Sharp inequalities for the coefficients of concave schlicht functions

Let D denote the open unit disc and let f: D → ℂ be holomorphic and injective in D. We further assume that f(D) is unbounded and ℂ \ f(D) is a convex domain. In this article, we consider the Taylor coefficients a n(f) of the normalized expansion f(z) = z + Σ n=2 ∞an(f)zn, z ∈ D, n=2 and we impose on such functions f the second normalization f(1) = ∞. We call these functions concave schlicht functions, as the image of D is a concave domain. We prove that the sharp inequalities |an(f)-n+1/2 ≤ n-1/2, n≥2, are valid. This settles a conjecture formulated in [2]. © Swiss Mathematical Society

On the coefficients of concave univalent functions

Let D denote the open unit disc and f : D → ℂ̄ be meromorphic and injective in D. We assume that f is holomorphic at zero and has the expansion f(z) = z + ∞σ anzn Especially, we consider f that map D onto a domain whose complement with respect to ℂ̄ is convex. We call these functions concave univalent functions and denote the set of these functions by Co. We prove that the sharp inequalities |an| ≥ 1, n ∈ ℕ, are valid for all concave univalent functions. Furthermore, we consider those concave univalent functions which have their pole at a point p ∈ (0, 1) and determine the precise domain of variability for the coefficients a2 and a3 for these classes of functions. © 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Application of Chip-Level EMC in Automotive Product Design

Integrated circuits (ICs) are often the source of the high-frequency noise that drives electromagnetic emissions from electronic products. A case study is presented where emissions from a printed circuit board containing an automotive microcontroller are reduced significantly through analysis of the coupling mechanisms from the chip to the board and attached cables. Noise generated by the IC is explored through measurements in a semi-anechoic chamber and TEM cell, through near-field scans, and through modifications to the printed circuit board. Noise is driven by the IC through both power and I/O connections. Results show that a ferrite in series with I/O power in this application reduced emissions by 10 dB or more at critical frequencies. Possible causes for emissions from the IC and modifications that might reduce these emissions are discussed

The Method of Auxiliary Sources as an Efficient Numerical Technique for Large 3D Semi Open Structures

The method of auxiliary sources (MAS) has been demonstrated as suitable for solution of diffraction and inverse problems in complex 2D large objects. Based on MAS numerical study of 3D RCS, EMC/EMI and SAR problems, related to the EM field resonance enhancement inside vehicles and the interaction of the cellular telephone radiation with the user\u27\u27s head are given in other work. The objective of this paper is to present details of MAS application to the wide 3D electrodynamic problems. The area of its efficient application, some features and advantages to achieving efficient solutions, are discussed. The extension of the MAS for semi-open structures with partitions is also presented

Electromagnetic Analysis for Vehicle Antenna Development Using Method of Auxiliary Sources

In paper [l] the electromagnetic analysis of large semi-open structures like vehicles was presented formulated as scattering problem, illuminated by a wide range of incident EM fields. The effect of resonances within the semi-open structure on the RCS, near fields and pattem of reradiated fields had been shown. In this paper the interaction of the entire semi-open structure on the performance of an antenna is considered together with the investigation of near field distributions inside the cavity. The Method of Auxiliary Sources (MAS) [2] is utilized. For a simple geometry the results are compared to measurements

Hydrodynamic object recognition using pressure sensing

Hydrodynamic sensing is instrumental to fish and some amphibians. It also represents, for underwater vehicles, an alternative way of sensing the fluid environment when visual and acoustic sensing are limited. To assess the effectiveness of hydrodynamic sensing and gain insight into its capabilities and limitations, we investigated the forward and inverse problem of detection and identification, using the hydrodynamic pressure in the neighbourhood, of a stationary obstacle described using a general shape representation. Based on conformal mapping and a general normalization procedure, our obstacle representation accounts for all specific features of progressive perceptual hydrodynamic imaging reported experimentally. Size, location and shape are encoded separately. The shape representation rests upon an asymptotic series which embodies the progressive character of hydrodynamic imaging through pressure sensing. A dynamic filtering method is used to invert noisy nonlinear pressure signals for the shape parameters. The results highlight the dependence of the sensitivity of hydrodynamic sensing not only on the relative distance to the disturbance but also its bearing

Classification of Complex Polynomial Vector Fields in One Complex Variable

A classification of the global structure of monic and centered one-variable complex polynomial vector fields is presented.Comment: 57 pages, 35 figures, submitted to the Journal of Difference Equations and Application

MAS-MoM Hybrid Method with Wire\u27s Image using in Excitation Problems

An important class of problems is the interaction of an antenna with the cavity of a semi-open metallic structure. In a working environment, an antenna may change its performance due to interactions with its surroundings. This is especially true in automotive applications. Therefore, it is important to consider the interaction of an antenna with possible resonating parts, and to solve these complex electrodynamics problems together. The development of methods for modeling and studying electromagnetic compatibility (EMC) problems has practical value. The method of auxiliary sources (MAS) with the method of moments (MoM) is applied to solve the excitation problem where a wire, with voltage source excitation, is connected to an open metallic surface. For verification of the proposed algorithm, an experimental structure was built and measured. Computer modeling results and the experimental results are in good agreement. Some aspects and principles are described, which provide hybridization of MAS and MoM. Image of objects is effectively applied for the solution of the particular problem

Field Extraction from Near Field Scanning for a Microstrip Structure

Currents associated with high-speed digital devices have significant impacts on EMI problems in VLSI design and operation. In this paper, a simple transmission line model was implemented as an initial step to represent the EMI mechanisms associated with an IC package. Numerical modeling results were compared with near field scanning measurements and show that the magnetic field deduced from the measurements agrees well with the numerical predictions

Strong asymptotics for Jacobi polynomials with varying nonstandard parameters

Strong asymptotics on the whole complex plane of a sequence of monic Jacobi polynomials $P_n^{(\alpha_n, \beta_n)}$ is studied, assuming that $$\lim_{n\to\infty} \frac{\alpha_n}{n}=A, \qquad \lim_{n\to\infty} \frac{\beta _n}{n}=B,$$ with $A$ and $B$ satisfying $A > -1$, $B>-1$, $A+B < -1$. The asymptotic analysis is based on the non-Hermitian orthogonality of these polynomials, and uses the Deift/Zhou steepest descent analysis for matrix Riemann-Hilbert problems. As a corollary, asymptotic zero behavior is derived. We show that in a generic case the zeros distribute on the set of critical trajectories $\Gamma$ of a certain quadratic differential according to the equilibrium measure on $\Gamma$ in an external field. However, when either $\alpha_n$, $\beta_n$ or $\alpha_n+\beta_n$ are geometrically close to $\Z$, part of the zeros accumulate along a different trajectory of the same quadratic differential.Comment: 31 pages, 12 figures. Some references added. To appear in Journal D'Analyse Mathematiqu