Schubert calculus of Richardson varieties stable under spherical Levi subgroups

We observe that the expansion in the basis of Schubert cycles for $H^*(G/B)$ 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 $A$. Namely, we describe $c_{u,v}^w$ when $u$ and $v$ are inverse to Grassmannian permutations with unique descents at $p$ and $q$, respectively. We offer some conjectures for similar rules in types $B$ and $D$, 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 (B$\chi$PT) with pion, nucleon, and $\Delta$(1232) degrees of freedom, up to and including the next-to-next-to-leading order (NNLO). We include the effects of order $p^2$, $p^3$ and $p^4/\varDelta$, with $\varDelta\approx 300$ MeV the $\Delta$-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, $p^4$). Estimating the theoretical uncertainty on the basis of natural size for $p^4$ 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 $(4.0\pm 0.7)\times 10^{-4}$ fm$^3$, in significant disagreement with the current PDG value. Unlike the previous $\chi$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 HB$\chi$PT and B$\chi$PT results for polarizabilities is found to be appreciable. We discuss the chiral behavior of proton polarizabilities in both HB$\chi$PT and B$\chi$PT 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

Lamron ℓ-groups

No Abstract

The yosida space of the vector lattice hull of an archimedean ℓ-group with unit

W is the category of archimedean ℓ-groups with distinguished weak order unit. For G ϵ W, we have the contravariantly functorial Yosida space YG. For an embedding G ≤ H; the resulting YG → 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 ≠ YG. Theorem. A compact space X is quasi-F if and only if: ∀G ϵ W with YG = X, also YvG = X. ( quasi-F means each dense cozero set is C-embedded.

Atypical teratoid/rhabdoid tumors—current 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/ß-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