Coherent States on Hilbert Modules

We generalize the concept of coherent states, traditionally defined as special families of vectors on Hilbert spaces, to Hilbert modules. We show that Hilbert modules over $C^*$-algebras are the natural settings for a generalization of coherent states defined on Hilbert spaces. We consider those Hilbert $C^*$-modules which have a natural left action from another $C^*$-algebra say, $\mathcal A$. The coherent states are well defined in this case and they behave well with respect to the left action by $\mathcal A$. Certain classical objects like the Cuntz algebra are related to specific examples of coherent states. Finally we show that coherent states on modules give rise to a completely positive kernel between two $C^*$-algebras, in complete analogy to the Hilbert space situation. Related to this there is a dilation result for positive operator valued measures, in the sense of Naimark. A number of examples are worked out to illustrate the theory

Cerebral small vessel disease, medial temporal lobe atrophy and cognitive status in patients with ischaemic stroke and transient ischaemic attack

BACKGROUND AND PURPOSE: Small vessel disease (SVD) and Alzheimer's disease (AD) are two common causes of cognitive impairment and dementia, traditionally considered as distinct processes. The relationship between radiological features suggestive of AD and SVD was explored, and the association of each of these features with cognitive status at 1 year was investigated in patients with stroke or transient ischaemic attack. METHODS: Anonymized data were accessed from the Virtual International Stroke Trials Archive (VISTA). Medial temporal lobe atrophy (MTA; a marker of AD) and markers of SVD were rated using validated ordinal visual scales. Cognitive status was evaluated with the Mini Mental State Examination (MMSE) 1 year after the index stroke. Logistic regression models were used to investigate independent associations between (i) baseline SVD features and MTA and (ii) all baseline neuroimaging features and cognitive status 1 year post-stroke. RESULTS: In all, 234 patients were included, mean (±SD) age 65.7 ± 13.1 years, 145 (62%) male. Moderate to severe MTA was present in 104 (44%) patients. SVD features were independently associated with MTA (P < 0.001). After adjusting for age, sex, disability after stroke, hypertension and diabetes mellitus, MTA was the only radiological feature independently associated with cognitive impairment, defined using thresholds of MMSE ≤ 26 (odds ratio 1.94; 95% confidence interval 1.28-2.94) and MMSE ≤ 23 (odds ratio 2.31; 95% confidence interval 1.48-3.62). CONCLUSION: In patients with ischaemic cerebrovascular disease, SVD features are associated with MTA, which is a common finding in stroke survivors. SVD and AD type neurodegeneration coexist, but the AD marker MTA, rather than SVD markers, is associated with post-stroke cognitive impairment

O(αs)O(\alpha_s) Corrections to B→Xse+e−B \to X_s e^+ e^- Decay in the 2HDM

$O(\alpha_s)$ QCD corrections to the inclusive $B \to X_s e^+ e^-$ decay are investigated within the two - Higgs doublet extension of the standard model (2HDM). The analysis is performed in the so - called off-resonance region; the dependence of the obtained results on the choice of the renormalization scale is examined in details. It is shown that $O(\alpha_s)$ corrections can suppress the $B \to X_s e^+ e^-$ decay width up to $1.5 \div 3$ times (depending on the choice of the dilepton invariant mass $s$ and the low - energy scale $\mu$). As a result, in the experimentally allowed range of the parameters space, the relations between the $B \to X_s e^+ e^-$ branching ratio and the new physics parameters are strongly affected. It is found also that though the renormalization scale dependence of the $B \to X_s e^+ e^-$ branching is significantly reduced, higher order effects in the perturbation theory can still be nonnegligible.Comment: 16 pages, latex, including 6 figures and 3 table

Two Higgs Doublet Model and Lepton Polarization in the B -> K tau+ tau- Decay

The decay width, forward-backward asymmetry and tau lepton longitudinal and transversal polarization for the exclusive (B -> K tau^+ tau^-) decay in a two Higgs doublet model are computed. It is shown that the forward-backward asymmetry and longitudinal polarization of the tau lepton are very effective tools for establishing new physics.Comment: 25 pages, 20 figures, LaTeX formatte

Squeezed States and Hermite polynomials in a Complex Variable

Following the lines of the recent paper of J.-P. Gazeau and F. H. Szafraniec [J. Phys. A: Math. Theor. 44, 495201 (2011)], we construct here three types of coherent states, related to the Hermite polynomials in a complex variable which are orthogonal with respect to a non-rotationally invariant measure. We investigate relations between these coherent states and obtain the relationship between them and the squeezed states of quantum optics. We also obtain a second realization of the canonical coherent states in the Bargmann space of analytic functions, in terms of a squeezed basis. All this is done in the flavor of the classical approach of V. Bargmann [Commun. Pur. Appl. Math. 14, 187 (1961)].Comment: 15 page

Exposure to NO2 in occupational built environments in urban centre in Lahore

Increased economic growth, urbanisation and substantial rise in automobile vehicles has contributed towards the elevated levels of air pollution in major cities in Pakistan. Aone week study was conducted by using passive samplers to assess NO2 concentration in occupational built environments at two most congested and populated sites of Lahore. Both sites were locatedon the busy roads of Lahore. At Site-I the highest concentration was in outdoors followed by corridor and indoor. While at Site II all the sampling location wereindoors and level were comparable to that of outdoor levelsat Site I. The results suggest the likely contribution of ambient sources in exposure to indoor NO2 in educational and other occupational built environments in urban centres