Compact wideband antenna above a wideband non-uniform artificial magnetic conductor

A compact wideband antenna place above a non-uniform artificial magnetic conductor (AMC) is presented. The antenna is composed of a wideband coplanar waveguide fed antenna, with wideband harmonic suppression characteristic using non-uniform defected ground structure. Besides, a non-uniform wideband AMC is designed. The AMC unit cell is composed of a square patch into which a four arms spiral shape is etched. It exhibits a wider ±90° bandwidth than the spiral unit cell and a smaller size than the square patch unit cell. The antenna is placed above the proposed AMC structure formed by 6 × 5 unit cells. The overall dimensions of the complete structure are 0.7 × 0.6 λ ₀ ² , where λ ₀ is the free-space wavelength at the lowest frequency. It offers a low-profile configuration with a total thickness of λ ₀/14.3, and it is matched between 2.5 and 5.4 GHz (73.5 %). Furthermore, it has a stable main lobe radiation pattern in the E- and H-planes within the operating frequency band. Moreover, compared with the antenna without AMC, the broadside realized gain is significantly increased. A prototype has been realized, and there is a good agreement between simulated and measured results. Furthermore, the proposed structure presents a size reduction of about 34 %, and better radiation characteristics in comparison with the conventional square AMC.     

Valuation of power plants by utility indifference and numerical computation

This paper presents a real option valuation model of a power plant, which accounts for physical constraints and market incompleteness. Switching costs, minimum on-off times, ramp rates, or non-constant heat rates are important characteristics that can lead, if neglected, to overestimated values. The existence of non-hedgeable uncertainties is also a feature of energy markets that can impact assets value. We use the utility indifference approach to define the value of the physical asset. We derive the associated mixed optimal switching-control problem and provide a characterization of its solution by means of a coupled system of reflected Backward Stochastic Differential Equations (BSDE). We relate this system to a system of variational inequalities, and we provide a numerical comparative study by implementing BSDE simulation algorithms, and PDE finite differences schemes.     

Isoperimetric, Sobolev, and Eigenvalue Inequalities via the Alexandroff-Bakelman-Pucci Method: A Survey

This paper presents the proof of several inequalities by using the technique introduced by Alexandroff, Bakelman, and Pucci to establish their ABP estimate. First, the author gives a new and simple proof of a lower bound of Berestycki, Nirenberg, and Varadhan concerning the principal eigenvalue of an elliptic operator with bounded measurable coefficients. The rest of the paper is a survey on the proofs of several isoperimetric and Sobolev inequalities using the ABP technique. This includes new proofs of the classical isoperimetric inequality, the Wulff isoperimetric inequality, and the Lions-Pacella isoperimetric inequality in convex cones. For this last inequality, the new proof was recently found by the author, Xavier Ros-Oton, and Joaquim Serra in a work where new Sobolev inequalities with weights came up by studying an open question raised by Haim Brezis.     

Herman Rings and Arnold Disks

For (,a) C* x C, let f_,a be the rational map defined by f_,a(z)= z² (az+1)/(z+a). If R/Z is a Brjuno number, we let D bethe set of parameters (,a) such that f_,a has a fixed Hermanring with rotation number (we consider that (e²ⁱ,0) D). Resultsobtained by McMullen and Sullivan imply that, for any g D, theconnected component of D(C* x (C/{0,1})) that contains g isisomorphic to a punctured disk. We show that there is a holomorphic injection F:DD such thatF(0) = (e²ⁱ ,0) and , where r is the conformal radius at 0 of the Siegel disk of the quadraticpolynomial z e²ⁱ z(1+z). As a consequence, we show that for a (0,1/3), if f_l,a has afixed Herman ring with rotation number and if m_a is the modulusof the Herman ring, then, as a0, we have e m_a=(r/a) + O(a). We finally explain how to adapt the results to the complex standardfamily z e^(a/2)(z-1/z).     

Gravitational radiation in quantum gravity

The effective field theory of quantum gravity generically predicts non-locality to be present in the effective action, which results from the low-energy propagation of gravitons and massless matter. Working to second order in gravitational curvature, we reconsider the effects of quantum gravity on the gravitational radiation emitted from a binary system. In particular, we calculate for the first time the leading order quantum gravitational correction to the classical quadrupole radiation formula which appears at second order in Newton’s constant.     

Enantioselective Iridium-Catalyzed Allylic Arylation

We describe herein the development of the first iridium-catalyzed allylic substitution using arylzinc nucleophiles. High enantioselectivities were obtained from the reactions, which used commercially available Grignard reagents as the starting materials. This methodology was also shown to be compatible with halogen/metal exchange reactions. Its synthetic potential is demonstrated by its application towards the formal synthesis of (+)-sertraline.     

Reduced energy functionals for a three-dimensional fast rotating Bose Einstein condensates

We prove that in the fast rotating regime, the three-dimensional Gross–Pitaevskii energy describing the state of a Bose Einstein condensate can be reduced to a two-dimensional problem and that the vortex lines are almost straight. Additionally, we prove that the minimum of this two-dimensional problem can be sought in a reduced space corresponding to the first eigenspace of an elliptic operator. This space is called the Lowest Landau level and is of infinite dimension