The (B) conjecture for uniform measures in the plane

We prove that for any two centrally-symmetric convex shapes $K,L \subset \mathbb{R}^2$, the function $t \mapsto |e^t K \cap L|$ is log-concave. This extends a result of Cordero-Erausquin, Fradelizi and Maurey in the two dimensional case. Possible relaxations of the condition of symmetry are discussed.Comment: 10 page

Adapting Real Quantifier Elimination Methods for Conflict Set Computation

The satisfiability problem in real closed fields is decidable. In the context of satisfiability modulo theories, the problem restricted to conjunctive sets of literals, that is, sets of polynomial constraints, is of particular importance. One of the central problems is the computation of good explanations of the unsatisfiability of such sets, i.e.\ obtaining a small subset of the input constraints whose conjunction is already unsatisfiable. We adapt two commonly used real quantifier elimination methods, cylindrical algebraic decomposition and virtual substitution, to provide such conflict sets and demonstrate the performance of our method in practice

Truth Table Invariant Cylindrical Algebraic Decomposition by Regular Chains

A new algorithm to compute cylindrical algebraic decompositions (CADs) is presented, building on two recent advances. Firstly, the output is truth table invariant (a TTICAD) meaning given formulae have constant truth value on each cell of the decomposition. Secondly, the computation uses regular chains theory to first build a cylindrical decomposition of complex space (CCD) incrementally by polynomial. Significant modification of the regular chains technology was used to achieve the more sophisticated invariance criteria. Experimental results on an implementation in the RegularChains Library for Maple verify that combining these advances gives an algorithm superior to its individual components and competitive with the state of the art

Speeding up Cylindrical Algebraic Decomposition by Gr\"obner Bases

Gr\"obner Bases and Cylindrical Algebraic Decomposition are generally thought of as two, rather different, methods of looking at systems of equations and, in the case of Cylindrical Algebraic Decomposition, inequalities. However, even for a mixed system of equalities and inequalities, it is possible to apply Gr\"obner bases to the (conjoined) equalities before invoking CAD. We see that this is, quite often but not always, a beneficial preconditioning of the CAD problem. It is also possible to precondition the (conjoined) inequalities with respect to the equalities, and this can also be useful in many cases.Comment: To appear in Proc. CICM 2012, LNCS 736

Electroproduction of the d* dibaryon

The unpolarized cross section for the electroproduction of the isoscalar $J^\pi = 3^+$ di-delta dibaryon $d^*$ is calculated for deuteron target using a simple picture of elastic electron-baryon scattering from the $\Delta \Delta (^7D_1)$ and the $NN (^3S_1)$ components of the deuteron. The calculated differential cross section at the electron lab energy of 1 GeV has the value of about 0.24 (0.05) nb/sr at the lab angle of 10$^\circ$ (30$^\circ$) for the Bonn B potential when the dibaryon mass is taken to be 2.1 GeV. The cross section decreases rapidly with increasing dibaryon mass. A large calculated width of 40 MeV for $d^*(\Delta\Delta ^7S_3)$ combined with a small experimental upper bound of 0.08 MeV for the $d^*$ decay width appears to have excluded any low-mass $d^*$ model containing a significant admixture of the $\Delta\Delta (^7S_3)$ configuration.Comment: 11 journal-style pages, 8 figure

A simple expression for the ADM mass

We show by an almost elementary calculation that the ADM mass of an asymptotically flat space can be computed as a limit involving a rate of change of area of a closed 2-surface. The result is essentially the same as that given by Brown and York. We will prove this result in two ways, first by direct calculation from the original formula as given by Arnowitt, Deser and Misner and second as a corollary of an earlier result by Brewin for the case of simplicial spaces.Comment: 9 pages, 1 figur

Selenium Concentrations in Forage on Some High Northwestern Ranges

Forages produced on some high northwestern ranges were analyzed for selenium concentration to determine the hazard of white muscle disease (WMD) in calves and lambs. The selenium concentration in 94 forage samples ranged from 0.01 to 0.78 ppm, of which 20 samples contained more than 0.10 ppm. The remaining 74 samples contained less than 0.10 ppm and 59 of those contained Less than 0.05 ppm. Approximately 90% of the summer ranges studied produce forage containing less than 0.10 ppm selenium. Thus, the hazard of WMD on these northwestern ranges may be high. Ranchers should work individually and in groups to ascertain losses from the disease and minimize them by injecting the animals with selenium

Selenium Concentrations in Alfalfa from Several Sources Applied to a Low Selenium, Alkaline Soil

Two laboratory-prepared ferric hydroxy bi-selenites and CuSeO? applied to Portneuf silt ham in the field provided slowly available Se to alfalfa, resulting in Se concentration adequate but nontoxic for livestock. These materials have potential as Se fertilizers at low application rates. The ferric hydroxy bi-selenites offer little or no advantage over CuSeO?. Se from BaSeO? alone, BaSeO?—BaSO? mixtures, and CuSeO? was absorbed by alfalfa in concentrations toxic to livestock. A small fraction of applied elemental Se was available immediately after application, providing adequate Se to alfalfa for livestock. The remaining elemental Se was rather inert, and supplies only slightly more Se to alfalfa than did the untreated soil the year following application

Effect of Phosphorus Fertilization on the Selenium Concentration in Alfalfa (Medicago sativa)

A study was conducted to determine the effect of P fertilization on the Se concentration in alfalfa. Adding P to the soil increased the Se concentration in alfalfa grown in the greenhouse on six of 14 soils from the northwestern United States. The Se concentration increase in alfalfa resulting from P addition was noted on some alkaline and some acid soils. Phosphorus addition increased the availability to alfalfa of both native and applied Se in the Portneuf silt loam. Applying 160 kg P/ha either as H?PO? or concentrated superphosphate to Gooding sandy loam in the field increased the Se concentration in alfalfa from a level marginal for animal requirements to an adequate level