Homfly Polynomials of Generalized Hopf Links

Following the recent work by T.-H. Chan in [HOMFLY polynomial of some generalized Hopf links, J. Knot Theory Ramif. 9 (2000) 865--883] on reverse string parallels of the Hopf link we give an alternative approach to finding the Homfly polynomials of these links, based on the Homfly skein of the annulus. We establish that two natural skein maps have distinct eigenvalues, answering a question raised by Chan, and use this result to calculate the Homfly polynomial of some more general reverse string satellites of the Hopf link.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-2.abs.htm

Conjugacy for positive permutation braids

Positive permutation braids on n strings, which are defined to be positive n-braids where each pair of strings crosses at most once, form the elementary but non-trivial building blocks in many studies of conjugacy in the braid groups. We consider conjugacy among these elementary braids which close to knots, and show that those which close to the trivial knot or to the trefoil are all conjugate. All such n-braids with the maximum possible crossing number are also shown to be conjugate. We note that conjugacy of these braids for n<6 depends only on the crossing number. In contrast, we exhibit two such braids on 6 strings with 9 crossings which are not conjugate but whose closures are each isotopic to the (2,5) torus knot

Will spin-relaxation times in molecular magnets permit quantum information processing?

Using X-band pulsed electron spin resonance, we report the intrinsic spin-lattice ($T_1$) and phase coherence ($T_2$) relaxation times in molecular nanomagnets for the first time. In Cr$_7M$ heterometallic wheels, with $M$ = Ni and Mn, phase coherence relaxation is dominated by the coupling of the electron spin to protons within the molecule. In deuterated samples $T_2$ reaches 3 $\mu$s at low temperatures, which is several orders of magnitude longer than the duration of spin manipulations, satisfying a prerequisite for the deployment of molecular nanomagnets in quantum information applications.Comment: 4 pages, 3 figures, in press at Physical Review Letter

Can the solar p-modes contribute to the high-frequency transverse oscillations of spicules?

Lateral motions of spicules serve as vital indicators of transverse waves in the solar atmosphere, and their study is crucial for understanding the wave heating process of the corona. Recent observations have focused on "high-frequency" transverse waves (periods < 100 s), which have the potential to transport sufficient energy for coronal heating. These high-frequency spicule oscillations are distinct from granular motions, which have much longer time scales of 5-10 min. Instead, it is proposed that they are generated through the mode conversion from high-frequency longitudinal waves that arise from a shock steepening process. Therefore, these oscillations may not solely be produced by the horizontal buffeting motions of granulation but also by the leakage of p-mode oscillations. To investigate the contribution of p-modes, our study employs a two-dimensional magneto-convection simulation spanning from the upper convection zone to the corona. During the course of the simulation, we introduce a p-mode-like driver at the bottom boundary. We reveal a notable increase in the mean velocity amplitude of the transverse oscillations in spicules, ranging from 10% to 30%, and attribute this to the energy transfer from longitudinal to transverse waves. This effect results in an enhancement of the estimated energy flux by 30-80%.Comment: Accepted for publication in ApJ, 14 pages, 6 figures, 2 tables, Comments are welcom

ESR spectra of PF_2 and SF_3 radicals

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Lipid Transfer Inhibitor Protein (Apolipoprotein F) Concentration in Normolipidemic and Hyperlipidemic Subjects

Lipid transfer inhibitor protein (LTIP) is an important regulator of cholesteryl ester transfer protein function. We report the development of an immunoassay for LTIP and its use to quantify LTIP in plasma of varying lipid contents. A rabbit antibody against bacterially produced recombinant LTIP detected two LTIP isoforms in plasma differing in carbohydrate content. This antibody was used in a competitive, enzyme-linked immunoassay that uses partially purified LTIP bound to microtiter plates. To optimize LTIP immunoreactivity, plasma samples required preincubation in 1% Tween-20 and 0.5% Nonidet P-40. In normolipidemic plasma, LTIP averaged 83.5 mg/ml. LTIP was 31% higher in males than in females. LTIP was positively associated with HDL cholesterol in normolipidemic males but not in females. In hypertriglyceridemic males, LTIP was only 56% of control values, whereas in hypertriglyceridemic females, LTIP tended to increase. Additionally, in males with normal cholesterol and triglyceride (TG) ≤ 200 mg/dl, LTIP varied inversely with plasma TG. Overall, we have confirmed the negative association between plasma TG levels and LTIP previously suggested by a small data set, but now we demonstrate that this effect is seen only in males. The mechanisms underlying this gender-specific response to TG, and why LTIP and HDL levels correlate in males but not in females, remain to be determined

Electron spin coherence in metallofullerenes: Y, Sc and La@C82

Endohedral fullerenes encapsulating a spin-active atom or ion within a carbon cage offer a route to self-assembled arrays such as spin chains. In the case of metallofullerenes the charge transfer between the atom and the fullerene cage has been thought to limit the electron spin phase coherence time (T2) to the order of a few microseconds. We study electron spin relaxation in several species of metallofullerene as a function of temperature and solvent environment, yielding a maximum T2 in deuterated o-terphenyl greater than 200 microseconds for Y, Sc and La@C82. The mechanisms governing relaxation (T1, T2) arise from metal-cage vibrational modes, spin-orbit coupling and the nuclear spin environment. The T2 times are over 2 orders of magnitude longer than previously reported and consequently make metallofullerenes of interest in areas such as spin-labelling, spintronics and quantum computing.Comment: 5 pages, 4 figure