Magnetic Tuning of a Microstrip Patch Antenna Fabricated on a Ferrite Film

A square, single-feed patch, fabricated on a ferrite film, that produced orthogonally polarized, well-formed radiation patterns is described. The application of a small in-plane magnetic field tuned the frequency, and hence phase, of one polarization only. Prior work on patch antennas fabricated on bulk ferrite substrates demonstrated magnetic tuning, but only linear polarization was obtained. The results indicate that 1) thin ferrite films, which are monolithically integrable, may be useful for a magnetically tunable antenna, and 2) the radiation polarization of the patch can be varied by the application of a small in-plane magnetic bias field

A probabilistic approach to some results by Nieto and Truax

In this paper, we reconsider some results by Nieto and Truax about generating functions for arbitrary order coherent and squeezed states. These results were obtained using the exponential of the Laplacian operator; more elaborated operational identities were used by Dattoli et al. \cite{Dattoli} to extend these results. In this note, we show that the operational approach can be replaced by a purely probabilistic approach, in the sense that the exponential of derivatives operators can be identified with equivalent expectation operators. This approach brings new insight about the kinks between operational and probabilistic calculus.Comment: 2nd versio

Explicit representations of biorthogonal polynomials

Given a parametrised weight function $\omega(x,\mu)$ such that the quotients of its consecutive moments are M\"obius maps, it is possible to express the underlying biorthogonal polynomials in a closed form \cite{IN2}. In the present paper we address ourselves to two related issues. Firstly, we demonstrate that, subject to additional assumptions, every such $\omega$ obeys (in $x$) a linear differential equation whose solution is a generalized hypergeometric function. Secondly, using a generalization of standard divided differences, we present a new explicit representation of the underlying orthogonal polynomials

A New Class of Non-Linear Stability Preserving Operators

We extend Br\"and\'en's recent proof of a conjecture of Stanley and describe a new class of non-linear operators that preserve weak Hurwitz stability and the Laguerre-P\'olya class.Comment: Fixed typos, spelling, and updated links in reference

Membrane-initiated nuclear trafficking of the glucocorticoid receptor in hypothalamic neurons

Glucocorticoid binding to the intracellular glucocorticoid receptor (GR) stimulates the translocation of the GR from the cytosol to the nucleus, which leads to the transactivation or transrepression of gene transcription. However, multiple lines of evidence suggest that glucocorticoid signaling can also be initiated from the plasma membrane. Here, we provide evidence for membrane-initiated glucocorticoid signaling by a membrane-impermeant dexamethasone-bovine serum albumin (Dex-BSA) conjugate, which induced GR nuclear trafficking in hypothalamic neurons in vitro and in vivo. The GR nuclear translocation induced by a membrane-impermeant glucocorticoid suggests trafficking of an unliganded GR. The membrane-initiated GR trafficking was not blocked by inhibiting ERK MAPK, p38 MAPK, PKA, Akt, Src kinase, or calcium signaling, but was inhibited by Akt activation. Short-term exposure of hypothalamic neurons to dexamethasone (Dex) activated the glucocorticoid response element (GRE), suggesting transcriptional transactivation, whereas exposure to the Dex-BSA conjugate failed to activate the GRE, suggesting differential transcriptional activity of the liganded compared to the unliganded GR. Microarray analysis revealed divergent transcriptional regulation by Dex-BSA compared to Dex. Together, our data suggest that signaling from a putative membrane glucocorticoid receptor induces the trafficking of unliganded GR to the nucleus, which elicits a pattern of gene transcription that differs from that of the liganded receptor. The differential transcriptional signaling by liganded and unliganded receptors may contribute to the broad range of genetic regulation by glucocorticoids, and may help explain some of the different off-target actions of glucocorticoid drugs

