Véges geometria = Finite geometry

Megmutattuk, hogy négyzet q-ra PG(2,q)-ban 4qlog q és q^(3/2)-q+2q^(1/2) között minden méretű minimális lefogó ponthalmaz létezik, sőt egy kicsit szűkebb intervallum minden értékére q-ban több, mint polinomnyi. Magasabb dimenziós projektív terekben a hipersíkokat r modulo p pontban metsző halmazok méretére bizonyos esetekben éles alsó becslést adtunk, amely a maximális ívek nemlétezésére vonatkozó Ball-Blokhuis-Mazzocca tétel általánosítása. Ez osztható lineáris kódok hosszára az n legalább (r-1)q+(p-1)r alsó becslést adja, ahol r az az érték, amellyel n és minden kódszó súlya is osztható. Megmutattuk, hogy PG(2,q) reguláris szemioválisai csak az oválisok és az unitálok. Segre típusí eredményt sikerült belátni másodrendű kúpok részleges kúpszeletnyalábjaira. Kis minimális lefogó ponthalmazok struktúrájáról azt sikerült megmutatni, hogy ezek minden egyenest 1 modulo p^e pontban metszenek, ahol e osztja h-t, ha q=p^h. Ezen túlmenően, ha a metszet p^e+1 elemű, akkor az GF(p^e) feletti részegyenes. Kis t-szeres lefogó ponthalmazokra az egyenesekkel való metszetekre beláttuk, hogy azok modulo p t-vel kongruensek, ahol t a karakterisztika. Ha q páros, akkor stabilitási eredményt bizonyítottunk PG(2,q) páros halmazaira. Az eredmény négyzet q-ra éles, és B. Segre ívek beágyazásáról szóló híres tételét általánosítja. Megmutattuk, hogy a Q(4,q) általánosított négyszögben nincsenek q^2-1 pontú maximális parciális ovoidok. | It was proven that in PG(2,q), q square, there is a minimal blocking set for any size between 4qlog q and q^(3/2)-q+2q^(1/2), Moreover, for a slightly smaller interval we also proved that the number of nonisomorphic minimal blocking sets of that size is more than polynomial in q. For sets intersecting all hyperplanes in r modulo p points we found a lower bound that is sharp in some cases. The proof generalizes the nonexistence of maximal arcs, due to Ball-Blokhuis-Mazzocca. For divisible linear codes it gives that the length is at least (r-1)q+(p-1)r, where divides the length and the weight of all codewords. We found that in PG(2,q) regular semiovals must be either ovals or unitals. We obtained a Segre type theorem for partial flocks of the quadratic cone. About the structure of small minimal blocking sets we obtained the following: each line intersects the set in 1 modulo p^e points, where e divides h and q=p^h. Furthermore, if the intersection has p^e+1 points, then it is a subline over GF(p^e). We proved that a small minimal t-fold blocking set intersects every line in t modulo p points, where p is the characteristics. For even q-s we proved a stability theorem for sets of even type in PG(2,q). The result is sharp when q is a square, and it generalizes a famous embeddability theorem for arcs, due to B. Segre. We also proved that the GQ Q(4,q) does not have maximal partial ovoids of size q^2-1

Measurement of the forward charged particle pseudorapidity density in pp collisions at √s=8 TeV using a displaced interaction point

The pseudorapidity density of charged particles dN(ch)/deta is measured by the TOTEM experiment in pp collisions at sqrt(s) = 8 TeV within the range 3.9 0 MeV/c, produced in inelastic interactions with at least one charged particle in -7 < eta < -6 or 3.7 < eta <4.8 . The dN(ch)/deta has been found to decrease with |eta|, from 5.11 +- 0.73 at eta = 3.95 to 1.81 +- 0.56 at eta= - 6.925. Several MC generators are compared to the data and are found to be within the systematic uncertainty of the measurement

Measurement of elastic pp scattering at √s=8 TeV in the Coulomb–nuclear interference region: determination of the ρ -parameter and the total cross-section

The TOTEM experiment at the CERN LHC has measured elastic proton-proton scattering at the centre-of- mass energy √s = 8 TeV and four-momentum transfers squared, |t|, from 6 × 10−4 GeV2 to 0.2 GeV2. Near the lower end of the t-interval the differential cross-section is sensitive to the interference between the hadronic and the electromagnetic scattering amplitudes. This article presents the elastic cross-section measurement and the constraints it imposes on the functional forms of the modulus and phase of the hadronic elastic amplitude. The data exclude the tradi- tional Simplified West and Yennie interference formula that requires a constant phase and a purely exponential modu- lus of the hadronic amplitude. For parametrisations of the hadronic modulus with second- or third-order polynomials in the exponent, the data are compatible with hadronic phase functions giving either central or peripheral behaviour in the impact parameter picture of elastic scattering. In both cases, the ρ-parameter is found to be 0.12 ± 0.03. The results for the total hadronic cross-section are σtot = (102.9 ± 2.3) mb and (103.0 ± 2.3) mb for central and peripheral phase for- mulations, respectively. Both are consistent with previous TOTEM measurements

