Explore the vast range of titles available.

We investigate the role played by curve singularity germs in the enumeration of inflection points in families of curves acquiring singular members. Let

Abstract A major challenge in understanding the process of nucleus-nucleus interactions is the examination of the processes that occur in the participant and spectator areas of interacting nuclei, considering the central nature of the reactions. Nearly thresholdless detection of the secondary charged particles is made possible by nuclear emulsion detectors (NED), which provide a complete 4πangular coverage. This work is mainly concerned with the multiplicity distributions (MD) and fluctuation of the average multiplicities of secondary charged particles (slow proton, fast proton, and shower) brought about by the collision of⁸⁴Kr-nuclei with emulsion nuclei at 1 A GeV. The MD of these particles has been computed by use of a modified cascade evaporation model (MCEM). The MD of each of the several charged secondary particles is correlated and analyzed. The observation demonstrates that the theoretical calculation results for the average multiplicities of shower particles, fast and slow protons agree well with the experimental data. Correlations seen experimentally between the multiplicities of different emitted particles are faithfully reproduced by the MCEM. There is good agreement between the experimental data and the theoretical calculation results.

The Allen–Cahn equation is a semilinear PDE which is deeply linked to the theory of minimal hypersurfaces via a singular limit. We prove curvature estimates and strong sheet separation estimates for stable solutions (building on recent work of Wang–Wei) of the Allen-Cahn equation on a 3-manifold. Using these, we are able to show that for generic metrics on a 3-manifold, minimal surfaces arising from Allen–Cahn solutions with bounded energy and bounded Morse index are two-sided and occur with multiplicity one and the expected Morse index. This confirms, in the Allen–Cahn setting, a strong form of the multiplicity one-conjecture and the index lower bound conjecture of Marques–Neves in 3-dimensions regarding min-max constructions of minimal surfaces. Allen–Cahn min-max constructions were recently carried out by Guaraco and Gaspar–Guaraco. Our resolution of the multiplicity-one and the index lower bound conjectures shows that these constructions can be applied to give a new proof of Yau's conjecture on infinitely many minimal surfaces in a 3-manifold with a generic metric (recently proven by Irie–Marques–Neves) with new geometric conclusions. Namely, we prove that a 3-manifold with a generic metric contains, for every p = 1, 2, 3,…, a two-sided embedded minimal surface with Morse index p and area ~ p 1 3 , as conjectured by Marques-Neves.

The pseudorapidity density and multiplicity distribution of charged particles produced in proton-proton collisions at the LHC, at a centre-of-mass energy $\\sqrt{s}=7$ TeV, were measured in the central pseudorapidity region |η| < 1. Comparisons are made with previous measurements at $\\sqrt{s}=0.9$ TeV and 2.36 TeV. At $\\sqrt{s}=7$ TeV, for events with at least one charged particle in |η| < 1, we obtain dNch/dη = 6.01 ± 0.01(stat.)$\\mathbb +0.20\\atop{-0.12} $(syst.). This corresponds to an increase of 57.6% ± 0.4%(stat.)$\\mathbb +3.6\\atop{-1.8} $(syst.) relative to collisions at 0.9 TeV, significantly higher than calculations from commonly used models. The multiplicity distribution at 7 TeV is described fairly well by the negative binomial distribution.

Questions often arise concerning when, whether, and how we should adjust our interpretation of the results from multiple hypothesis tests. Strong arguments have been put forward in the epidemiological literature against any correction or adjustment for multiplicity, but regulatory requirements (particularly for pharmaceutical trials) can sometimes trump other concerns. The formal basis for adjustment is often the control of error rates, and hence the problems of multiplicity may seem rooted in a purely frequentist paradigm, though this can be a restrictive viewpoint. Commentators may never wholly agree on any of these things. This article draws some of the key threads from the discussion and suggests further reading.

