An Analytic Model for left invertible Weighted Translation Semigroups

M. Embry and A. Lambert initiated the study of a semigroup of operators $\{S_t\}$ indexed by a non-negative real number $t$ and termed it as weighted translation semigroup. The operators $S_t$ are defined on $L^2(\mathbb R_+)$ by using a weight function. The operator $S_t$ can be thought of as a continuous analogue of a weighted shift operator. In this paper, we show that every left invertible operator $S_t$ can be modeled as a multiplication by $z$ on a reproducing kernel Hilbert space $\cal H$ of vector-valued analytic functions on a certain disc centered at the origin and the reproducing kernel associated with $\cal H$ is a diagonal operator. As it turns out that every hyperexpansive weighted translation semigroup is left invertile, the model applies to these semigroups. We also describe the spectral picture for the left invertible weighted translation semigroup. In the process, we point out the similarities and differences between a weighted shift operator and an operator $S_t.$Comment: 14 page

Non-syndromic multiple odontogenic keratocysts: report of case

Odontogenic keratocysts (OKCs) are epithelial developmental cysts which were first described by Phillipsen in 1956. Lesions are frequently multiple and a component of Nevoid Basal Cell Carcinoma Syndrome (NBCCS) (Gorlin Goltz syndrome/Bifid rib syndrome). We hereby report a case of multiple OKCs in a non – syndromic patient and highlight the general practitioner the importance of diagnosing the disease and enforcing a strict long-term follow-up whenever such a case is identified

Odontogenic tumors and giant cell lesions of jaws - a nine year study

<p>Abstract</p> <p>Objectives</p> <p>A definite geographic variation has been observed in the frequency of odontogenic tumors and giant cell lesions of the jaws reported from different parts of the world. However, there are a few studies on these lesions, especially giant cell lesions, reported from India. Hence, this study was designed to provide a demographic data on the odontogenic tumors and giant cell lesions reported from our institute located in the city of Hyderabad. Hyderabad is the capital city of the southern state of Andhra Pradesh in India. A retrospective analysis of odontogenic tumors and giant cell lesions of jaws reported in our institute between the years 2000 and 2009 was done and this data was compared with previous reports from different parts of the world and India.</p> <p>Methods</p> <p>Biopsies of the lesions received between the years 2000 and 2009 were reviewed and patient's history, clinical, radiological and histopathological characteristics were analyzed.</p> <p>Results</p> <p>A total of 77 biopsies were received during the nine year study period. These lesions were more frequently seen in the males, in a younger age group and showed a predilection for the mandible. Most of them presented as radiolucent, slow growing and painless lesions. Ameloblastomas (71.4%) constituted the majority of odontogenic tumors while central giant cell granulomas (7.8%) constituted the majority of giant cell lesions.</p> <p>Conclusion</p> <p>These lesions showed a definite geographic variation with ameloblastomas being the most common odontogenic tumors and odontomas being relatively rarer lesions in our region.</p

An analytic model for left invertible weighted translation semigroups

M. Embry and A. Lambert initiated the study of a semigroup of operators {St} indexed by a non-negative real number t and termed it as weighted translation semigroup. The operators St are defined on L 2 (R+) by using a weight function. The operator St can be thought of as a continuous analogue of a weighted shift operator. In this paper, we show that every left invertible operator St can be modeled as a multiplication by z on a reproducing kernel Hilbert space H of vector-valued analytic functions on a certain disc centered at the origin and the reproducing kernel associated with H is a diagonal operator. As it turns out that every hyperexpansive weighted translation semigroup is left invertible, the model applies to these semigroups. We also describe the spectral picture for the left invertible weighted translation semigroup. In the process, we point out the similarities and differences between a weighted shift operator and an operator St

The Migdal effect in semiconductors for dark matter with masses below ∼ 100 MeV

Abstract Dark matter scattering off a nucleus has a small probability of inducing an observable ionization through the inelastic excitation of an electron, called the Migdal effect. We use an effective field theory to extend the computation of the Migdal effect in semiconductors to regions of small momentum transfer to the nucleus, where the final state of the nucleus is no longer well described by a plane wave. Our analytical result can be fully quantified by the measurable dynamic structure factor of the semiconductor, which accounts for the vibrational degrees of freedom (phonons) in a crystal. We show that, due to the sum rules obeyed by the structure factor, the inclusive Migdal rate and the shape of the electron recoil spectrum is well captured by approximating the nuclei in the crystal as free ions; however, the exclusive differential rate with respect to energy depositions to the crystal depends on the phonon dynamics encoded in the dynamic structure function of the specific material. Our results now allow the Migdal effect in semiconductors to be evaluated even for the lightest dark matter candidates (m χ ≳ 1 MeV) that can kinematically excite electrons