Coherent and stochastic contributions of compound resonances in atomic processes: Electron recombination, photoionization, and scattering

In open-shell atoms and ions, processes such as photoionization, combination (Raman) scattering, electron scattering, and recombination are often mediated by many-electron compound resonances. We show that their interference (neglected in the independent-resonance approximation) leads to a coherent contribution, which determines the energy-averaged total cross sections of electron- and photon-induced reactions obtained using the optical theorem. In contrast, the partial cross sections (e.g., electron recombination or photon Raman scattering) are dominated by the stochastic contributions. Thus, the optical theorem provides a link between the stochastic and coherent contributions of the compound resonances. Similar conclusions are valid for reactions via compound states in molecules and nuclei.

Sets of p-multiplicity in locally compact groups

We initiate the study of sets of p-multiplicity in locally compact groups and their operator versions. We show that a closed subset E of a second countable locally compact group G is a set of p-multiplicity if and only if E∗={(s,t):ts−1∈E} is a set of operator p-multiplicity. We exhibit examples of sets of p-multiplicity, establish preservation properties for unions and direct products, and prove a p-version of the Stone–von Neumann Theorem.

Comments on “Wirtinger-based integral inequality: Application to time-delay systems [Automatica 49 (2013) 2860–2866]”

In a recent paper (Automatica 49 (2013) 2860–2866), the Wirtinger-based inequality has been introduced to derive tractable stability conditions for time-delay or sampled-data systems. We point out that there exist two errors in Theorem 8 for the stability analysis of sampled-data systems, and the correct theorem is presented.

Thermodynamics of trajectories and local fluctuation theorems for harmonic quantum networks

We present a general method to undertake a thorough analysis of the thermodynamics of the quantum jump trajectories followed by an arbitrary quantum harmonic network undergoing linear and bilinear dynamics. The approach is based on the phase-space representation of the state of a harmonic network. The large deviation function associated with this system encodes the full counting statistics of exchange and also allows one to deduce for fluctuation theorems obeyed by the dynamics. We illustrate the method showing the validity of a local fluctuation theorem about the exchange of excitations between a restricted part of the environment (i.e., a local bath) and a harmonic network coupled with different schemes.

Productive Knowledge of English Binomials by Japanese Learners of English

The purpose of this research is to reveal (1) which English binomials Japanese learners of English have productive knowledge of and (2) what strategies they use to produce English binomials when they do not know the binomials. One hundred and three Japanese learners of English with intermediate proficiency level completed an online survey of 44 binomials. The participants were given the first word of a binomial and asked to type a word following “and”. The target word was provided by more than 75% of participants for 19 of the 44 binomials, meaning that learners have productive knowledge for certain binomials. An analysis of errors suggested that the participants relied heavily on semantic relationships between items in binomials.However, the use of a semantic strategy for producing the second words often leads to non-binomial expressions. From these results we suggest that giving more input to learners, as well as teaching the “Me first” principle (Cooper & Ross, 1975) explicitly would help the learners to develop more accurate and effective strategies for uncertain or unfamiliar binomials.

Between-taxon matching of common and rare species richness patterns

Aim: Our primary aim is to understand how assemblages of rare (restricted range) and common (widespread) species are correlated with each other among different taxa. We tested the proposition that marine species richness patterns of rare and common species differ, both within a taxon in their contribution to the richness pattern of the full assemblage and among taxa in the strength of their correlations with each other. Location The UK intertidal zone. Methods: We used high-resolution marine datasets for UK intertidal macroalgae, molluscs and crustaceans each with more than 400 species. We estimated the relative contribution of rare and common species, treating rarity and commonness as a continuous spectrum, to spatial patterns in richness using spatial crosscorrelations. Correlation strength and significance was estimated both within and between taxa. Results: Common species drove richness patterns within taxa, but rare species contributed more when species were placed on an equal footing via scaling by binomial variance. Between taxa, relatively small sub-assemblages (fewer than 60 species) of common species produced the maximum correlation with each other, regardless of taxon pairing. Cross-correlations between rare species were generally weak, with maximum correlation occurring between small sub-assemblages in only one case. Cross-correlations between common and rare species of different taxa were consistently weak or absent. Main conclusions: Common species in the three marine assemblages were congruent in their richness patterns, but rare species were generally not. The contrast between the stronger correlations among common species and the weak or absent correlations among rare species indicates a decoupling of the processes driving common and rare species richness patterns. The internal structure of richness patterns of these marine taxa is similar to that observed for terrestrial taxa.