31 research outputs found
Schubert calculus of Richardson varieties stable under spherical Levi subgroups
We observe that the expansion in the basis of Schubert cycles for
of the class of a Richardson variety stable under a spherical Levi subgroup is
described by a theorem of Brion. Using this observation, along with a
combinatorial model of the poset of certain symmetric subgroup orbit closures,
we give positive combinatorial descriptions of certain Schubert structure
constants on the full flag variety in type . Namely, we describe
when and are inverse to Grassmannian permutations with unique descents
at and , respectively. We offer some conjectures for similar rules in
types and , associated to Richardson varieties stable under spherical
Levi subgroups of SO(2n+1,\C) and SO(2n,\C), respectively.Comment: Section 4 significantly shortened, and other minor changes made as
suggested by referees. Final version, to appear in Journal of Algebraic
Combinatoric
Stability of strange quark matter: MIT bag versus Color Dielectric Model
We discuss the properties of strange matter, in particular the minimum of the
energy per baryon number as a function of the strangeness fraction. We utilize
both the MIT bag model and the Color Dielectric Model and compare the energy
per baryon with the masses of hyperons having the corresponding strangeness
fraction, which are coherently calculated within both models. We also take into
account the perturbative exchange of gluons. The results obtained in the two
approaches allow to discuss the stability of strangelets. While the MIT bag
model and the double minimum version of the Color Dielectric Model allow the
existence of strangelets, the single minimum version of the Color Dielectric
Model excludes this possibility.Comment: 26 pages, 9 figure
Hybrid stars with the color dielectric and the MIT bag models
We study the hadron-quark phase transition in the interior of neutron stars
(NS). For the hadronic sector, we use a microscopic equation of state (EOS)
involving nucleons and hyperons derived within the Brueckner-Bethe-Goldstone
many-body theory, with realistic two-body and three-body forces. For the
description of quark matter, we employ both the MIT bag model with a density
dependent bag constant, and the color dielectric model. We calculate the
structure of NS interiors with the EOS comprising both phases, and we find that
the NS maximum masses are never larger than 1.7 solar masses, no matter the
model chosen for describing the pure quark phase.Comment: 11 pages, 5 figures, submitted to Phys. Rev.
Predictive powers of chiral perturbation theory in Compton scattering off protons
We study low-energy nucleon Compton scattering in the framework of baryon
chiral perturbation theory (BPT) with pion, nucleon, and (1232)
degrees of freedom, up to and including the next-to-next-to-leading order
(NNLO). We include the effects of order , and , with
MeV the -resonance excitation energy. These are
all "predictive" powers in the sense that no unknown low-energy constants enter
until at least one order higher (i.e, ). Estimating the theoretical
uncertainty on the basis of natural size for effects, we find that
uncertainty of such a NNLO result is comparable to the uncertainty of the
present experimental data for low-energy Compton scattering. We find an
excellent agreement with the experimental cross section data up to at least the
pion-production threshold. Nevertheless, for the proton's magnetic
polarizability we obtain a value of fm, in
significant disagreement with the current PDG value. Unlike the previous
PT studies of Compton scattering, we perform the calculations in a
manifestly Lorentz-covariant fashion, refraining from the heavy-baryon (HB)
expansion. The difference between the lowest order HBPT and BPT
results for polarizabilities is found to be appreciable. We discuss the chiral
behavior of proton polarizabilities in both HBPT and BPT with the
hope to confront it with lattice QCD calculations in a near future. In studying
some of the polarized observables, we identify the regime where their naive
low-energy expansion begins to break down, thus addressing the forthcoming
precision measurements at the HIGS facility.Comment: 24 pages, 9 figures, RevTeX4, revised version published in EPJ
The yosida space of the vector lattice hull of an archimedean â-group with unit
W is the category of archimedean â-groups with distinguished weak order unit. For G Ï” W, we have the contravariantly functorial Yosida space YG. For an embedding G †H; the resulting YG â YH is surjective; when this is one-to-one, we write YH = YG . This is the case with the divisible hull G †dG, where, always, YdG = YG; however for the vector lattice hull G †vG, we frequently have YvG â YG. Theorem. A compact space X is quasi-F if and only if: âG Ï” W with YG = X, also YvG = X. ( quasi-F means each dense cozero set is C-embedded.
Atypical teratoid/rhabdoid tumorsâcurrent concepts, advances in biology, and potential future therapies
Atypical teratoid/rhabdoid tumor (AT/RT) is the most common malignant CNS tumor of children below 6 months of age. The majority of AT/RTs demonstrate genomic alterations in SMARCB1 (INI1, SNF5, BAF47) or, to a lesser extent, SMARCA4 (BRG1) of the SWItch/sucrose nonfermentable chromatin remodeling complex. Recent transcription and methylation profiling studies suggest the existence of molecular subgroups. Thus, at the root of these seemingly enigmatic tumors lies a network of factors related to epigenetic regulation, which is not yet completely understood. While conventional-type chemotherapy may have significant survival benefit for certain patients, it remains to be determined which patients will eventually prove resistant to chemotherapy and thus need novel therapeutic strategies. Elucidation of the molecular consequences of a disturbed epigenome has led to the identification of a series of transduction cascades, which may be targeted for therapy. Among these are the pathways of cyclin D1/cyclin-dependent kinases 4 and 6, Hedgehog/GLI1, Wnt/Ă-catenin, enhancer of zeste homolog 2, and aurora kinase A, among others. Compounds specifically targeting these pathways or agents that alter the epigenetic state of the cell are currently being evaluated in preclinical settings and in experimental clinical trials for AT/RT