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,.     

Structure and electrical characteristics of Ce4+-doped Ba2In2O5

The In-site of Ba₂In₂O₅ with Brownmillerite structure was partially substituted for Ce⁴⁺ ions in order to examine the doping effect on the order-disorder transition. Ba₂In_{2 – x} Ce _x O_{5 + x/2} (x = 0.1, 0.2, 0.3, 0.5, 1.0, and 1.5) were prepared by solid state reaction. X-Ray diffraction analyses of these powder samples demonstrated that Ba₂In_{2 – x} Ce _x O_{5 + x/2} (x = 0.1 and 0.2) possesses Brownmillerite structure. With increasing content of Ce⁴⁺ ion the crystal system of Ba₂In_{2 – x} Ce _x O_{5 + x/2} (x = 0.3, 0.5, and 1.0) changed to cubic perovskite structure above the order-disorder transition temperature of Ba₂In₂O₅. Arrhenius plots of the electrical conductivities of Ba₂In_{2 – x} Ce _x O_{5 + x/2} (x = 0.2, 0.3, and 1.0) exhibited no discontinuity. These compounds had high transference numbers of oxide ion above 973 k.     

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.     

Verhalten von Magnesiumlegierungen für Anwendungen im Fahrzeugbau bei mechanisch‐elektrochemischer Komplexbeanspruchung: Einfluss passivierender Deckschichten und Mechanismen der lokalen Schädigung

Behavior of Magnesium‐Alloys for Automotive Applications under Mechanical and Environmental Loading: Influence of Passivating Films and Mechanisms of Local Breakdown To assure an efficient design of components under cyclic loading, all available data concerning fatigue have to be observed. Therefore the influences of manufacturing on the material condition, the mechanical loads and environmental effects have to be analysed. Magnesium‐alloys are of special interest for lightweight applications because of their excellent strength‐density ratio. The corrosion resistance of magnesium‐alloys depends on the same factors that are critical to other metals. The alloys have a good stability to atmospheric exposure and a good resistance to attack by alkali, chromic and hydrofluoric acids. However, because of the electrochemical activity of magnesium, the relative importance of some factors is greatly amplified. The nature and composition of passive films formed on magnesium‐alloys depend on the prevailing conditions, viz. alloy‐composition, passivation potential, pH, electrolyte composition and temperature. Passive films may be damaged by local breakdown. Because of this, magnesium‐alloys suffer a degradation of their properties when exposed to an aqueous environment. The main topic of the present investigations is the verification of mechanisms of the local breakdown of the protecting film. At least two mechanisms are possible for this localization: mechanical breakdown by slip steps and electrochemical breakdown (for e.g. by the effects of chloride ions). Corrosion and passivation of different high purity alloys have been studied in different solutions (neutral, alkaline with specific anions and cations) using electrochemical techniques. The diecasted alloys were tested as produced and machined. The results clarified that depending on alloy/material and surface condition/corrosion environment different mechanisms for electrochemical breakdown of the protecting films are possible. Hence fatigue life under environmental loading is influenced by surface and testing conditions.     

Java multimedia telecollaboration

Using Java-based tools in multimedia collaborative environments accessed over the Internet can increase an application's client base. Most operating systems support Java, and its "compile once-run everywhere" architecture is easy to maintain and update. The Java-based tools presented here let users share Internet resources, including resources originally designed for single use.     

The anisotropic effect of a weak magnetic field on the photoconductivity of C<Subscript>60</Subscript> single crystals

The effect of crystal orientation on the photogeneration of free charge carriers was studied for C₆₀ single crystals in a weak magnetic field. The photoconductivity sharply depends on the orientation of magnetic field with respect to the crystallographic directions, showing a 5–8% increase for seven axes of the C₆₀ crystal.     

Thermodynamic stability of GaInSb,InAsSb, and GaInP epitaxial films

The miscibility gaps and the critical temperatures of spinodal decomposition of ternary semiconducting Ga-In-Sb, Ga-In-P, and In-As-Sb systems are calculated by taking into account the deformation energy and the effect of plastic relaxation caused by the misfit dislocations. It is shown that taking into consideration elastic energy narrows the ranges of spinodal decomposition and lowers its critical temperature. The introduction of the phenomenological parameter into Matthews-Blakeslee formula makes it possible to reach a satisfactory agreement between theoretically calculated values of critical thickness of epitaxial films and the experimental data.     

Effects of surface charge, micro-bubble size and particle size on removal efficiency of electro-flotation.

Flotation is a water treatment alternative to sedimentation, and uses small bubbles to remove low-density particles from potable water and wastewater. The effect of zeta potential, bubble size and particle size on removal efficiency of the electro-flotation process was investigated because previous model-simulations indicated that these attributes are critical for high collision efficiency between micro-bubbles and particles. Solutions containing Al3+ as the metal ion were subjected to various conditions. The zeta potentials of bubbles and particles were similar under identical conditions, and their charges were influenced by metal ion concentration and pH. Maximum removal efficiency was 98 and 12% in the presence and absence of flocculation, respectively. Removal efficiency was higher when particle size was similar to bubble size. These results agree with modelling simulations and indicate that collision efficiency is greater when the zeta potential of one is negative and that of the other is positive and when their sizes are similar.     

Cover Picture: Arresting,Fixing, and Separating Dimers Composed of Uniform Silica Colloidal Spheres (Adv. Funct. Mater. 12/2006)

In colloidal suspensions of silica, particles undergo constant collisions. By controlling various parameters, the repulsive barrier can be reduced, thereby substantially increasing the number of collision‐induced dimerization events. Xia and co‐workers report on p. 1627 that the dimers could be arrested and then permanently fixed by introducing a small amount of fresh tetraethylorthosilicate into the colloidal suspension, with monodisperse dimer yields of up to 50 %. This yield could be increased to 80 % by centrifugation in a density gradient medium. When fresh tetraethylorthosilicate is introduced into a colloidal suspension of silica spheres, it hydrolyzes and condenses in situ to arrest and fix the dimers resulting from constant collisions between the spheres. By optimizing the experimental parameters (including the length of aging time) and the diameter of the silica spheres, as well as the concentrations of counterions, water, and ammonia, it is possible to routinely produce monodisperse dimers with a yield as high as 50 %. When combined with centrifugation using a density gradient medium, the yield of such dimers could be further increased to 80 %. It is believed that this method will provide a simple and versatile approach to the high‐volume production of dimers from spherical colloids composed of different materials. These dimers may find widespread use in a range of applications such as fabrication of photonic crystals and fundamental studies related to colloidal science.     

A Digital Deformation Vacuum Gauge with an LC-Generator

The design of a sylphon bellows sensor and the basic circuits of an LC-generator and of a microprocessor unit are presented. An analytical pressure–frequency conversion function and a special method of adjusting the sensor ensure an error of less than 0.05%. The dynamic range is up to 10⁵. The instruments developed cover the ranges 10³, 10⁴, and 10⁵ Pa.