Note on B-splines, wavelet scaling functions, and Gabor frames

Let g be a continuous, compactly supported function on such that the integer translates of g constitute a partition of unity. We show that the Gabor system (g,a,b), with window g and time-shift and frequency-shift parameters a,b>0 has no lower frame bound larger than 0 if b=2,3,... and a>0. In particular, (g,a,b) is not a Gabor frame if g is a continuous, compactly supported wavelet scaling function and if b=2,3,... and a>0. We give an example for our result for the case that g=B/sub 1/, the triangle function supported by [-1,1], by showing pictures of the canonical dual corresponding to (g,a,b) where ab=1/4 and b crosses the lines N=2,3,.     

On the origin of strain hardening in glassy polymers

The influence of network density on the strain hardening behaviour of amorphous polymers is studied. The network density of polystyrene is altered by blending with poly(2,6-dimethyl-1,4-phenylene-oxide) and by cross-linking during polymerisation. The network density is derived from the rubber-plateau modulus determined by dynamic mechanical thermal analysis. Subsequently uniaxial compression tests are performed to obtain the intrinsic deformation behaviour and, in particular, the strain hardening modulus. At room temperature, the strain hardening modulus proves to be proportional to the network density, irrespective of the nature of the network, i.e. physical entanglements or chemical cross-links. With increasing temperature, the strain hardening modulus is observed to decrease. This decrease appears to be related to the influence of thermal mobility of the chains, determined by the distance to the glass-transition temperature (T−T_g).     

Methods of Verifying Continuous Automatic Belt Weighers: State and Prospects

The basic methods of verifying continuous automatic belt weighers are described. A comparative analysis of these methods on the basis of experimental studies is made and ways of implementing the results in industry are recommended.     

Managing Fashion Goods Inventories: Dynamic Recourse for Retailers with Outlet Stores

The proliferation of both online and bricks and mortar outlet stores underscores the observation that secondary markets are readily accessible to retailers of short-life-cycle products. These secondary markets provide recourse channels for retailers to sell excess inventory of out-of-favor items at reduced prices when overstocking occurs in a primary market. We study the problem of determining when a retailer should terminate its primary selling season by selling remaining inventory on a secondary market. The retailer has a single opportunity to procure prior to a primary selling season consisting of multiple periods. Demand in each period is random, but correlated. At the end of each period, any remaining inventory incurs a holding cost. Then, based upon the current level of inventory and the cumulative demand-to-date, the retailer decides either to terminate the primary selling season by selling all or part of the remaining inventory on a secondary market, or to extend the current primary selling season by another period. We develop structural properties of the optimal policy for determining when to terminate the primary selling season, and we develop corresponding implications for procurement.     

Deformation-Strength Relationships in Short-Term Tension of Heat-Resistant Materials

The analysis of 124 curves obtained in short-term tensile tests demonstrate that they can be described by varying strain hardening and softening characteristics. Different stress–strain curves can be produced at invariable yield strength and ultimate strength and interrelated proportional variations of the above characteristics. To determine some specific stress–strain curve, it is necessary to take account of yield strength and ultimate strength as well as strain corresponding to the latter. The relations between yield strength, ultimate strength and hardening and their practically complete absence between these parameters and softening were statistically established.     

Modellierungs- und Simulationsverfahren für die optische Verbindungstechnik auf elektrischen Leiterplatten

Optical interconnection technology on the printed circuit board level is a key technology for future microelectronic equipment. The consideration of functional, technological, and economical requirements results in a hybrid solution, where electrical and optical interconnects are integrated into one substrate called electrical optical printed circuit board. The significant part of the entire design process for electrical optical printed circuit boards is marked by the design supporting modelling and simulation of optical interconnects. Based on an abstract model for an entire optical interconnect a simulation model for optical multimode-waveguides is presented, taking into account all significant waveguide properties. Apart from that, the modeling of active components (laser- and photo-diodes) is addressed.     

Untersuchung der Verteilung und Intensität filamentierter Barrierenplasmen für die Behandlung von Oberflächen

The application of barrier discharges at atmospheric pressure in air expands on the market of plasma technology, because it is an ecological and cost‐effective alternative to other processes of surface treatment. These plasmas usually consist of a multitude of spatially and temporally localized filaments, whose distribution should be as even as possible for homogeneous treatment. This holds especially for the plasma treatment of sensitive goods such as wool or other textiles. In equipment for continuous pass of material the barrier arrangements often consist of a system cylinder – cylinder or cylinder – plane, whereby the gap width changes locally. Space distribution and intensity of filaments has been investigated by means of short‐time photography and spatially resolved measurement of current distribution and energy distribution derived from it. The local dependency found can be explained by means of a capacitive equivalent circuit.     

On the linear correlation between microhardness and mechanical properties in polar polymers and blends

The tensile elastic modulus (E), yield stress (σ_Y) and microhardness (MH) of neat and binary and ternary blends of glassy semicrystalline ethylene–vinyl alcohol copolymer (EVOH), a glassy amorphous polyamide and a semicrystalline nylon‐containing ionomer covering a broad range of properties were examined. The tests were carried out on dry and water‐equilibrated samples to produce stiffer and softer materials, respectively. From the results, more accurate linear correlations were found to describe adequately the microhardness, modulus and yield stress of these strongly self‐associated polymers through hydrogen bonding. Copyright © 2003 Society of Chemical Industry     

Effect of Strain Rate on Discontinuous Flow and Mechanical Characteristics of High-Nitrogenous Steel

Experimental study on the effect of strain rate on discontinuous flow and mechanical characteristics of the high-nitrogenous steel Kh23AG19F has been performed. Within the range of strain rates from 4.62 · 10^-5 to 1.85 · 10 ^-4 s^-1, discontinuous flow, reflected by serration on the tensile diagram, is chiefly determined by intergranular deformation mechanisms. Under strain rates over 1.85 · 10^-2 s^-1, combined deformation modes prevail, which cause a change in the character of discontinuous flow and transform a serrated tensile diagram into a wavy graph, with the yield stress of steel increased significantly.