6,658 research outputs found
Integral-Partial Differential Equations of Isaacs' Type Related to Stochastic Differential Games with Jumps
In this paper we study zero-sum two-player stochastic differential games with
jumps with the help of theory of Backward Stochastic Differential Equations
(BSDEs). We generalize the results of Fleming and Souganidis [10] and those by
Biswas [3] by considering a controlled stochastic system driven by a
d-dimensional Brownian motion and a Poisson random measure and by associating
nonlinear cost functionals defined by controlled BSDEs. Moreover, unlike the
both papers cited above we allow the admissible control processes of both
players to depend on all events occurring before the beginning of the game.
This quite natural extension allows the players to take into account such
earlier events, and it makes even easier to derive the dynamic programming
principle. The price to pay is that the cost functionals become random
variables and so also the upper and the lower value functions of the game are a
priori random fields. The use of a new method allows to prove that, in fact,
the upper and the lower value functions are deterministic. On the other hand,
the application of BSDE methods [18] allows to prove a dynamic programming
principle for the upper and the lower value functions in a very
straight-forward way, as well as the fact that they are the unique viscosity
solutions of the upper and the lower integral-partial differential equations of
Hamilton-Jacobi-Bellman-Isaacs' type, respectively. Finally, the existence of
the value of the game is got in this more general setting if Isaacs' condition
holds.Comment: 30 pages
The Integration of EFA and CFA: One Method of Evaluating the Construct Validity
The approach of evaluating the construct validity has little development in the past one hundred years As the theory of EFA and CFA had been proposed and refined these years we can find that they are good methods to evaluating the construct validity This paper give a concepts of construct validity firstly and then analyzed the shortcoming of existing methods of construct validity evaluating then stated the traits of EFA and CFA based on them we summarized that using EFA and CFA together is a good way to evaluating the construct validit
On a heuristic point of view concerning the optical activity
Motivated by a recent finding that Fresnel's phenomenological description of
the optical activity in the chiral medium is not self-consistent, we conduct a
thorough investigation into the nature of the polarization of a plane light
wave. We demonstrate that the polarization of light is the reflection of one of
its quantum-mechanical properties, called the quasi-spin. Unexpectedly, the
quasi-spin is not an observable with respect to the laboratory coordinate
system. Instead, it is with respect to the momentum-dependent local coordinate
system. The representative operators for the quasi-spin are the Pauli matrices.
The wavefunction is the Jones vector. In order to completely determine a state
of polarization, two different kinds of degrees of freedom are needed. One is
the degrees of freedom to characterize the state of quasi-spin. They are the
Stokes parameters, the expectation values of the Pauli matrices in the state
described by the Jones vector. The other is the degrees of freedom to specify
the local coordinate system, including the propagation direction and an angle
of rotation about it. Accordingly, there are two independent mechanisms to
change the state of polarization. One is to change the state of quasi-spin in a
fixed local coordinate system. This is the traditional mechanism that can be
expressed as an SU(2) rotation of the Jones vector. The other is to change the
local coordinate system with the state of quasi-spin remaining fixed in it. At
last, we show that it is the newly-identified mechanism that accounts for the
optical activity.Comment: 24 page
Stokes parameters alone cannot completely characterize the polarization of plane light waves
It was generally assumed that the Stokes parameters are complete
characterization for the state of polarization of a plane light wave so that
their counterparts in quantum optics, called the Stokes operators, represent
the polarization of photons. Here we show, through analyzing the properties of
polarized plane waves in an optically active medium, that the Stokes parameters
are not able to completely characterize the state of polarization of a plane
wave. The key point is that only when a plane wave is expanded in terms of the
orthogonal base modes, which are physically meaningful, can the two expansion
coefficients make up the Jones vector. Taking this into consideration, we
demonstrate that the Stokes parameters of any elliptically polarized wave in an
isotropic chiral medium, determined solely by its Jones vector, are transmitted
unchanged. They are not able to reflect the rotation of its polarization
ellipse along with the propagation. The relationship of the Stokes parameters
with the polarization of light needs further investigation.Comment: 13 page
Constraining the spatial curvature of the local Universe with deep learning
We use the distance sum rule (DSR) method to constrain the spatial curvature
of the Universe with a large sample of 161 strong gravitational lensing (SGL)
systems, whose distances are calibrated from the Pantheon compilation of type
Ia supernovae (SNe Ia) using deep learning. To investigate the possible
influence of mass model of the lens galaxy on constraining the curvature
parameter , we consider three different lens models. Results show
that a flat Universe is supported in the singular isothermal sphere (SIS) model
with the parameter . While in the power-law
(PL) model, a closed Universe is preferred at confidence level,
with the parameter . In extended power-law
(EPL) model, the 95 confidence level upper limit of is .
As for the parameters of the lens models, constrains on the three models
indicate that the mass profile of the lens galaxy could not be simply described
by the standard SIS model.Comment: 17 pages, 7 figure
Drug-Loaded Chitosan Film Prepared via Facile Solution Casting and Air-Drying of Plain Water-Based Chitosan Solution for Ocular Drug Delivery
Chitosan is a nature-based polymer with low toxicity, excellent biocompatibility and biodegradability. However, the intractable solubility of chitosan in water and most conventional solvents hampers its biomedical applications. Following the dissolution method for dissolving chitosan in plain water developed by us, chitosan was dissolved in ionic liquid followed by overnight freezing at −20 °C and subsequent solvent exchange with plain water at room temperature. In this study, we fabricated a drug-carrying chitosan film via solution casting and air-drying by using the plain water-based chitosan solution. Specifically, brimonidine tartrate (BT), an antiglaucoma drug, was dissolved in the plain-water based solution and used to prepare BT-loaded chitosan film, i.e., chitosan-BT film. The resulting film is transparent, structurally stable, and mucoadhesive. Micro-sized antiglaucoma BT drug crystals form and are well dispersed in the chitosan film. The chitosan-BT film enables BT to have a high corneal permeability with fast drug release kinetics for potential ocular drug delivery
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