15,154 research outputs found
A Maximum Principle for Optimal Control of Stochastic Evolution Equations
A general maximum principle is proved for optimal controls of abstract
semilinear stochastic evolution equations. The control variable, as well as
linear unbounded operators, acts in both drift and diffusion terms, and the
control set need not be convex.Comment: 20 page
Notes on the Cauchy Problem for Backward Stochastic Partial Differential Equations
Backward stochastic partial differential equations of parabolic type with
variable coefficients are considered in the whole Euclidean space. Improved
existence and uniqueness results are given in the Sobolev space
() under weaker assumptions than those used by X. Zhou [Journal of
Functional Analysis 103, 275--293 (1992)]. As an application, a comparison
theorem is obtained.Comment: 20 page
Kinetics and Mechanisms of Phosphorus Adsorption in Soils from Diverse Ecological Zones in the Source Area of a Drinking-Water Reservoir.
On-site soils are increasingly used in the treatment and restoration of ecosystems to harmonize with the local landscape and minimize costs. Eight natural soils from diverse ecological zones in the source area of a drinking-water reservoir in central China are used as adsorbents for the uptake of phosphorus from aqueous solutions. The X-ray fluorescence (XRF) spectrometric and BET (Brunauer-Emmett-Teller) tests and the Scanning Electron Microscopy (SEM) and Fourier Transform Infrared (FTIR) spectral analyses are carried out to investigate the soils' chemical properties and their potential changes with adsorbed phosphorous from aqueous solutions. The intra-particle diffusion, pseudo-first-order, and pseudo-second-order kinetic models describe the adsorption kinetic processes. Our results indicate that the adsorption processes of phosphorus in soils occurred in three stages and that the rate-controlling steps are not solely dependent on intra-particle diffusion. A quantitative comparison of two kinetics models based on their linear and non-linear representations, and using the chi-square (χ2) test and the coefficient of determination (r2), indicates that the adsorptive properties of the soils are best described by the non-linear pseudo-second-order kinetic model. The adsorption characteristics of aqueous phosphorous are determined along with the essential kinetic parameters
Implications of chiral symmetry on -wave pionic resonances and the scalar charmed mesons
The chiral symmetry of QCD requires energy-dependent pionic strong
interactions at low energies. This constraint, however, is not fulfilled by the
usual Breit--Wigner parameterization of pionic resonances, leading to masses
larger than the real ones. We derive relations between nonleptonic three-body
decays of the -meson into a -meson and a pair of light pseudoscalar
mesons based on SU(3) chiral symmetry. Employing effective field theory
methods, we demonstrate that taking into account the final-state interactions,
the experimental data of the decays , , , and
can all be described by the nonperturbative
- scattering amplitudes previously obtained from a
combination of chiral effective field theory and lattice QCD calculations. The
results provide a strong support of the scenario that the broad scalar charmed
meson should be replaced by two states, the lower one of which
has a mass of around 2.1 GeV, much smaller than that extracted from
experimental data using a Breit--Wigner parameterization.Comment: 26 pages, 9 figuere
One-loop renormalization of the chiral Lagrangian for spinless matter fields in the SU(N) fundamental representation
We perform the leading one-loop renormalization of the chiral Lagrangian for
spinless matter fields living in the fundamental representation of SU(N). The
Lagrangian can also be applied to any theory with a spontaneous symmetry
breaking of to and spinless matter fields in
the fundamental representation. For QCD, the matter fields can be kaons or
pseudoscalar heavy mesons. Using the background field method and heat kernel
expansion techniques, the divergences of the one-loop effective generating
functional for correlation functions of single matter fields are calculated up
to . They are absorbed by counterterms not only from the
third order but also from the second order chiral Lagrangian.Comment: 13 page
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