Lagrangian Matroids: Representations of Type BnB_n

We introduce the concept of orientation for Lagrangian matroids represented in the flag variety of maximal isotropic subspaces of dimension N in the real vector space of dimension 2N+1. The paper continues the study started in math.CO/0209100.Comment: Requires amssymb.sty; 17 page

Lagrangian Pairs and Lagrangian Orthogonal Matroids

Represented Coxeter matroids of types $C_n$ and $D_n$, that is, symplectic and orthogonal matroids arising from totally isotropic subspaces of symplectic or (even-dimensional) orthogonal spaces, may also be represented in buildings of type $C_n$ and $D_n$, respectively. Indeed, the particular buildings involved are those arising from the flags or oriflammes, respectively, of totally isotropic subspaces. There are also buildings of type $B_n$ arising from flags of totally isotropic subspaces in odd-dimensional orthogonal space. Coxeter matroids of type $B_n$ are the same as those of type $C_n$ (since they depend only upon the reflection group, not the root system). However, buildings of type $B_n$ are distinct from those of the other types. The matroids representable in odd dimensional orthogonal space (and therefore in the building of type $B_n$) turn out to be a special case of symplectic (flag) matroids, those whose top component, or Lagrangian matroid, is a union of two Lagrangian orthogonal matroids. These two matroids are called a Lagrangian pair, and they are the combinatorial manifestation of the ``fork'' at the top of an oriflamme (or of the fork at the end of the Coxeter diagram of $D_n$). Here we give a number of equivalent characterizations of Lagrangian pairs, and prove some rather strong properties of them.Comment: Requires amssymb.sty; 12 pages, 2 LaTeX figure

Control system for hunger and its implications in animals and man

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Simulations of disk galaxies with cosmic ray driven galactic winds

We present results from high-resolution hydrodynamic simulations of isolated SMC- and Milky Way-sized galaxies that include a model for feedback from galactic cosmic rays (CRs). We find that CRs are naturally able to drive winds with mass loading factors of up to ~10 in dwarf systems. The scaling of the mass loading factor with circular velocity between the two simulated systems is consistent with \propto v_c^{1-2} required to reproduce the faint end of the galaxy luminosity function. In addition, simulations with CR feedback reproduce both the normalization and the slope of the observed trend of wind velocity with galaxy circular velocity. We find that winds in simulations with CR feedback exhibit qualitatively different properties compared to SN driven winds, where most of the acceleration happens violently in situ near star forming sites. In contrast, the CR-driven winds are accelerated gently by the large-scale pressure gradient established by CRs diffusing from the star-forming galaxy disk out into the halo. The CR-driven winds also exhibit much cooler temperatures and, in the SMC-sized system, warm (T~10^4 K) gas dominates the outflow. The prevalence of warm gas in such outflows may provide a clue as to the origin of ubiquitous warm gas in the gaseous halos of galaxies detected via absorption lines in quasar spectra.Comment: ApJL accepted. Replaced with accepted version. Minor revision in response to referee comment

PRIVATIZATION AND TRANSITION ISSUES IN RUSSIAN AGRICULTURE

Agricultural and Food Policy,