1,072 research outputs found
PT Symmetric, Hermitian and P-Self-Adjoint Operators Related to Potentials in PT Quantum Mechanics
In the recent years a generalization of the
harmonic oscillator using a complex deformation was investigated, where
\epsilon\ is a real parameter. Here, we will consider the most simple case:
\epsilon even and x real. We will give a complete characterization of three
different classes of operators associated with the differential expression H:
The class of all self-adjoint (Hermitian) operators, the class of all PT
symmetric operators and the class of all P-self-adjoint operators.
Surprisingly, some of the PT symmetric operators associated to this expression
have no resolvent set
Preparation of Functionalized Aryl, Heteroaryl, and Benzylic Potassium Organometallics Using Potassium Diisopropylamide in Continuous Flow
We report the preparation of lithiumâsaltâfree KDA (potassium diisopropylamide; 0.6âm in hexane) complexed with TMEDA (N,N,NâČ,NâČâtetramethylethylenediamine) and its use for the flowâmetalation of (hetero)arenes between â78â°C and 25â°C with reaction times between 0.2â
s and 24â
s and a combined flow rate of 10â
mLâminâ1 using a commercial flow setup. The resulting potassium organometallics react instantaneously with various electrophiles, such as ketones, aldehydes, alkyl and allylic halides, disulfides, Weinreb amides, and Me3SiCl, affording functionalized (hetero)arenes in high yields. This flow procedure is successfully extended to the lateral metalation of methylâsubstituted arenes and heteroaromatics, resulting in the formation of various benzylic potassium organometallics. A metalation scaleâup was possible without further optimization
Improved spectral descriptions of planetary nebulae central stars
Context. At least 492 central stars of Galactic planetary nebulae (CSPNs) have been assigned spectral types. Since many CSPNs are faint, these classification efforts are frequently made at low spectral resolution. However, the stellar Balmer absorption lines are contaminated with nebular emission; therefore in many cases a low-resolution spectrum does not enable the determination of the H abundance in the CSPN photosphere. Whether or not the photosphere is H deficient is arguably the most important fact we should expect to extract from the CSPN spectrum, and should be the basis for an adequate spectral classification system.
Aims. Our purpose is to provide accurate spectral classifications and contribute to the knowledge of central stars of planetary nebulae and stellar evolution.
Methods. We have obtained and studied higher quality spectra of CSPNs described in the literature as weak emission-line star (WELS). We provide descriptions of 19 CSPN spectra. These stars had been previously classified at low spectral resolution. We used medium-resolution spectra taken with the Gemini Multi-Object Spectrograph (GMOS). We provide spectral types in the Morgan-Keenan (MK) system whenever possible.
Results. Twelve stars in our sample appear to have normal H rich photospheric abundances, and five stars remain unclassified. The rest (two) are most probably H deficient. Of all central stars described by other authors as WELS, we find that at least 26% of them are, in fact, H rich O stars, and at least 3% are H deficient. This supports the suggestion that the denomination WELS should not be taken as a spectral type, because, as a WELS is based on low-resolution spectra, it cannot provide enough information about the photospheric H abundance.Facultad de Ciencias AstronĂłmicas y GeofĂsicasInstituto de AstrofĂsica de La Plat
Studying the properties in pA collisions via the decay
Within transport calculations we study the production and decay of
-mesons in reactions at COSY energies including elastic and
inelastic rescattering, the Dalitz decay
as well as rescattering. The resulting invariant mass
distributions indicate that in-medium modifications of the -meson may
be observed experimentally.Comment: 5 pages, espcrc2-style, including 5 ps-figure
On Information Theory, Spectral Geometry and Quantum Gravity
We show that there exists a deep link between the two disciplines of
information theory and spectral geometry. This allows us to obtain new results
on a well known quantum gravity motivated natural ultraviolet cutoff which
