25 research outputs found
Global estimates for solutions to the linearized Monge--Amp\`ere equations
In this paper, we establish global estimates for solutions to the
linearized Monge-Amp\`ere equations under natural assumptions on the domain,
Monge-Amp\`ere measures and boundary data. Our estimates are affine invariant
analogues of the global estimates of Winter for fully nonlinear,
uniformly elliptic equations, and also linearized counterparts of Savin's
global estimates for the Monge-Amp\`ere equations.Comment: v2: presentation improve
Certain aspects of regularity in scalar field cosmological dynamics
We consider dynamics of the FRW Universe with a scalar field. Using
Maupertuis principle we find a curvature of geodesics flow and show that zones
of positive curvature exist for all considered types of scalar field potential.
Usually, phase space of systems with the positive curvature contains islands of
regular motion. We find these islands numerically for shallow scalar field
potentials. It is shown also that beyond the physical domain the islands of
regularity exist for quadratic potentials as well.Comment: 15 pages with 4 figures; typos corrected, final version to appear in
Regular and Chaotic Dynamic
Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm
We present the first results of the Fermilab Muon g-2 Experiment for the
positive muon magnetic anomaly . The anomaly is
determined from the precision measurements of two angular frequencies.
Intensity variation of high-energy positrons from muon decays directly encodes
the difference frequency between the spin-precession and cyclotron
frequencies for polarized muons in a magnetic storage ring. The storage ring
magnetic field is measured using nuclear magnetic resonance probes calibrated
in terms of the equivalent proton spin precession frequency
in a spherical water sample at 34.7C. The
ratio , together with known fundamental
constants, determines
(0.46\,ppm). The result is 3.3 standard deviations greater than the standard
model prediction and is in excellent agreement with the previous Brookhaven
National Laboratory (BNL) E821 measurement. After combination with previous
measurements of both and , the new experimental average of
(0.35\,ppm) increases the
tension between experiment and theory to 4.2 standard deviationsComment: 10 pages; 4 figure