Bilinear Forms on the Dirichlet Space

Let $\mathcal{D}$ be the classical Dirichlet space, the Hilbert space of holomorphic functions on the disk. Given a holomorphic symbol function $b$ we define the associated Hankel type bilinear form, initially for polynomials f and g, by $T_{b}(f,g):= _{\mathcal{D}}$, where we are looking at the inner product in the space $\mathcal{D}$. We let the norm of $T_{b}$ denotes its norm as a bilinear map from $\mathcal{D}\times\mathcal{D}$ to the complex numbers. We say a function $b$ is in the space $\mathcal{X}$ if the measure $d\mu_{b}:=| b^{\prime}(z)| ^{2}dA$ is a Carleson measure for $\mathcal{D}$ and norm $\mathcal{X}$ by $$\Vert b\Vert_{\mathcal{X}}:=| b(0)| +\Vert | b^{\prime}(z)| ^{2}dA\Vert_{CM(\mathcal{D})}^{1/2}.$$ Our main result is $T_{b}$ is bounded if and only if $b\in\mathcal{X}$ and $$\Vert T_{b}\Vert_{\mathcal{D\times D}}\approx\Vert b\Vert_{\mathcal{X}}.$$Comment: v1: 29 page

L-Band MMICs for Space-based SAR system

The design and performance of an L-Band GaAs chip-set is presented.The chip-set consists of a 6-bit attenuator circuit,a Low-Noise Amplifier (LNA)and a Multi Function Chip that is the combination of a 6-bit attenuator and 6-bit Phase shifter circuit.The chip-set is developed for the pre-flight engineering T/R (Transmit and Receive)modules currently in development with Astrium in a space-based SAR (Synthetic Aperture Radar)system.The MMICs are realised in the 0.25 µm PHEMT (PH25)technology of UMS.Only one iteration was needed for the MMICs in order to be fully compliant with the specifications

Stable comparison of multidimensional persistent homology groups with torsion

The present lack of a stable method to compare persistent homology groups with torsion is a relevant problem in current research about Persistent Homology and its applications in Pattern Recognition. In this paper we introduce a pseudo-distance d_T that represents a possible solution to this problem. Indeed, d_T is a pseudo-distance between multidimensional persistent homology groups with coefficients in an Abelian group, hence possibly having torsion. Our main theorem proves the stability of the new pseudo-distance with respect to the change of the filtering function, expressed both with respect to the max-norm and to the natural pseudo-distance between topological spaces endowed with vector-valued filtering functions. Furthermore, we prove a result showing the relationship between d_T and the matching distance in the 1-dimensional case, when the homology coefficients are taken in a field and hence the comparison can be made

A Calibrated Time Domain Envelope Measurement System for the Behavioral Modeling of Power Amplifiers

This paper presents a set-up which enables the generation and the calibrated time domain measurements of complex envelopes of modulated signals at both ports of non linear microwave power amplifiers. The architecture of the characterization tool is given. Examples of error corrected time domain envelopes at the input / output RF ports of a 36 dBm output power – 30dB power gain L-band SSPA are shown. Futhermore, the use of this characterization tool and a suitable processing of measurement data are applied to a novel measurement based behavioral modeling approach of non linear devices accounting for memory effects

Integrated Circuits Based on 300 GHz fT Metamorphic HEMT Technology for Millimeter-Wave and Mixed-Signal Applications

Advanced circuits based on metamorphic HEMT (MHEMT)technologies on 4 ”GaAs substrates for both millimeter-wave,and mixed- signal applications are presented.Extrinsic cut-off frequencies of ft =293 GHz and fmax =337 GHz were achieved for a 70 nm gate length metamorphic HEMT echnology.The MMIC process obtains high yield on transistor and circuit level.Single-stage low-noise amplifiers demonstrate a small signal gain of 13 dB and a noise figure of 2.8 dB at 94 GHz.An amplifier MMIC developed for D-Band operation features a gain of 15 dB at 160 GHz.The achieved results are comparable to state- of-the-art InP-based HEMT technologies.In order to realize 80 Gbit/s digital circuits,a process with 100 nm gate length enhancement type HEMTs with a transit frequency of 200 GHz is used.Three metalization layers are available for interconnects.The parasitic capacitance of the interconnects is kept low by using BCB and plated air bridge technology.Based on this process,static and dynamic frequency dividers achieve a maximu toggle frequency of 70 GHz and 108 GHz,respectively

