A constructive fixed point theorem for min-max functions

Min-max functions, F :R n R n , arise in modelling the dynamic behaviour of discrete event systems. They form a dense subset of those functions which are homogeneous, F i (x 1 + h, .. . , x n + h) = Fi(x 1 , . . . , x n ) + h, monotonic , x y F(x) F(y), and nonexpansive in the l infinity norm-so-called topical functions-which have appeared recently in the work of several authors. Our main result characterizes those min-max functions which have a (generalized) fixed point, where Fi(x) = x i + h for some h R. We deduce several earlier fixed point results. The proof is inspired by Howard's policy improvement scheme in optimal control and yields an algorithm for finding a fixed point, which appears efficient in an important special case. An extended introduction sets the context for this paper in recent work on the dynamics of topical functions.     

Four different approaches for the measurement of IC surface temperature: application to thermal testing

Silicon die surface temperature can be used to monitor the health state of digital and analogue integrated circuits (IC). In the present paper, four different sensing techniques: scanning thermal microscope, laser reflectometer, laser interferometer and electronic built-in differential temperature sensors are used to measure the temperature at the surface of the same IC containing heat sources (hot spots) that behave as faulty digital gates. The goal of the paper is to describe the techniques as well as to present the performances of these sensing methods for the detection and localisation of hot spots in an IC.     

Molecular formula analysis by an MS/MS/MS technique to expedite dereplication of natural products

A facile and sensitive mass spectrometric method has been developed for the dereplication of natural products. The method provides information about the molecular formula and substructure of a precursor molecule and its fragments, which are invaluable aids in dereplication of natural products at their early stages of purification and characterization. Collision-induced MS/MS technique is used to fragment a precursor ion into several product ions, and individual product ions are selected and subjected to collision-induced MS/MS/MS analysis. This method enables the identification of the fragmentation pathway of a precursor molecule from its first-generation fragments (MS/MS), through to the nth generation product ions (MSn). It also allows for the identification of the corresponding neutral products released (neutral losses). Elements used in the molecular formula analysis include C, H, N, O, and S, as most natural products are constituted by these five elements. High-resolution mass separation and accurate mass measurements afforded the unique identification of molecular formula of small neutral products. Through sequential add-up of the molecular formulas of the small neutral products, the molecular formula of the precursor ion and its productions were uniquely determined. The molecular formula of the precursor molecule was then reversely used to identify or confirm the molecular formula of the neutral products and that of the productions. The molecular formula of the neutral fragments allowed for the identification of substructures, leading to a rapid and efficient characterization of precursor natural product. The method was applied to paclitaxel (C47H51NO14; 853 amu) to identify its molecular formula and its substructures, and to characterize its potential fragmentation pathways. The method was further validated by correctly identifying the molecular formula of minocycline (C23H27N3O7; 457 amu) and piperacillin (C23H27N5O7S; 517 amu).     

M9住宅一期

建筑师:Sid Lee建筑事务所+Aedifica项目地点:加拿大,魁北克建筑面积:789M.C.摄影:Stephane Brugger Architects:Sid Lee Architecture+Aedifica Location:Montreal,Quebec,Canada Gross Floor Area:789M.C.Photos:Stéphane Brügger     

Spectroscopic Study on Ultrafast Carrier Dynamics and Terahertz Amplified Stimulated Emission in Optically Pumped Graphene

This paper reviews recent advances in spectroscopic study on ultrafast carrier dynamics and terahertz (THz) stimulated emission in optically pumped graphene. The gapless and linear energy spectra of electrons and holes in graphene can lead to nontrivial features such as negative dynamic conductivity in the THz spectral range, which may lead to the development of new types of THz lasers. First, the non-equilibrium carrier relaxation/recombination dynamics is formulated to show how photoexcited carriers equilibrate their energy and temperature via carrier-carrier and carrier-phonon scatterings and in what photon energies and in what time duration the dynamic conductivity can take negative values as functions of temperature, pumping photon energy/intensity, and carrier relaxation rates. Second, we conduct time-domain spectroscopic studies using an optical pump and a terahertz probe with an optical probe technique at room temperature and show that graphene sheets amplify an incoming terahertz field. Two different types of samples are prepared for the measurement; one is an exfoliated monolayer graphene on SiO₂/Si substrate and the other is a heteroepitaxially grown non-Bernal stacked multilayer graphene on a 3C-SiC/Si epi-wafer.     

