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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
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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
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