Unbounded convex mappings of the ball in

In this paper, we study univalent holomorphic mappings of the unit ball in that have the property that the image contains a line for some , . We show that under certain rather reasonable conditions, up to composition with a holomorphic automorphism of the ball, the mapping is an extension of the strip mapping in the plane to higher dimensions.

     

Light Irradiation through Small Particles and Its Applications for Surface Nanostructuring in Near Field

We investigate the light scattering through small particles and its applications in nanostructuring, such as nanobumping, nanopatterning and dry laser cleaning. The theoretical calculation based on Mie theory provides an exact solution for sphere cavity resonance and plasmon resonance, which are two mechanisms for dielectric and metallic particles assisted surface nanostructuring in near field. The experimental results indicate that nanobumps on glass surface and subwavelength holes array on silicon surface can be formed without cracks with the self-assembly of 1 μm silica particle mask under laser irradiation. It is also found that the scattering wave by 40 nm gold particles can propagate 200 times away in terms of particle radius as recorded by photoresist under the UV light irradiation. Meanwhile, dry laser cleaning of 40nm gold particle on silicon wafer is demonstrated at plasmonic resonance frequency. The total cleaning efficiency is estimated to be 80%.     

System feasibility study of a microwave/millimeter-wave radar for space debris tracking

A 35 GHz millimeter-wave radar system has been studied for space debris tracking. The objective is to track the particles ranging in size from 4 mm to 80 mm up to a range of 25 km. The system requires various state-of-the-art technologies including phased arrays, monopulse tracking, pulse compression, high power transmitters, low noise receivers, and pulse integration signal processing techniques.     

Complex variables in junior high school: the role and potential impact of an outreach mathematician

Outreach mathematicians are college faculty who are trainedin mathematics but who undertake an active role in improvingprimary and secondary education. This role is examined througha study where an outreach mathematician introduced the conceptof complex variables to junior high school students in the UnitedStates with the goal of stimulating their interest in mathematicsand improving their algebra skills. Comparison of pre- and post-testresults showed that ninth-grade students displayed a significantchange in algebraic skills while the eighth-grade students madelittle progress. The outreach mathematician lacked some awarenessof the eighth-grade students’ foundational backgroundand motivation. This illustrates the importance of working moreclosely with the participating teacher, who understands betterthe curriculum and the students’ background knowledge,levels of maturity and levels of motivation.     

Extraordinarily high drive currents in asymmetrical double-gate MOSFETs

Numerical simulation results derived from a Schrödinger–Poisson tool applied to scaled double-gate (DG) MOSFETs, supplemented by analytical characterizations of the pertinent physics, are presented to give insight concerning the near-ideal features of DG devices and to explain how the low-voltage drive current of the asymmetrical DG MOSFET, having only one predominant channel, can be comparable to, and even higher than, that of the symmetrical-gate counterpart designed to have the same off-state current.     

Probabilistic modeling of forced ignition of alternative jet fuels

Fast and reliable high altitude re-ignition is a critical requirement for the development of alternative jet fuels (AJFs). To achieve stable combustion, a spark kernel needs to transit in a partially or fully extinguished flow to develop a flame front. Understanding the relight characteristics of the AJFs is complicated by the chaoticity of the turbulent flow and variations in the spark properties. The focus of this study is the prediction of such characteristics by high-fidelity simulations, with a specific focus on fuel composition effect on the ignition process. For this purpose, a previously developed computational framework is applied, which utilizes high-fidelity LES simulations, a hybrid tabulation approach for modeling forced ignition and detailed quantification of uncertainty resulting from initial and boundary conditions to predict ignition probability. The method is applied to two alternative fuels (named C1 and C5) and Jet-A fuel (named A2) under gaseous conditions. Results show that the mixing of kernel and fuel–air mixture is not affected by the ignition process, but chemistry effects strongly dominate ignition probability. In particular, C1 exhibits much lower ignition probability than the other two fuels, especially at lean operating conditions. More importantly, this behavior is contradictory to ignition delay experiments which predict longer delay times for C5 compared to C1. Comparisons with experiments show that the comprehensive modeling approach captures the ignition trends. Analysis of kernel trajectories in composition space shows that the variations are caused by the relative effects of kernel mixing, response to strain, and ignition properties of the fuel.     

Simple all-microwave entangling gate for fixed-frequency superconducting qubits

We demonstrate an all-microwave two-qubit gate on superconducting qubits which are fixed in frequency at optimal bias points. The gate requires no additional subcircuitry and is tunable via the amplitude of microwave irradiation on one qubit at the transition frequency of the other. We use the gate to generate entangled states with a maximal extracted concurrence of 0.88, and quantum process tomography reveals a gate fidelity of 81%.