Computation of continuous wavelet transform at dyadic scales by subdivision scheme

A new algorithm to compute continuous wavelet transforms at dyadic scales is proposed here. Our approach has a similar implementation with the standard algorithme a trous and can coincide with it in the one dimensional lower order spline case. Our algorithm can have arbitrary order of approximation and is applicable to the multidimensional case. We present this algorithm in a general case with emphasis on splines and quasi-inter polations. Numerical examples are included to justify our theorerical discussion.     

Thermal analysis as a tool for investigations in metal oxide chemistry

Applications of thermoanalytical methods for the controlled preparation of metal oxides from various initial compounds (‘precursors’) as well as for investigations of physical properties and the chemical behaviour of oxidic phases as function of temperature and atmosphere are presented. Studies elucidating the course of such processes yield important contributions to the understanding of the reactivity of solids in general. Moreover, they are, e.g. in the field of heterogeneous catalysis, of practical relevance. It is shown, however, that the capability of mere thermal analysis suffers from limitations which have to be overcome by using additional, independent methods such as X-ray diffraction as well as light and electron microscopy.     

Verallgemeinerte Regelflächen

Ohne ZusammenfassungDie wesentlichen Teile dieser Arbeit sind während eines Gastaufenthaltes des erstgenannten Verfassers an der Technischen Universität München im Sommersemester 1975 entstanden     

Infinitesimale Deformationen von Diedersingularitäten

Denote by T¹ the vector space of infinitesimal deformations of a dihedral singularity of type D_{n, q}. Using Pinkham's method for quotient surface singularities we prove a formula for dim T¹.     

Polytypie bei Doppeloxiden: AgCoO2, AgFeO2, AgCrO2

Polytypes of AgFeO₂, AgCrO₂ and AgCoO₂ were found by indexing of high-resolution X-ray powder diagrams and, in the case of AgFeO₂ also by complementary single-crystal X-ray photographs. The abovementioned compounds occur at least in the polytype 6H (RAMSDELL-notation). The hexagonal unit cell dimensions are as follows:      

Infrared reflectivity of MTPA (TCNQ)2 single crystals

Polarized infrared reflectivity of single crystal MTPA (TCNQ)₂ was measured in the 40–4000 cm^?1 region and evaluated to obtain the dielectric function and conductivity. For E ⊥ b polarization, a very strong coupling between TCNQ intramolecular vibrations and electronic motion is observed. The bare electronic absorption is modelled by a sum of two classical oscillators.     

Über die Anwendung algebraischer Methoden in der Deformationstheorie komplexer Räume

Es handelt sich um einen Beweis der folgenden Sätze, die zuerst von Grauert angegeben wurden (Publ. Math. I.H.E.S. No. 5, 1960; vgl. dies Zbl.100, 80 (1963)):Es seif:X Y eine eigentliche holomorphe Abbildung komplexer Räume, sei einef-platte kohärente analytische Garbe überX; es bezeichneX _y die Faser vonf über einem Punkty Y und die analytische Einschränkung von aufX _y . Dann gilt: (I) Die Funktionend _q (y)=dimH _q (X _y , sind halbstetig nach oben. (II) Ist für einq die Funktiond _q (y) konstant undY reduziert, so ist dieq-te direkte Bildgarbe von unterf lokal frei überY. (III) Die Euler-Poincaré-Charakteristikx(y)=(–1) ^q dimH _q (X _y ,) ist lokal konstant überY. — Der Beweis benutzt systematisch den Begriff des Steinschen Kompaktums (= kompakte semianalytische Menge mit Steinscher Umgebungsbasis). Mit Hilfe der von Frisch bewiesenen Tatsache, daß die Algebra der Schnitte in der Strukturgarbe eines komplexen Raumes über einem Steinschen Kompaktum noethersch ist (Invent. Math.4, 118–138 (1967); vgl. dies Zbl.167, 68 (1969)), gelingt es, die Grothendieckschen Methoden im algebraischen Fall (EGA III) auf die analytische Situation zu übertragen.