Remarkable spectral difference between different polarized modes in four-level two-electron atomic system

The spectral difference between different polarized modes in two-dimensional (2D) four-level two-electron atomic system is investigated by simultaneously solving Maxwell's equations and rate equations of electronic population. A new physical model including pumping dynamics is introduced, and the transitions between the energy levels are governed by coupling rate equations and the Pauli Exclusion Principle. Results indicated that polarized lasing modes have different field pattern, spectral range, and intensity. The photons in TE field are easier to leak from random media than those in TM field. The quality factor of TM modes is larger than that of TE modes and the loss of TM modes to be lower than that of TE modes. The spectral properties in four-level two-electron atomic system are polarization-dependent.     

A Characterization of Approximate Solutions of Multiobjective Stochastic Optimal Control Problems

We introduce several concepts of approximate solutions of multiobjective optimization problems, prove existence results and an k -minimum principle for multiobjective stochastic optimal control problems.     

原子分子在Ni(100)表面吸附的第一性原理研究

本文采用密度泛函理论,结合周期性平板模型,通过对原子H、N、O、S和C,分子CO、N2、NH3、NO,以及自由基CH3、CH、CH2、OH在Ni(100)表面吸附的研究,比较了它们的吸附能,稳定吸附位点,吸附结构及扩散能垒等信息. 这些吸附质与表面结合能力从小到大依次是N2相似文献   

Pontryagin Type Maximum Principle for budget-constrained infinite horizon optimal control problems with linear dynamics

In this paper a class of infinite horizon optimal control problems with an isoperimetrical constraint, also interpreted as a budget constraint, is considered. Herein a linear both in the state and in the control dynamic is allowed. The problem setting includes a weighted Sobolev space as the state space. For this class of problems, we establish the necessary optimality conditions in form of a Pontryagin Type Maximum Principle including a transversality condition. The proved theoretical result is applied to a linear–quadratic regulator problem.     

Probing the gravitational redshift with an Earth-orbiting satellite

We present an approach to testing the gravitational redshift effect using the RadioAstron satellite. The experiment is based on a modification of the Gravity Probe A scheme of nonrelativistic Doppler compensation and benefits from the highly eccentric orbit and ultra-stable atomic hydrogen maser frequency standard of the RadioAstron satellite. Using the presented techniques we expect to reach an accuracy of the gravitational redshift test of order ${10}^{?5}$, a magnitude better than that of Gravity Probe A. Data processing is ongoing, our preliminary results agree with the validity of the Einstein Equivalence Principle.     

Testing noncommutative spacetimes and violations of the Pauli Exclusion Principle through underground experiments

We propose to deploy limits that arise from different tests of the Pauli Exclusion Principle: i) to provide theories of quantum gravity with experimental guidance; ii) to distinguish, among the plethora of possible models, the ones that are already ruled out by current data; iii) to direct future attempts to be in accordance with experimental constraints. We first review experimental bounds on nuclear processes forbidden by the Pauli Exclusion Principle,which have been derived by several experimental collaborations making use of various detector materials. Distinct features of the experimental devices entail sensitivities on the constraints hitherto achieved that may differ from one another by several orders of magnitude. We show that with choices of these limits, well-known examples of flat noncommutative space-time instantiations of quantum gravity can be heavily constrained, and eventually ruled out.We devote particular attention to the analysis of the κ-Minkowski and θ-Minkowski noncommutative spacetimes.These are deeply connected to some scenarios in string theory, loop quantum gravity, and noncommutative geometry.We emphasize that the severe constraints on these quantum spacetimes, although they cannot rule out theories of top-down quantum gravity to which they are connected in various ways, provide a powerful limitation for those models. Focus on this will be necessary in the future.     

Quantum and Classical Disparity and Accord

Discrepancies and accords between quantum (QM) and classical mechanics (CM) related to expectation values and periods are generally found for both the harmonic oscillator (SHO) and a free particle in a box (FPB), which may apply generally. These indicate non-locality is expected throughout QM. The FPB energy states violate the Correspondence Principle. Previously unexpected accords are found and proven that 〈x ²〉 _CM =〈x ²〉 _QM and τ _CM =τ _QMb (beat period i.e. beats between the phases for adjoining energy states) for the SHO for all quantum numbers, n. However, for the FPB the beat periods differ at small n. It is shown that a particle’s velocity in an infinite square well varies, no matter how wide the box, nor how far the particle is from the walls. The quantum free particle variances share an indirect commonality with the Aharonov-Bohm and Aharonov-Casher effects in that there is a quantum action in the absence of a force. The concept of an “Expectation Value over a Partial Well Width” is introduced. This paper raises the question as to whether these inconsistencies are undetectable, or can be empirically ascertained. These inherent variances may need to be fixed, or nature is manifestly more non-classical than expected.     

半线性抛物型方程的双移动边界问题

本文运用Fourier方法和压缩映像不动点原理,证明了半线性抛物型方程的双移动边界问题 u_t=a~2u_(xx) F(x,t,u,u_x),(x,t)∈D_∞, u(l_1(t),t)=0,l_1(0)=0,t∈(0, ∞), u(l_2(t),t)=0,l_2(0)=l_0,t∈(0, ∞), u(x,0)=φ(x),0≤x≤l_0,φ(0)=φ(l_0)=0.解的存在唯一性,其中D_∞={(x,t)|l_1(t)相似文献