We study limit theorems for time-dependent averages of the form Xt:=12L(t)∫−L(t)L(t)u(t,x)dx, as t→∞, where L(t)=exp(λt) and u(t,x) is solution to a stochastic heat equation on ℝ +×ℝ driven by space-time white noise with u0(x)=1 all x∈ℝ. show that Xt weak law large numbers holds when λ>λ1, strong λ>λ2, central theorem λ>λ3, but fails λ<λ4≤λ3, quantitative λ>λ5, λi’s are positive constants depen...

A bstract Consistency with position space OPE limit requires three-point momentum CFT correlators to have only total energy singularity. We show that this requirement gives a simple proof of the known result in three dimensions parity-odd structure cannot exist for exactly conserved currents spins s i , j k when triangle inequality ? + is violated. also even parity correlation functions propert...

Let A ⊆ R be a set definable in an o-minimal expansion S of the real field, A′ ⊆ R be its projection, and assume that the non-empty fibers Aa ⊆ R n are compact for all a ∈ A′ and uniformly bounded. If L is the Hausdorff limit of a sequence of fibers Aai , we give an upper-bound for the Betti numbers bk(L) in terms of definable sets explicitly constructed from a generic fiber Aa. In particular, ...

The present work describes a new solution-free strategy for preparation of cluster-like nano/micro CuO/ZnO particles in dielectric barrier discharge (DBD) in which the brass acts as the inner electrode. The cataluminescence (CTL) behaviour of such prepared material for acetic acid was studied for analytical application. Under the optimized conditions, the linear range of CTL intensity versus co...

I describe analysis of correlations in the outputs of the three LIGO interferometers from LIGO's first science run, held over 17 days in August and September of 2002, and the resulting upper limit set on a stochastic background of gravitational waves. By searching for cross-correlations between the LIGO detectors in Livingston, LA and Hanford, WA, we are able to set a 90% confidence level upper...

In quantum physics, the state space of a countable chain of (n+1) -level atoms becomes, in the continuous field limit, a Fock space with multiplicity n. In a more functional analytic language, the continuous tensor product space over IR of copies of the space C is the symmetric Fock space Γs(L 2(IR;C)). In this article we focus on the probabilistic interpretations of these facts. We show that t...

We use discrete analogs of Riemann–Hilbert problem’s methods to derive the discrete Bessel kernel which describes the poissonized Plancherel measures for symmetric groups. To do this we define a discrete analog of 2 by 2 Riemann–Hilbert problems of special type. We also give an example, explicitly solvable in terms of classical special functions, when a discrete Riemann–Hilbert problem converge...

In standard interval mapping of quantitative trait loci (QTL), the QTL effect is described by a normal mixture model. At any given location in the genome, the evidence of a putative QTL is measured by the likelihood ratio of the mixture model compared to a single normal distribution (the LOD score). This approach can occasionally produce spurious LOD score peaks in regions of low genotype infor...

In this work, we developed a novel, label-free, colorimetric sensor for Pb(2+) detection based on the acceleration of gold leaching by graphene oxide (GO) at room temperature. Gold nanoparticles (AuNPs) can be dissolved in a thiosulfate (S2O3(2-)) aqueous environment in the presence of oxygen; however, the leaching rate is very slow due to the high activation energy (27.99 kJ mol(-1)). In order...