describes an upper bound on the spatial density of information. Concretely, we
show that, together with an infrared cutoff, this natural ultraviolet cutoff
beautifully reduces the path integral of quantum field theory on curved space
to a finite number of ordinary integrations. We then show, in particular, that
the subsequent removal of the infrared cutoff is safe.Comment: 4 page
Dynamic studies of aldosterone in anephric man
Dynamic studies of aldosterone in anephric man. Aldosterone metabolism in the absence of a functioning renin-angiotensin system was evaluated in twelve anephric subjects. Plasma aldosterone concentrations determined while subjects were in a supine position were usually low, correlated with the plasma potassium concentration (r = 0.38; P < 0.01) and responded to acute alterations in plasma potassium concentration (r = 0.64; P < 0.001), thus indicating an important role for potassium in aldosterone regulation in anephric man. In contrast, plasma aldosterone concentration did not increase following volume and sodium depletion with ultrafiltration hemodialysis. Its response to angiotensin and corticotropin administration was usually diminished. We felt this was due in part to potassium depletion secondary to maintenance hemodialysis, since potassium repletion in two subjects improved aldosterone responsiveness. Another factor in the diminished aldosterone responsiveness in anephric subjects may be renin deficiency. Upright posture caused increases in plasma aldosterone concentration which could not be explained by concomitant alterations in the concentrations of adrenocorticotropic hormone (ACTH) or plasma electrolytes or metabolic clearance rate of aldosterone.Etudes dynamiques de l'aldostĂ©rone chez l'homme anĂ©phrique. Le mĂ©tabolisme de l'aldostĂ©rone en l'absence d'un systĂšme rĂ©nine angiotensine fonctionnel a Ă©tĂ© Ă©valuĂ© chez douze sujets anĂ©phriques. Les concentrations d'aldostĂ©rone en position debout Ă©taient habituellement basses, corrĂ©lĂ©es avec la kaliĂ©mie (r = 0,38; P < 0,01) et rĂ©pondaient aux modifications aiguĂ«s de la kaliĂ©mie (r = 0,64; P < 0,001), ce qui indique un rĂŽle important du potassium dans la rĂ©gulation de l'aldostĂ©rone chez l'homme anĂ©phrique. Au contraire, la concentration d'aldostĂ©rone du plasma n'a pas augmentĂ© aprĂšs une dĂ©plĂ©tion d'eau et de sodium rĂ©alisĂ©e par ultrafiltration au cours de l'hĂ©modialyse. La rĂ©ponse Ă l'angiotensine et Ă l'ACTH Ă©tait habituellement diminuĂ©e. Il est proposĂ© que cela soit du en partie Ă la dĂ©plĂ©tion en potassium secondaire Ă l'hĂ©modialyse chronique puisque la recharge en potassium chez deux sujets a amĂ©liorĂ© la rĂ©ponse aux stimuli. Un autre facteur dans la diminution de la rĂ©ponse chez les sujets anĂ©phriques peut ĂȘtre le dĂ©ficit de rĂ©nine. La position debout a dĂ©terminĂ© des augmentations de l'aldostĂ©rone du plasma qui ne peuvent pas ĂȘtre expliquĂ©es par des modifications concomitantes de l'ACTH, des Ă©lectrolytes du plasma ou du dĂ©bit de la clearance mĂ©tabolique de l'aldostĂ©rone
Relative Oscillation Theory, Weighted Zeros of the Wronskian, and the Spectral Shift Function
We develop an analog of classical oscillation theory for Sturm-Liouville
operators which, rather than measuring the spectrum of one single operator,
measures the difference between the spectra of two different operators.
This is done by replacing zeros of solutions of one operator by weighted
zeros of Wronskians of solutions of two different operators. In particular, we
show that a Sturm-type comparison theorem still holds in this situation and
demonstrate how this can be used to investigate the finiteness of eigenvalues
in essential spectral gaps. Furthermore, the connection with Krein's spectral
shift function is established.Comment: 26 page
Green's function for a Schroedinger operator and some related summation formulas
Summation formulas are obtained for products of associated Lagurre
polynomials by means of the Green's function K for the Hamiltonian H =
-{d^2\over dx^2} + x^2 + Ax^{-2}, A > 0. K is constructed by an application of
a Mercer type theorem that arises in connection with integral equations. The
new approach introduced in this paper may be useful for the construction of
wider classes of generating function.Comment: 14 page
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