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State Highlights 4/2/1952
This is the student newspaper from Western State High School, the high school that was on the campus of Western Michigan University, then called State Highlights, in 1952
OSp(4|2) Superconformal Mechanics
A new superconformal mechanics with OSp(4|2) symmetry is obtained by gauging
the U(1) isometry of a superfield model. It is the one-particle case of the new
N=4 super Calogero model recently proposed in arXiv:0812.4276 [hep-th].
Classical and quantum generators of the osp(4|2) superalgebra are constructed
on physical states. As opposed to other realizations of N=4 superconformal
algebras, all supertranslation generators are linear in the odd variables,
similarly to the N=2 case. The bosonic sector of the component action is
standard one-particle (dilatonic) conformal mechanics accompanied by an
SU(2)/U(1) Wess-Zumino term, which gives rise to a fuzzy sphere upon
quantization. The strength of the conformal potential is quantized.Comment: 1+20 pages, v2: typos fixed, for publication in JHE
On the Classical Algebra
We consider the classical \w42 algebra from the integrable system viewpoint.
The integrable evolution equations associated with the \w42 algebra are
constructed and the Miura maps , consequently modifications, are presented.
Modifying the Miura maps, we give a free field realization the classical \w42
algebra. We also construct the Toda type integrable systems for it.Comment: 14 pages, latex, no figure
On the Veldkamp Space of GQ(4, 2)
The Veldkamp space, in the sense of Buekenhout and Cohen, of the generalized
quadrangle GQ(4, 2) is shown not to be a (partial) linear space by simply
giving several examples of Veldkamp lines (V-lines) having two or even three
Veldkamp points (V-points) in common. Alongside the ordinary V-lines of size
five, one also finds V-lines of cardinality three and two. There, however,
exists a subspace of the Veldkamp space isomorphic to PG(3, 4) having 45 perps
and 40 plane ovoids as its 85 V-points, with its 357 V-lines being of four
distinct types. A V-line of the first type consists of five perps on a common
line (altogether 27 of them), the second type features three perps and two
ovoids sharing a tricentric triad (240 members), whilst the third and fourth
type each comprises a perp and four ovoids in the rosette centered at the
(common) center of the perp (90). It is also pointed out that 160 non-plane
ovoids (tripods) fall into two distinct orbits -- of sizes 40 and 120 -- with
respect to the stabilizer group of a copy of GQ(2, 2); a tripod of the
first/second orbit sharing with the GQ(2, 2) a tricentric/unicentric triad,
respectively. Finally, three remarkable subconfigurations of V-lines
represented by fans of ovoids through a fixed ovoid are examined in some
detail.Comment: 6 pages, 7 figures; v2 - slightly polished, subsection on fans of
ovoids and three figures adde
New Super Calogero Models and OSp(4|2) Superconformal Mechanics
We report on the new approach to constructing superconformal extensions of
the Calogero-type systems with an arbitrary number of involved particles. It is
based upon the superfield gauging of non-abelian isometries of some
supersymmetric matrix models. Among its applications, we focus on the new N=4
superconformal system yielding the U(2) spin Calogero model in the bosonic
sector, and the one-particle case of this system, which is a new OSp(4|2)
superconformal mechanics with non-dynamical U(2) spin variables. The
characteristic feature of these models is that the strength of the conformal
inverse-square potential is quantized.Comment: 12 pages, talk presented by E.Ivanov at the XIII International
Conference "Symmetry Methods in Physics", Dubna, July 6-9, 200
Fermi-Bose mixtures and BCS-BEC crossover in high-Tc superconductors
In this review article we consider theoretically and give experimental
support to the models of the Fermi-Bose mixtures and the BCS-BEC crossover
compared with the strong-coupling approach, which can serve as the cornerstones
on the way from high-temperature to room-temperature superconductivity in
pressurized metallic hydrides. We discuss some key theoretical ideas and
mechanisms proposed for unconventional superconductors (cuprates, pnictides,
chalcogenides, bismuthates, diborides, heavy-fermions, organics, bilayer
graphene, twisted graphene, oxide hetero-structures), superfluids and balanced
or imbalanced ultracold Fermi gases in magnetic traps. We build a bridge
between unconventional superconductors and recently discovered pressurized
hydrides superconductors H3S and LaH10 with the critical temperature close to
room temperature. We discuss systems with line of nodal Dirac points close to
the Fermi surface, superconducting shape resonances and hyperbolic
superconducting networks which are very important for the development of novel
topological superconductors, for the energetics, for the applications in
nano-electronics and quantum computations.Comment: 19 pages, 7 figure
Good Code Sets from Complementary Pairs via Discrete Frequency Chips
It is shown that replacing the sinusoidal chip in Golay complementary code
pairs by special classes of waveforms that satisfy two conditions,
symmetry/anti-symmetry and quazi-orthogonality in the convolution sense,
renders the complementary codes immune to frequency selective fading and also
allows for concatenating them in time using one frequency band/channel. This
results in a zero-sidelobe region around the mainlobe and an adjacent region of
small cross-correlation sidelobes. The symmetry/anti-symmetry property results
in the zero-sidelobe region on either side of the mainlobe, while
quasi-orthogonality of the two chips keeps the adjacent region of
cross-correlations small. Such codes are constructed using discrete
frequency-coding waveforms (DFCW) based on linear frequency modulation (LFM)
and piecewise LFM (PLFM) waveforms as chips for the complementary code pair, as
they satisfy both the symmetry/anti-symmetry and quasi-orthogonality
conditions. It is also shown that changing the slopes/chirp rates of the DFCW
waveforms (based on LFM and PLFM waveforms) used as chips with the same
complementary code pair results in good code sets with a zero-sidelobe region.
It is also shown that a second good code set with a zero-sidelobe region could
be constructed from the mates of the complementary code pair, while using the
same DFCW waveforms as their chips. The cross-correlation between the two sets
is shown to contain a zero-sidelobe region and an adjacent region of small
cross-correlation sidelobes. Thus, the two sets are quasi-orthogonal and could
be combined to form a good code set with twice the number of codes without
affecting their cross-correlation properties. Or a better good code set with
the same number codes could be constructed by choosing the best candidates form
the two sets. Such code sets find utility in multiple input-multiple output
(MIMO) radar applications
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