Effective superpotentials for compact D5-brane Calabi-Yau geometries

For compact Calabi-Yau geometries with D5-branes we study N=1 effective superpotentials depending on both open- and closed-string fields. We develop methods to derive the open/closed Picard-Fuchs differential equations, which control D5-brane deformations as well as complex structure deformations of the compact Calabi-Yau space. Their solutions encode the flat open/closed coordinates and the effective superpotential. For two explicit examples of compact D5-brane Calabi-Yau hypersurface geometries we apply our techniques and express the calculated superpotentials in terms of flat open/closed coordinates. By evaluating these superpotentials at their critical points we reproduce the domain wall tensions that have recently appeared in the literature. Finally we extract orbifold disk invariants from the superpotentials, which, up to overall numerical normalizations, correspond to orbifold disk Gromov-Witten invariants in the mirror geometry.Comment: 55 pages; v2: references added, typos correcte

Propagator of a Charged Particle with a Spin in Uniform Magnetic and Perpendicular Electric Fields

We construct an explicit solution of the Cauchy initial value problem for the time-dependent Schroedinger equation for a charged particle with a spin moving in a uniform magnetic field and a perpendicular electric field varying with time. The corresponding Green function (propagator) is given in terms of elementary functions and certain integrals of the fields with a characteristic function, which should be found as an analytic or numerical solution of the equation of motion for the classical oscillator with a time-dependent frequency. We discuss a particular solution of a related nonlinear Schroedinger equation and some special and limiting cases are outlined.Comment: 17 pages, no figure

Monomiality principle, Sheffer-type polynomials and the normal ordering problem

We solve the boson normal ordering problem for $(q(a^\dag)a+v(a^\dag))^n$ with arbitrary functions $q(x)$ and $v(x)$ and integer $n$, where $a$ and $a^\dag$ are boson annihilation and creation operators, satisfying $[a,a^\dag]=1$. This consequently provides the solution for the exponential $e^{\lambda(q(a^\dag)a+v(a^\dag))}$ generalizing the shift operator. In the course of these considerations we define and explore the monomiality principle and find its representations. We exploit the properties of Sheffer-type polynomials which constitute the inherent structure of this problem. In the end we give some examples illustrating the utility of the method and point out the relation to combinatorial structures.Comment: Presented at the 8'th International School of Theoretical Physics "Symmetry and Structural Properties of Condensed Matter " (SSPCM 2005), Myczkowce, Poland. 13 pages, 31 reference

Scalar Casimir Effect on a D-dimensional Einstein Static Universe

We compute the renormalised energy momentum tensor of a free scalar field coupled to gravity on an (n+1)-dimensional Einstein Static Universe (ESU), RxS^n, with arbitrary low energy effective operators (up to mass dimension n+1). A generic class of regulators is used, together with the Abel-Plana formula, leading to a manifestly regulator independent result. The general structure of the divergences is analysed to show that all the gravitational couplings (not just the cosmological constant) are renormalised for an arbitrary regulator. Various commonly used methods (damping function, point-splitting, momentum cut-off and zeta function) are shown to, effectively, belong to the given class. The final results depend strongly on the parity of n. A detailed analytical and numerical analysis is performed for the behaviours of the renormalised energy density and a quantity `sigma' which determines if the strong energy condition holds for the `quantum fluid'. We briefly discuss the quantum fluid back-reaction problem, via the higher dimensional Friedmann and Raychaudhuri equations, observe that equilibrium radii exist and unveil the possibility of a `Casimir stabilisation of Einstein Static Universes'.Comment: 37 pages, 15 figures, v2: minor changes in sections 1, 2.5, 3 and 4; version published in CQ

Some Orthogonal Polynomials Arising from Coherent States

We explore in this paper some orthogonal polynomials which are naturally associated to certain families of coherent states, often referred to as nonlinear coherent states in the quantum optics literature. Some examples turn out to be known orthogonal polynomials but in many cases we encounter a general class of new orthogonal polynomials for which we establish several qualitative results.Comment: 21 page