arXiv subjects

G. Salazar

Publications and source records attributed to G. Salazar.

3 recordsLinked to original sources

arXiv2015

Charged Pion Production in $ν_μ$ Interactions on Hydrocarbon at $\langle E_ν\rangle$= 4.0 GeV

Charged pion production via charged current $ν_μ$ interactions on plastic (CH) is studied using the MINERvA detector exposed to the NuMI wideband neutrino beam at Fermilab. Events with hadronic invariant mass W $<$ 1.4 GeV are selected to isolate single pion production, which is expected to occur primarily through the $Δ(1232)$ resonance. Cross sections as functions of pion production angle and kinetic energy are reported and compared to predictions from different theoretical calculations and generator-based models, for neutrinos ranging in energy from 1.5 GeV to 10 GeV. The data are best described by calculations which include significant contributions from pion intranuclear rescattering. These measurements constrain the primary interaction rate and the role of final state interactions in pion production, both of which need to be well understood by neutrino oscillation experiments.

hep-ex↗

arXiv2008

3--symmetric and 3--decomposable drawings of $K_n$ (extended version)

Even the most superficial glance at the vast majority of crossing-minimal geometric drawings of $K_n$ reveals two hard-to-miss features. First, all such drawings appear to be 3-fold symmetric (or simply {\em 3-symmetric}) . And second, they all are {\em 3-decomposable}, that is, there is a triangle $T$ enclosing the drawing, and a balanced partition $A, B, C$ of the underlying set of points $P$, such that the orthogonal projections of $P$ onto the sides of $T$ show $A$ between $B$ and $C$ on one side, $B$ between $A$ and $C$ on another side, and $C$ between $A$ and $B$ on the third side. In fact, we conjecture that all optimal drawings are 3-decomposable, and that there are 3-symmetric optimal constructions for all $n$ multiple of 3. In this paper, we show that any 3-decomposable geometric drawing of $K_n$ has at least $0.380029\binom{n}{4}+Θ(n^3)$ crossings. On the other hand, we produce 3-symmetric and 3-decomposable drawings that improve the {\em general} upper bound for the rectilinear crossing number of $K_n$ to $0.380488\binom{n}{4}+Θ(n^3)$. We also give explicit 3-symmetric and 3-decomposable constructions for $n<100$ that are at least as good as those previously known.

math.CO↗

arXiv2004

Improved bounds for the crossing numbers of K_m,n and K_n

It has been long--conjectured that the crossing number cr(K_m,n) of the complete bipartite graph K_m,n equals the Zarankiewicz Number Z(m,n):= floor((m-1)/2) floor(m/2) floor((n-1)/2) floor(n/2). Another long--standing conjecture states that the crossing number cr(K_n) of the complete graph K_n equals Z(n):= floor(n/2) floor((n-1)/2) floor((n-2)/2) floor((n-3)/2)/4. In this paper we show the following improved bounds on the asymptotic ratios of these crossing numbers and their conjectured values: (i) for each fixed m >= 9, lim_{n->infty} cr(K_m,n)/Z(m,n) >= 0.83m/(m-1); (ii) lim_{n->infty} cr(K_n,n)/Z(n,n) >= 0.83; and (iii) lim_{n->infty} cr(K_n)/Z(n) >= 0.83. The previous best known lower bounds were 0.8m/(m-1), 0.8, and 0.8, respectively. These improved bounds are obtained as a consequence of the new bound cr(K_{7,n}) >= 2.1796n^2 - 4.5n. To obtain this improved lower bound for cr(K_{7,n}), we use some elementary topological facts on drawings of K_{2,7} to set up a quadratic program on 6! variables whose minimum p satisfies cr(K_{7,n}) >= (p/2)n^2 - 4.5n, and then use state--of--the--art quadratic optimization techniques combined with a bit of invariant theory of permutation groups to show that p >= 4.3593.

math.CO↗