E. H. Dirksens Beiträge zu den Grundlagen der Analysis

Enno Heeren Dirksen (1788–1850) was one of several mathematicians originating from Eastern Frisia at the end of the eighteenth century to acquire prominence in neohumanist reformed Prussia. While striving—like so many of his contemporaries—for more rigour in the foundations of calculus, his work is significant due to his unusual emphasis on the semiotic aspects of the basic concepts. As a clear-sighted propagator of Cauchy's conceptual innovations in Germany, his achievements in improving sign expressions of such concepts enabled him to clarify hitherto not differentiated multiple limit processes—although less successfully in constructive concept formation itself. The contribution is based on the analysis of Dirksen's published texts and on the numerous texts which remained drafts for his projected voluminousOrganon der gesamten Analysis.

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Menso Folkerts zum 60. Geburtstag gewidmet     

DISPERSION COMPENSATION CFBG IN100km 10Gbit／s RECIRCULATING SYSTEMS

A 10Gbit/s recirculating system is configured with Chirped Fiber Bragg Grating (CFBG) for the dispersion compensation. For the first time, the transmission distance in the loop reaches 1000km with bit error rate of 10-9. The effect of the group delay ripple of the fiber grating is also investigated in the recirculating systems, and it is shown that the transmission distance is limited to 4 cycles (4×167.1km ) in the loop with the power penalty fluctuation below 1.0dB. Thus the group delay ripple should be reduced to allow for the wavelength drift of±5GHz. At the end of this letter, the principles are given for designing long haul recirculating systems with dispersion compensation CFBG.     

Popular biorthogonal wavelet filters via a lifting scheme and its application in image compression

A technique using a lifting scheme is presented for constructing compactly supported wavelets whose coefficients are composed of free variables locating in an interval. An efficient approach-based wavelet for image compression is developed by selecting the coefficients of the 9-7 wavelet filter and associated lifting scheme. Furthermore, the rationalised coefficients wavelet filter that can be implemented with simple integer arithmetic is achieved and its characteristic is close to the well known original irrational coefficients 9-7 wavelet filters developed by A. Cohen et al. (Commun. Pure Appl. Maths., vol.45, no.1, p.485-560, 1992). To reduce the computational cost of image coding applications further, an acceleration technique is proposed for the lifting steps. Software and hardware simulations show that the new method has very low complexity, and simultaneously preserves the high quality of the compressed image.     

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.     

Synthesis and characterization of biocompatible hydroxyapatite coated ferrite

Ferrite particles coated with biocompatible phases can be used for hyperthermia treatment of cancer. We have synthesized substituted calcium hexaferrite, which is not stable on its own but is stabilized with small substitution of La. Hexaferrite of chemical composition (CaO)_0.75(La₂0₃)_0.20(Fe₂O₃)₆ was prepared using citrate gel method. Hydroxyapatite was prepared by precipitating it from aqueous solution of Ca(NO₃)₂ and (NH₄)₂HPO₄ maintaining pH above 11. Four different methods were used for coating of hydroxyapatite on ferrite particles. SEM with EDX and X-ray diffraction analysis shows clear evidence of coating of hydroxyapatite on ferrite particles. These coated ferrite particles exhibited coercive field up to 2 kOe, which could be made useful for hysteresis heating in hyperthermia. Studies by culturing BHK-21 cells and WBC over the samples show evidence of biocompatibility. SEM micrographs and cell counts give clear indication of cell growth on the surface of the sample. Finally coated ferrite particle was implanted in Kasaulli mouse to test its biocompatibility. The magnetic properties and biocompatibility studies show that these hydroxyapatite coated ferrites could be useful for hyperthermia.     

Electrochemical synthesis and characterization of chloride doped polyaniline

Chloride doped polyaniline conducting polymer films have been prepared in a protic acid medium (HCl) by potentiodynamic method in an electrochemical cell and studied by cyclic voltammetry and FTIR techniques. The FTIR spectra confirmed Cl^- ion doping in the polymers. The polymerization rate was found to increase with increasing concentration of aniline monomer. But the films obtained at high monomer concentration were rough having a nonuniform flaky polyaniline distribution. Results showed that the polymerization rate did not increase beyond a critical HCl concentration. Cyclic voltammetry suggested that, the oxidation-reduction current increased with an increase in scan rate and that the undoped polyaniline films were not hygroscopic whereas chloride doped polyaniline films were found to be highly hygroscopic.     

An MPEG‐4 Compliant Interactive Multimedia Streaming Platform Using Overlay Networks

This paper presents a multimedia streaming platform for efficiently transmitting MPEG‐4 content over IP networks. The platform includes an MPEG‐4 compliant streaming server and client, supporting object‐based representation of multimedia scenes, interactivity, and advanced encoding profiles defined by the ISO standard. For scalability purposes, we employ an application‐layer multicast scheme for media transmission using overlay networks. The overlay network, governed by the central entity of the network distribution manager, is dynamically deployed according to a set of pre‐defined criteria. The overlay network supports both broadcast delivery and video‐on‐demand content. The multimedia streaming platform is standards‐compliant and utilizes widespread multimedia protocols such as MPEG‐4, real‐time transport protocol, real‐time transport control protocol, and real‐time streaming protocol. The design of the overlay network was architected with the goal of transparency to both the streaming server and the client. As a result, many commercial implementations that use industry‐standard protocols can be plugged into the architecture relatively painlessly and can enjoy the benefits of the platform.     

On the Feasibility of Growing Pb[(Zn1/3Nb2/3)0.91Ti0.09]O3 Single Crystals

Pb[(Zn_1/3Nb_2/3)_0.91Ti_0.09]O₃ (PZNT91/9) single crystals were grown by two methods: from solution using PbO as a self‐fluxing agent (SC method) and directly from the melt without fluxing (MC method). In both growth methods, an allomeric Pb[(Mg_1/3‐Nb_2/3)_0.69Ti_0.31]O₃ (PMNT69/31) single crystal was used as a seed. X‐ray diffraction patterns of ground crystals showed that phase‐pure perovskite PZNT91/9 single crystals were successfully fabricated by the above two methods. The composition of the crystals obtained by both the SC and MC methods was analyzed using X‐ray fluorescence, which confirmed that the crystal composition is close to the nominal value, although volatilization of PbO and segregation during crystal growth are inevitable. The MC PZNT91/9 crystals exhibit excellent piezoelectric properties, with the piezoelectric constant, d₃₃, in the range of 1800–2200 pC N^–1. This value is comparable to that of the SC crystals. However, the MC crystals show an abnormal dielectric behavior. In contrast with the SC crystals, in the MC crystals a much broader dielectric peak appears in the dielectric response curves, accompanied by a much lower peak temperature of around 105 °C. Furthermore, frequency dispersion is apparent over a much wider temperature range (even more apparent than in pure relaxors), where a large, i.e., about 70 °C, full width at half maximum (FWHM) for the dielectric peaks is observed in the dielectric response. It is speculated that such an unusual phenomenon correlates with defects, microinhomogeneities, and polar regions in the as‐grown MC crystals. The origins of this abnormality have not been interpreted in detail until now. However, optical observation of the domain structure confirms that both the SC and MC crystals possess complex structural states.