A generalized Kolmogorov inequality for the Hilbert transform

If we can define the Hilbert transform almost everywhere (Lebesgue) and obtain an estimate for where is a suitable finite measure. The classical Kolmogorov inequality for the Lebesgue measure of is obtained by a scaling argument.

     

Computational algorithms for blocking probabilities in circuit-switched networks

In this paper, we develop two new general purpose recursive algorithms for the exact computation of blocking probabilities in multi-rate product-form circuit-switched networks with fixed routing. The first algorithm is a normalization constant approach based on the partition function of the state distribution. The second is a mean-value type of algorithm with a recursion cast in terms of blocking probabilities and conditional probabilities. The mean value recursion is derived from the normalization constant recursion. Both recursions are general purpose ones that do not depend on any specific network topology. The relative advantage of the mean-value algorithm is numerical stability, but this is obtained at the expense of an increase in computational costs.The results of section 2 were presented in part at the 7th ITC Seminar on Broadband Technologies, Morristown, NJ, October 1990.Supported in part by the National Science Foundation, Grant No. CCR-9015717.     

A probabilistic approach to a theorem of Gilbarg and Serrin

We give a probabilistic proof via coupling of an extended version of a theorem of Gilbarg and Serrin.     

QCD anomaly mediation of ψ′ → ψπ0 and ψ′ → ψη

We comment on various decay processes mediated dominantly by pseudoscalar couplings to the QCD axial-vector anomaly. Using coupling strengths of our earlier calculation, we compute $\text{ψ′ → π}{}^0\text{ψ}\text{ψ′}\text{→ ηψ}$ and obtain good agreement with experiment.     

Asymptotics of the principal eigenvalue and expected hitting time for positive recurrent elliptic operators in a domain with a small puncture

Let X(t) be a positive recurrent diffusion process corresponding to an operator L on a domain D⊆R^d with oblique reflection at ∂D if D≠R^d. For each x∈D, we define a volume-preserving norm that depends on the diffusion matrix a(x). We calculate the asymptotic behavior as ε→0 of the expected hitting time of the ε-ball centered at x and of the principal eigenvalue for L in the exterior domain formed by deleting the ball, with the oblique derivative boundary condition at ∂D and the Dirichlet boundary condition on the boundary of the ball. This operator is non-self-adjoint in general. The behavior is described in terms of the invariant probability density at x and Det(a(x)). In the case of normally reflected Brownian motion, the results become isoperimetric-type equalities.     

States of 12ΛC formed in the reaction 12C(K−, π−)

States of ¹²_ΛC formed in the (K^?, π^?) reaction have been studied for momentum transfers up to 260 MeV/c, using an incident K^? beam of 800 MeV/c momentum. The angular distributions for the g.s. and for a peak at 11 meV have been measured between 0° and 19° in the laboratory. Limits on the splitting of the 11 MeV peak and on the formation of low-lying excited states are given.