Knight\u27s-TourLetterSquares

In this article, I present a new subject for logological study: the knight\u27s-tour letter square. Such a square is constructed by first creating a knight\u27s tour on the chessboard, in which each square of the chessboard is visited exactly once by successive knight\u27s moves. Normally, knight\u27s tours are displayed by numbering the squares of the chessboard with the numbers 1 through 64 to show the knight\u27s path

Smith-Knight/Rayleigh-Knight Essay

On a complex variety X, two different approaches to K-theory are available: the algebraic K-theory of the variety, and the topological K-theory of the underlying topological space. In this context, the algebraic variant known as Hermitian K-theory corresponds to topological KO-theory. Our aim is to compare the two approaches. We start by constructing a comparison map from certain Hermitian K-groups of X to the KO-groups of X. It is clear what this map must be on groups in degree zero, but the definitions of relative and higher groups differ widely in the algebraic and the topological setting. This difficulty can be overcome by viewing relative and higher groups as subgroups of degree zero groups of certain auxiliary spaces. Once the definition of our comparison map is in place, we prove a number of fundamental properties, in particular compatibility with pushforwards along closed embeddings. We also show how we can use it to compare an exact sequence relating usual algebraic K-theory to Hermitian K-theory with a portion of the Bott sequence in topology. This finally allows us to deduce that the map is an isomorphism on smooth cellular varieties. We conclude with some details concerning projective spaces, for which independent computations of the algebraic and the topological groups exist.This work was supported by the Engineering and Physical Sciences Research Council [LFAG/067]

Spin Susceptibility of the Topological Superconductor UPt3 from Polarized Neutron Diffraction

Experiment and theory indicate that UPt3 is a topological superconductor in an odd-parity state, based in part from temperature independence of the NMR Knight shift. However, quasiparticle spin-flip scattering near a surface, where the Knight shift is measured, might be responsible. We use polarized neutron scattering to measure the bulk susceptibility with H||c, finding consistency with the Knight shift but inconsistent with theory for this field orientation. We infer that neither spin susceptibility nor Knight shift are a reliable indication of odd-parity

Thematic Knight\u27s Tour Quotes

Knight\u27s Tour Quotes (KTQs), also called Knight\u27s Tour Crypts, are a word puzzle enjoying a new vogue in the National Puzzlers\u27 League since David Silverman reintroduced them in 1973. Dmitri Borgmann presented some examples in Chesswords in the May 1974 Word Ways. A KTQ is a quote written out along a knight\u27s tour. It is a form, usually rectangular, with each square containing a single letter or punctuation mark. Stepping from letter to letter by knight\u27s moves (two squares horizontally or vertically, then one square perpendicular to that), visiting all letters once, one can spell out a message. To reduce the task from drudgery to pleasure, the starting letter is underlined and the word lengths and punctuation of the message are given

Inverting Ray-Knight identity

We provide a short proof of the Ray-Knight second generalized Theorem, using a martingale which can be seen (on the positive quadrant) as the Radon-Nikodym derivative of the reversed vertex-reinforced jump process measure with respect to the Markov jump process with the same conductances. Next we show that a variant of this process provides an inversion of that Ray-Knight identity. We give a similar result for the Ray-Knight first generalized Theorem.Comment: 18 page

Knight shift vs hole concentration in Hg1201 and Hg1212

We studied the hole concentration dependences of 63Cu Knight shifts in single-CuO2-layer high-Tc cuprate superconductors HgBa2CuO4+d and double-layer HgBa2CaCu2O6+d. We found that the spin Knight shift at room temperature as a function of the hole concentration in the single-layer superconductor is different from that in the double-layer superconductor. Two type relations between the spin Knight shift and the hole doping level serve to estimate the individual hole concentrations of the non-equivalent CuO2 planes in a unit cell.Comment: 4 pages, 4 figures, submitted to Physics Procedia, ISS2014 (27th International Symposium on Superconductivity, Tokyo

Anisotropic Behavior of Knight Shift in Superconducting State of Na_xCoO_2yH_2O

The Co Knight shift was measured in an aligned powder sample of Na_xCoO_2yH_2O, which shows superconductivity at T_c \sim 4.6 K. The Knight-shift components parallel (K_c) and perpendicular to the c-axis (along the ab plane K_{ab}) were measured in both the normal and superconducting (SC) states. The temperature dependences of K_{ab} and K_c are scaled with the bulk susceptibility, which shows that the microscopic susceptibility deduced from the Knight shift is related to Co-3d spins. In the SC state, the Knight shift shows an anisotropic temperature dependence: K_{ab} decreases below 5 K, whereas K_c does not decrease within experimental accuracy. This result raises the possibility that spin-triplet superconductivity with the spin component of the pairs directed along the c-axis is realized in Na_xCoO_2yH_2O.Comment: 5 pages, 5 figures, to be published in Journal of Physical Society of Japan vol. 75, No.

Evidence for a two component magnetic response in UPt3

The magnetic response of the heavy fermion superconductor UPt_3 has been investigated on a microscopic scale by muon Knight shift studies. Two distinct and isotropic Knight shifts have been found for the field in the basal plane. While the volume fractions associated with the two Knight shifts are approximately equal at low and high temperatures, they show a dramatic and opposite temperature dependence around T_N. Our results are independent on the precise muon localization site. We conclude that UPt_3 is characterized by a two component magnetic response.Comment: 5 pages, 4 figure