On routing with guaranteed delivery in three-dimensional ad hoc wireless networks

We study the problem of routing in three-dimensional ad hoc networks. We are interested in routing algorithms that guarantee delivery and are k-local, i.e., each intermediate node v’s routing decision only depends on knowledge of the labels of the source and destination nodes, of the subgraph induced by nodes within distance k of v, and of the neighbour of v from which the message was received. We model a three-dimensional ad hoc network by a unit ball graph, where nodes are points in three-dimensional space, and for each node v, there is an edge between v and every node u contained in the unit-radius ball centred at v. The question of whether there is a simple local routing algorithm that guarantees delivery in unit ball graphs has been open for some time. In this paper, we answer this question in the negative: we show that for any fixed k, there can be no k-local routing algorithm that guarantees delivery on all unit ball graphs. This result is in contrast with the two-dimensional case, where 1-local routing algorithms that guarantee delivery are known. Specifically, we show that guaranteed delivery is possible if the nodes of the unit ball graph are contained in a slab of thickness \(1/\sqrt{2}.\) However, there is no k-local routing algorithm that guarantees delivery for the class of unit ball graphs contained in thicker slabs, i.e., slabs of thickness \(1/\sqrt{2} + \epsilon\) for some \( \epsilon > 0.\) The algorithm for routing in thin slabs derives from a transformation of unit ball graphs contained in thin slabs into quasi unit disc graphs, which yields a 2-local routing algorithm. We also show several results that further elaborate on the relationship between these two classes of graphs.     

Synthesis of nanocomposite films from wheat gluten matrix and MMT intercalated with different quaternary ammonium salts by way of hydroalcoholic solvent casting

Protein-based nanocomposites consisting of wheat gluten matrix (WG) and montmorillonite (MMT) modified with quaternary ammonium salts (QA) were developed by hydroalcoholic solvent casting. A simple clay-modifying method using five QA salts of different molecular lengths composed of 4, 5, 16, 40 and 72 carbon atoms, represented by C₄N, C₅OHN, C₁₆N, C₄₀N and C₇₂N, was used for mineral intercalation. XRD analysis of composites containing Na–MMT, C₁₆N–MMT, C₄₀N–MMT, and C₇₂N–MMT indicated the diffraction peaks corresponding to the interlayer spacing were absent, demonstrating that these particles were significantly dispersed in the WG matrix. Concentration and dispersion of MMT in the WG protein were the main factors affecting on permeability to water vapor P_wv through the films. There was a decrease of P_wv when either the raw or the modified MMT was added. The more prominent decrease of the P_wv was found for dispersed mineral particles, such as C₁₆N–MMT, C₄₀N–MMT, and C₇₂N–MMT.     

Diameter-dependent electromechanical properties of GaN nanowires

The diameter-dependent Young's modulus, E, and quality factor, Q, of GaN nanowires were measured using electromechanical resonance analysis in a transmission electron microscope. E is close to the theoretical bulk value ( approximately 300 GPa) for a large diameter nanowire (d=84 nm) but is significantly smaller for smaller diameters. At room temperature, Q is as high as 2,800 for d=84 nm, significantly greater than what is obtained from micromachined Si resonators of comparable surface-to-volume ratio. This implies significant advantages of smooth-surfaced GaN nanowire resonators for nanoelectromechanical system (NEMS) applications. Two closely spaced resonances are observed and attributed to the low-symmetry triangular cross section of the nanowires.