On the X-rank with respect to linear projections of projective varieties

In this paper we improve the known bound for the $X$-rank $R_{X}(P)$ of an element $P\in {\mathbb{P}}^N$ in the case in which $X\subset {\mathbb P}^n$ is a projective variety obtained as a linear projection from a general $v$-dimensional subspace $V\subset {\mathbb P}^{n+v}$. Then, if $X\subset {\mathbb P}^n$ is a curve obtained from a projection of a rational normal curve $C\subset {\mathbb P}^{n+1}$ from a point $O\subset {\mathbb P}^{n+1}$, we are able to describe the precise value of the $X$-rank for those points $P\in {\mathbb P}^n$ such that $R_{X}(P)\leq R_{C}(O)-1$ and to improve the general result. Moreover we give a stratification, via the $X$-rank, of the osculating spaces to projective cuspidal projective curves $X$. Finally we give a description and a new bound of the $X$-rank of subspaces both in the general case and with respect to integral non-degenerate projective curves.Comment: 10 page

Polynomial-based non-uniform interpolatory subdivision with features control

Starting from a well-known construction of polynomial-based interpolatory 4-point schemes, in this paper we present an original affine combination of quadratic polynomial samples that leads to a non-uniform 4-point scheme with edge parameters. This blending-type formulation is then further generalized to provide a powerful subdivision algorithm that combines the fairing curve of a non-uniform refinement with the advantages of a shape-controlled interpolation method and an arbitrary point insertion rule. The result is a non-uniform interpolatory 4-point scheme that is unique in combining a number of distinctive properties. In fact it generates visually-pleasing limit curves where special features ranging from cusps and flat edges to point/edge tension effects may be included without creating undesired undulations. Moreover such a scheme is capable of inserting new points at any positions of existing intervals, so that the most convenient parameter values may be chosen as well as the intervals for insertion. Such a fully flexible curve scheme is a fundamental step towards the construction of high-quality interpolatory subdivision surfaces with features control

Microwave Circuits Based on Negative Refractive Index Material Structures

The paper presents the fundamentals of composite right/left-handed (CRLH)transmission lines and materials,and proposes an accurate circuit model of these structures for the design of practical applications.Three novel applications of CRLH meta-structures,developed at UCLA,are demonstrated:an arbitrary coupling-level backward-wave coupler,a zero th order resonator and a distributed planar negative lens

Ledge Design of InGaP Emitter GaAs Based HBTs

A wide range of emitter composition, thickness, and doping is studied via dc current gain measurements on large area GaAs based heterojunction bipolar transistors (HBTs) at both room and elevated temperatures. InGaP emitters offer the widest thickness and doping design window in terms of dc peak current gain, as compared with AlGaAs emitters. Remarkably, a 50 Å InGaP emitter HBT retains 50% gain of a more standard 500 Å emitter device. For state-of-the-art HBTs, a degraded peak gain is argued to be caused by an increased reverse hole injection current (IRHI). In light of previously published results which implicate IRHI as a mechanism for materials limited HBT reliability, we suggest dc current gain measurements on large-area HBTs give meaningful insights into the long term reliability of the structure. Specifically, the wider emitter thickness and doping design window offered by an InGaP emitter HBT could apply to reliability as well as to the demonstrated gain stability

Ku & C Band solid state switch matrix for satellite payloads using LTCC multilayer substrate

This paper describes the design and development of Ku and C band solid state switch matrix for multimedia satellite payloads. The design, through the use of advanced packaging techniques, allows significant savings on mass and volume with respect to traditional electromechanical switches while guaranteeing a comparable reliability