In this paper, we establish concentration and multiplicity properties of ground state solutions to the following perturbed double phase problem with competing potentials: - ϵ p Δ p u - ϵ q Δ q u + V ( x ) ( | u | p - 2 u + | u | q - 2 u ) = K ( x ) f ( u ) , in R N , u ∈ W 1 , p ( R N ) ∩ W 1 , q ( R N ) , u > 0 , in R N , where 1 < p < q < N , Δ s u = div ( | ∇ u | s - 2 ∇ u ) , with s ∈ { p , q } , is the s -Laplacian operator, and ϵ is a small positive parameter. We assume that the potentials V , K and the nonlinearity f are continuous but are not necessarily of class C 1 . Under some natural hypotheses, using topological and variational tools from Nehari manifold analysis and Ljusternik–Schnirelmann category theory, we study the existence of positive ground state solutions and the relation between the number of positive solutions and the topology of the set where V attains its global minimum and K attains its global maximum. Moreover, we determine two concrete sets related to the potentials V and K as the concentration positions and we describe the concentration of ground state solutions as ϵ → 0 . The asymptotic convergence and the exponential decay of positive solutions are also explored. Finally, we establish a sufficient condition for the non-existence of ground state solutions.

A bstract A search for squarks and gluinos in final states containing high- p T jets, missing transverse momentum and no electrons or muons is presented. The data were recorded in 2012 by the ATLAS experiment in s = 8 TeV proton-proton collisions at the Large Hadron Collider, with a total integrated luminosity of 20 . 3 fb −1 . Results are interpreted in a variety of simplified and specific supersymmetry-breaking models assuming that R -parity is conserved and that the lightest neutralino is the lightest supersymmetric particle. An exclusion limit at the 95% confidence level on the mass of the gluino is set at 1330 GeV for a simplified model incorporating only a gluino and the lightest neutralino. For a simplified model involving the strong production of first- and second-generation squarks, squark masses below 850 GeV (440 GeV) are excluded for a massless lightest neutralino, assuming mass degenerate (single light-flavour) squarks. In mSUGRA/CMSSM models with tan β = 30, A 0 = −2 m 0 and μ > 0, squarks and gluinos of equal mass are excluded for masses below 1700 GeV. Additional limits are set for non-universal Higgs mass models with gaugino mediation and for simplified models involving the pair production of gluinos, each decaying to a top squark and a top quark, with the top squark decaying to a charm quark and a neutralino. These limits extend the region of supersymmetric parameter space excluded by previous searches with the ATLAS detector.

A major challenge in understanding the process of nucleus-nucleus interactions is the examination of the processes that occur in the participant and spectator areas of interacting nuclei, considering the central nature of the reactions. Nearly thresholdless detection of the secondary charged particles is made possible by nuclear emulsion detectors (NED), which provide a complete 4π angular coverage. This work is mainly concerned with the multiplicity distributions (MD) and fluctuation of the average multiplicities of secondary charged particles (slow proton, fast proton, and shower) brought about by the collision of [Formula: see text]-nuclei with emulsion nuclei at 1 A GeV. The MD of these particles has been computed by use of a modified cascade evaporation model (MCEM). The MD of each of the several charged secondary particles is correlated and analyzed. The observation demonstrates that the theoretical calculation results for the average multiplicities of shower particles, fast and slow protons agree well with the experimental data. Correlations seen experimentally between the multiplicities of different emitted particles are faithfully reproduced by the MCEM. There is good agreement between the experimental data and the theoretical calculation results.

We describe a new instrument, the Argonne Auger Radioisotope Microscope (ARM), capable of characterizing the Auger electron (AE) emission of radionuclides, including candidates relevant in nuclear medicine. Our approach relies on event-by-event ion–electron coincidence, time-of-flight, and spatial readout measurement to determine correlated electron multiplicity and energy distributions of Auger decays. We present a proof-of-principle measurement with the ARM using x-ray photoionization of stable krypton beyond the K-edge and identify a bifurcation in the electron multiplicity distribution depending on the emission of K-LX electrons. Extension of the ARM to the characterization of radioactive sources of AE emissions is enabled by the combination of two recent developments: (1) cryogenic buffer gas beam technology to introduce Auger emitters into the detection region with well-defined initial conditions, and (2) large-area micro-channel plate detectors with multi-hit detection capabilities to simultaneously detect multiple electrons emitted in a single decay.