First measurement of elastic, inelastic and total cross-section at √s=13 TeV by TOTEM and overview of cross-section data at LHC energies: TOTEM Collaboration

The TOTEM collaboration has measured the proton-proton total cross section at $\sqrt{s}=13$ TeV with a luminosity-independent method. Using dedicated $\beta^{*}=90$ m beam optics, the Roman Pots were inserted very close to the beam. The inelastic scattering rate has been measured by the T1 and T2 telescopes during the same LHC fill. After applying the optical theorem the total proton-proton cross section is $\sigma_{\rm tot}=(110.6 \pm 3.4$) mb, well in agreement with the extrapolation from lower energies. This method also allows one to derive the luminosity-independent elastic and inelastic cross sections: $\sigma_{\rm el} = (31.0 \pm 1.7)$ mb and $\sigma_{\rm inel} = (79.5 \pm 1.8)$ mb

φ meson production in d + Au collisions at sNN =200 GeV

The PHENIX collaboration has measured φ meson production in d+Au collisions at √sN N = 200 GeV using the dimuon and dielectron decay channels. The φ meson is measured in the forward (backward) d-going (Au-going) direction, 1.2 < y < 2.2 (−2.2 < y < −1.2) in the transverse- momentum (pT ) range from 1–7 GeV/c, and at midrapidity |y| < 0.35 in the pT range below 7 GeV/c. The φ meson invariant yields and nuclear-modification factors as a function of pT , rapidity, and centrality are reported. An enhancement of φ meson production is observed in the Au-going direction, while suppression is seen in the d-going direction, and no modification is observed at midrapidity relative to the yield in p+p collisions scaled by the number of binary collisions. Similar behavior was previously observed for inclusive charged hadrons and open heavy flavor indicating similar cold-nuclear-matter effects

Measurement of long-range angular correlation and quadrupole anisotropy of pions and (anti)protons in central d+Au collisions at √sN N = 200 GeV

We present azimuthal angular correlations between charged hadrons and energy deposited in calorimeter towers in central d + Au and minimum bias p + p collisions at root s(NN) = 200 GeV. The charged hadron is measured at midrapidity vertical bar eta vertical bar 2.75 is observed in d + Au collisions. Using the event plane method applied to the Au-going energy distribution, we extract the anisotropy strength v(2) for inclusive charged hadrons at midrapidity up to p(T) = 4.5 GeV/c. We also present the measurement of v(2) for identified pi(+/-) and (anti)protons in central d + Au collisions, and observe a mass-ordering pattern similar to that seen in heavy-ion collisions. These results are compared with viscous hydrodynamic calculations and measurements from p + Pb at root s(NN) = 5.02 TeV. The magnitude of the mass ordering in d + Au is found to be smaller than that in p + Pb collisions, which may indicate smaller radial flow in lower energy d + Au collisions

Measurement of the relative yields of ψ(2S) to ψ(1S) mesons produced at forward and backward rapidity in p+p, p+Al, p+Au, and 3He+Au collisions at √sNN=200 GeV

The PHENIX Collaboration has measured the ratio of the yields of $\psi(2S)$ to $\psi(1S)$ mesons produced in $p$$+$$p$, $p$$+$Al, $p$$+$Au, and $^{3}$He$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV over the forward and backward rapidity intervals $1.2<|y|<2.2$. We find that the ratio in $p$$+$$p$ collisions is consistent with measurements at other collision energies. In collisions with nuclei, we find that in the forward ($p$-going or $^{3}$He-going) direction, the relative yield of $\psi(2S)$ mesons to $\psi(1S)$ mesons is consistent with the value measured in \pp collisions. However, in the backward (nucleus-going) direction, the $\psi(2S)$ is preferentially suppressed by a factor of $\sim$2. This suppression is attributed in some models to breakup of the weakly-bound $\psi(2S)$ through final state interactions with comoving particles, which have a higher density in the nucleus-going direction. These breakup effects may compete with color screening in a deconfined quark-gluon plasma to produce sequential suppression of excited quarkonia states