A Non-Analytic Growth Bound for Laplace Transforms and Semigroups of Operators

Let f : \mathbbR₊ ? \mathbbC f : \mathbb{R}_{+} \longrightarrow \mathbb{C} be an exponentially bounded, measurable function. We introduce a growth bound z(f) \zeta(f) which measures the extent to which f f can be approximated by holomorphic functions. This growth bound is related to the location of the domain of holomorphy of the Laplace transform of f f far from the real axis. The denition extends to vector and operator-valued cases. For a C₀ C_{0} -semigroup T T of operators, z(T) \zeta(T) is closely related to the critical growth bound of T T .     

Monitoring an Exponential Smoothing Forecasting System

The first part of this paper is concerned with the variance of the smoothed error when the forecasting system being used is exponential smoothing. The expression derived for this variance involves the variance of the noise, the smoothing constant and a sum of squared binomial coefficients. It is also shown that the variance of the sum of errors equals the variance of the smoothed error for one less degree of freedom divided by the square of the smoothing constant.The second part of the paper considers the practical application of the above result and also gives values for the tracking signal limits, obtained by simulation, which could be used in the automatic monitoring of a forecasting system.     

Subcentrality of restrictions of boundary measures on state spaces of C1-algebras

Let F be a closed face of the weak¹ compact convex state space of a unital C¹-algebra A. The author has already shown that F is a Choquet simplex if and only if p_φ^Fπ_φ(A)″p_φ^F is abelian for any φ in F with associated cyclic representation ($\text{H}$_φ,π_φ,ξ_φ), where p_φ^F is the orthogonal projection of $\text{H}$_φ onto the subspace spanned by vectors η defining vector states a → 〈π_φ(a)η, η)〉 lying in F. It is shown here that if B is a C¹-subalgebra of A containing the unit and such that ξ_φ is cyclic in $\text{H}$_φ for π_φ(B) for any φ in F, then the boundary measures on F are subcentral as measures on the state space of B if and only if p_φ^F(π_φ(A), π_φ(B)′)″p_φ^F is abelian for all φ in F. If A is separable, this is equivalent to the condition that any state in F with (π_φ(A)′ ∩ π_φ(B)″) one-dimensional is pure. Taking A to be the crossed product of a discrete C¹-dynamical system (B, G, α), these results generalise known criteria for the system to be G-central.     

Doppler-shifted nuclear gamma rays following stopped K− capture in aluminium

The Doppler broadened ²⁶Mg^* decay gamma peak hasma peak has been observed in coincidence with stopped kaons in an Al target. The results are compared with predictions based on single-nucleon absorption of the kaon.     

E2 nuclear resonance effects in pionic and kaonic atoms

The attenuation due to the E2 nuclear resonance effect has been measured in hadronic atoms using pions with ¹¹¹Cd and ¹¹²Cd, and for kaons with ¹²²Sn. Energies of the relevant X-ray and γ-ray transitions and of the X-ray cascade intensities have also been measured so as to give a self-consistent set of information. The results are found to be in very good agreement with theoretical calculations.     

Kaonic Hydrogen atom X-rays

The X-ray spectrum obtained with kaons stopping in liquid hydrogen has been measured. Possible candidates for X-ray lines from kaonic hydrogen atoms have been identified and the results compared with previous experiments and with theoretical predictions. X-ray lines from σ^?p atoms may also have been observed.     

Optical-model analysis of exotic atom data: (I). Kaonic atoms

Data for kaonic atoms are fitted using a simple optical model with a potential proportional to the nuclear density. Very satisfactory fits to strong interaction shift and width values are obtained but difficulties in fitting yield values indicate that the model is not completely satisfactory. The potential strength can be related to the free kaon-nucleon scattering lengths using a model due to Deloft. A good overall representation of the data is obtained with a black-sphere model.     

Extensions of Isometric Dual Representations of Semigroups

Let T be a dual representation of a suitable subsemigroup Sof a locally compact abelian group G by isometries on a dualBanach space X=(X_*)^*. It is shown that (X, T) can be extendedto a dual representation of G on a dual Banach space Y containingX, and that this extension can be done in a canonical way. Inthe case of a representation by *-monomorphisms of a von Neumannalgebra, the extension is a representation of G by *-automorphismsof a von Neumann algebra.