DELAY DIFFERENTIAL EQUATIONS AND THEIR APPLICATION TO MICRO ELECTRO MECHANICAL SYSTEMS

Delay differential equations have a wide range of applications in engineering. This work is devoted to the analysis of delay Duffing equation, which plays a crucial role in modeling performance on demand Micro Electro Mechanical Systems (MEMS). We start with the stability analysis of a linear delay model. We also show that in certain cases the delay model can be efficiently approximated with a much simpler model without delay. We proceed with the analysis of a non-linear Duffing equation. This model is a significantly more complex mathematical model. For instance, the existence of a periodic solution for this equation is a highly nontrivial question, which was established by Struwe. The main result of this work is to establish the existence of a periodic solution to delay Duffing equation. The paper claimed to establish the existence of such solutions, however their argument is wrong. In this work we establish the existence of a periodic solution under the assumption that the delay is sufficiently small

L1L_{1}-maximal regularity for quasilinear second order differential equation with damped term

We investigated a quasilinear second order equation with damped term on the real axis. We gave some suitable conditions for existence of the $L_{1}$-maximal regular solutions of this equation

The Measurement of the Asymmetry of Tensor-Polarized Deuteron Electrodisintegration at 180 MeV Electron Energy

The nucleon emission asymmetry in d(e, pn)e' reaction was measured using the tensor-polarized deuterium jet target in the VEPP-2 electron storage ring. At the present experimental accuracy, the results for the proton energy interval Ep= 12-100 MeV do not contradict the nonrelativistic calculations.

New Results from the MINOS Experiment

In this paper we present the latest results from the MINOS Experiment. This includes a new measurement of the atmospheric neutrino oscillation parameters based on 3.36 x 10^20 protons-on-target of data and a first analysis of neutral current events in the Far Detector. The prospects for nu-e appearance measurements in MINOS are also discussed.Comment: 6 pages, 4 figures, for the Proceedings of the Neutrino 2008 Conference, Christchurch, N

The comparative analysis of payments for negative environmental impact in Russia and Kazakhstan

The article represents the calculation of the payment for negative environmental impact caused by the development of the uranium ores deposits in the Republic of Kazakhstan. To compare the deposits in Kazakhstan and the Russian Federation, the event is simulated as if the object were located in the territory of the Russian Federation. The comparison of the results serves as an evidence to substantiate the experts' claim that the financial mechanism of land management in Russia should be reformed

New constraints on muon-neutrino to electron-neutrino transitions in MINOS

This paper reports results from a search for ν_μ → ν_e transitions by the MINOS experiment based on a 7×10^(20) protons-on-target exposure. Our observation of 54 candidate ν_e events in the far detector with a background of 49.1±7.0(stat)±2.7(syst) events predicted by the measurements in the near detector requires 2sin^2(2θ_(13))sin^2θ_(23)<0.12(0.20) at the 90% C.L. for the normal (inverted) mass hierarchy at δ_(CP)=0. The experiment sets the tightest limits to date on the value of θ_(13) for nearly all values of δ_(CP) for the normal neutrino mass hierarchy and maximal sin^2(2θ_(23))

Measurement of the Neutrino Mass Splitting and Flavor Mixing by MINOS

Measurements of neutrino oscillations using the disappearance of muon neutrinos from the Fermilab NuMI neutrino beam as observed by the two MINOS detectors are reported. New analysis methods have been applied to an enlarged data sample from an exposure of 7.25×10^(20) protons on target. A fit to neutrino oscillations yields values of |Δm^2|=(2.32_(-0.08)^(+0.12))×10^(-3)  eV^2 for the atmospheric mass splitting and sin^2(2θ)>0.90 (90% C.L.) for the mixing angle. Pure neutrino decay and quantum decoherence hypotheses are excluded at 7 and 9 standard deviations, respectively

Search for sterile neutrino mixing in the MINOS long-baseline experiment

A search for depletion of the combined flux of active neutrino species over a 735 km baseline is reported using neutral-current interaction data recorded by the MINOS detectors in the NuMI neutrino beam. Such a depletion is not expected according to conventional interpretations of neutrino oscillation data involving the three known neutrino flavors. A depletion would be a signature of oscillations or decay to postulated noninteracting sterile neutrinos, scenarios not ruled out by existing data. From an exposure of 3.18×1020 protons on target in which neutrinos of energies between ~500¿¿MeV and 120 GeV are produced predominantly as ¿µ, the visible energy spectrum of candidate neutral-current reactions in the MINOS far detector is reconstructed. Comparison of this spectrum to that inferred from a similarly selected near-detector sample shows that of the portion of the ¿µ flux observed to disappear in charged-current interaction data, the fraction that could be converting to a sterile state is less than 52% at 90% confidence level (C.L.). The hypothesis that active neutrinos mix with a single sterile neutrino via oscillations is tested by fitting the data to various models. In the particular four-neutrino models considered, the mixing angles ¿24 and ¿34 are constrained to be less than 11° and 56° at 90% C.L., respectively. The possibility that active neutrinos may decay to sterile neutrinos is also investigated. Pure neutrino decay without oscillations is ruled out at 5.4 standard deviations. For the scenario in which active neutrinos decay into sterile states concurrently with neutrino oscillations, a lower limit is established for the neutrino decay lifetime t3/m3&gt;2.1×10-12¿¿s/eV at 90% C.L

Search for sterile neutrino mixing in the MINOS long-baseline experiment

A search for depletion of the combined flux of active neutrino species over a 735 km baseline is reported using neutral-current interaction data recorded by the MINOS detectors in the NuMI neutrino beam. Such a depletion is not expected according to conventional interpretations of neutrino oscillation data involving the three known neutrino flavors. A depletion would be a signature of oscillations or decay to postulated noninteracting sterile neutrinos, scenarios not ruled out by existing data. From an exposure of 3.18×10^(20) protons on target in which neutrinos of energies between ∼500  MeV and 120 GeV are produced predominantly as ν_μ, the visible energy spectrum of candidate neutral-current reactions in the MINOS far detector is reconstructed. Comparison of this spectrum to that inferred from a similarly selected near-detector sample shows that of the portion of the ν_μ flux observed to disappear in charged-current interaction data, the fraction that could be converting to a sterile state is less than 52% at 90% confidence level (C.L.). The hypothesis that active neutrinos mix with a single sterile neutrino via oscillations is tested by fitting the data to various models. In the particular four-neutrino models considered, the mixing angles θ_(24) and θ_(34) are constrained to be less than 11° and 56° at 90% C.L., respectively. The possibility that active neutrinos may decay to sterile neutrinos is also investigated. Pure neutrino decay without oscillations is ruled out at 5.4 standard deviations. For the scenario in which active neutrinos decay into sterile states concurrently with neutrino oscillations, a lower limit is established for the neutrino decay lifetime τ_3/m_3>2.1×10^(-12) s/eV at 90% C.L