resolution better than 100Å. Upon examining reasons for the 100Å limitation, it becomes clear that this is based more on tradition than reason, and in particular, it is a condition imposed upon the microscope by adherence to thermal sources of electrons.

Life Beyond 1MeV

1980 ◽  
Vol 38 ◽  
pp. 30-33
Author(s):  
K.H. Westmacott
Keyword(s):  
Electron Microscopy ◽  
Past Experience ◽  
The Other ◽  
Good Case ◽  
Other Hand ◽  
The U.S

Life beyond 1MeV – like life after 40 – is not too different unless one takes advantage of past experience and is receptive to new opportunities. At first glance, the returns on performing electron microscopy at voltages greater than 1MeV diminish rather rapidly as the curves which describe the well-known advantages of HVEM often tend towards saturation. However, in a country with a significant HVEM capability, a good case can be made for investing in instruments with a range of maximum accelerating voltages. In this regard, the 1.5MeV KRATOS HVEM being installed in Berkeley will complement the other 650KeV, 1MeV, and 1.2MeV instruments currently operating in the U.S. One other consideration suggests that 1.5MeV is an optimum voltage machine – Its additional advantages may be purchased for not much more than a 1MeV instrument. On the other hand, the 3MeV HVEM's which seem to be operated at 2MeV maximum, are much more expensive.

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