关于有消失矩的函数的Hilbert变换的加权范数不等式

为刻划一类权函数W,使具有N阶消失矩的函数f的Hilbert变换f满足带权L~P强型不等式Adams给出了一个充要条件。利用A_P权的性质,本文进一步完善了这个结果。     

The incompatibility between local hidden variable theories and the fundamental conservation laws

I discuss in detail the result that the Bell’s inequalities derived in the context of local hidden variable theories for discrete quantized observables can be satisfied only if a fundamental conservation law is violated on the average. This result shows that such theories are physically nonviable, and makes the demarcating criteria of the Bell’s inequalities redundant. I show that a unique correlation function can be derived from the validity of the conservation law alone and this coincides with the quantum mechanical correlation function. Thus, any theory with a different correlation function, like any local hidden variable theory, is incompatible with the fundamental conservation laws and space-time symmetries. The results are discussed in the context of two-particle singlet and triplet states, GHZ states, and two-particle double slit interferometry. Some observations on quantum entropy, entanglement, and nonlocality are also discussed.     

The Asymmetric One-Dimensional Constrained Ising Model: Rigorous Results

We study a one-dimensional spin (interacting particle) system, with product Bernoulli (p) stationary distribution, in which a site can flip only when its left neighbor is in state +1. Such models have been studied in physics as simple exemplars of systems exhibiting slow relaxation. In our East model the natural conjecture is that the relaxation time (p), that is 1/(spectral gap), satisfies log (p) as p0. We prove this up to a factor of 2. The upper bound uses the Poincaré comparison argument applied to a wave (long-range) comparison process, which we analyze by probabilistic techniques. Such comparison arguments go back to Holley (1984, 1985). The lower bound, which atypically is not easy, involves construction and analysis of a certain coalescing random jumps process.     

Weighted Estimations from a Conjugate Operator

In this Letter we develop a general procedure leading from a Mourre-type estimation for a given self-adjoint operator H to a Hardy-type weighted inequality. We use this method in order to prove exponential decay for eigenvectors of a large class of perturbations of operators of convolution with bounded analytic functions.     

On a class of singular biharmonic problems involving critical exponents

This paper deals with the following class of singular biharmonic problems

     

Optimal control for semilinear evolutionary variational bilateral problem

This paper is concerned with an optimal control problem for some semilinear evolutionary variational inequalities associated with bilateral constraints. The control domain is a general separable metric space and has no algebraic structure, in particular, it is not necessarily convex. Existence and optimality conditions of optimal pairs are established.     

Weighted Discrepancy and High-Dimensional Numerical Integration

The concept of weighted discrepancy of sequences was introduced by Sloan and Woniakowski when they proved a general form of a Koksma–Hlawka inequality for the numerical integration of functions. This version takes imbalances in the importance of the projections of the integrand into account.In this paper we give estimates for the weighted discrepancy of several important point sets. Further we carry out various (high-dimensional) numerical integration experiments and we compare the results with the error bounds provided by the generalized Koksma–Hlawka inequality and by the estimates for the weighted discrepancy. Finally we discuss various consequences.     

Exploring inequality violations by classical hidden variables numerically

There are increasingly suggestions for computer simulations of quantum statistics which try to violate Bell type inequalities via classical, common cause correlations. The Clauser–Horne–Shimony–Holt (CHSH) inequality is very robust. However, we argue that with the Einstein–Podolsky–Rosen setup, the CHSH is inferior to the Bell inequality, although and because the latter must assume anti-correlation of entangled photon singlet states. We simulate how often quantum behavior violates both inequalities, depending on the number of photons. Violating Bell 99% of the time is argued to be an ideal benchmark. We present hidden variables that violate the Bell and CHSH inequalities with 50% probability, and ones which violate Bell 85% of the time when missing 13% anti-correlation. We discuss how to present the quantum correlations to a wide audience and conclude that, when defending against claims of hidden classicality, one should demand numerical simulations and insist on anti-correlation and the full amount of Bell violation.     

An Intermediate-Energy Experimental Test of Bell's Inequalty with Recoil Polarimeters

To date there has been only one test for local reality which used fermions. Lamehi-Rachti and Mittig measured correlated protons with a recoil polarimeter at Saclay. We discuss this experiment and survey the published criticism. We then propose an experiment involving a 500 MeV electron beam on a ³He target. The two protons in the ³He nucleus originally have their spins anti-aligned. The spins of the ejected protons can be measured with a recoil polarimeter and the correlation function obtained, which will be a good test of Local Reality and Bell's inequality.