Asymptotic behaviour of oscillatory solutions of n-th order differential equations with quasiderivatives

Sufficient conditions are given under which the sequence of the absolute values of all local extremes of y[i], i {0,1,..., n – 2} of solutions of a differential equation with quasiderivatives y ^[n] = f(t, y ^[0],..., y ^[n–1]) is increasing and tends to . The existence of proper, oscillatory and unbounded solutions is proved.     

Development of special optical fibers for evanescent-wave chemical sensing

The paper summarizes results achieved in the Institute of Radio Engineering and Electronics in the field of investigation and fabrication of novel fiber-optic structures for evanescent-wave chemical sensing. Several approaches for increasing the evanescent-wave sensitivity of multimode silica optical fibers to gaseous and liquid chemicals are shown. These approaches make use of the decrease of the core diameter in sectorial and capillary sectorial fibers, modification of trajectories of optical rays in the cores of inverted-graded-index fibers, tailoring of the refractive index of porous layers applied on silica cores, an output mode filter preventing the detection of rays propagating at low axial angles or fibers bent in single or multiple turns. Presented at the 1st Czech-Chinese Workshop “Advanced Materials for Optoelectronics”, Prague, Czech Republic, June 13–17, 1998. This work was supported by the Grant Agency of the Czech Republic (projects No. 102/96/0939 and No. 102/98/1358) and by joint project No. 4104 of AS CR and CNRS, France.     

Regularity of ultrafilters

If there arek ⁺⁺ eventually functions fromk ⁺ intok or if there arek ⁺⁺ eventually different functions fromk ⁺ then uniform ultrafilters onk ⁺ are (k, k ⁺)-regular. The research of the first author was supported in part by NSF grant. The second author is a Miller’s Fellow at the University of California in Berkeley.     

Cocoa Shell as a Step Forward to Functional Chocolates—Bioactive Components in Chocolates with Different Composition

Chocolate is considered as both caloric and functional food. Its nutritional properties may be improved by addition of fiber; however, this may reduce polyphenols content. The aim of this research was to determine the influence of cocoa shell addition (as a source of fiber) and its combination with different ingredients (cocoa butter equivalents (CBE), emulsifiers, dairy ingredients) on polyphenols of dark and milk chocolates. Total polyphenol (TPC) and total flavonoid (TFC) contents were determined spectrophotometrically, identification and quantification of individual compounds by high pressure liquid chromatography and antioxidant capacity by ferric reducing antioxidant power (FRAP) assay. Results showed that even though addition of cocoa shell to chocolate results in reduced contents of TPC, TFC, and individual compounds, it is not significant compared to ones reported by other authors for commercial chocolates. Other ingredients influence determined values for all investigated parameters; however, additional research is needed to reveal exact mechanisms and implications.     

Disappearing Polymorphs in Metal–Organic Framework Chemistry: Unexpected Stabilization of a Layered Polymorph over an Interpenetrated Three-Dimensional Structure in Mercury Imidazolate

The “disappearing polymorph” phenomenon is well established in organic solids, and has had a profound effect in pharmaceutical materials science. The first example of this effect in metal-containing systems in general, and in coordination-network solids in particular, is here reported. Specifically, attempts to mechanochemically synthesize a known interpenetrated diamondoid (dia) mercury(II) imidazolate metal–organic framework (MOF) yielded a novel, more stable polymorph based on square-grid (sql) layers. Simultaneously, the dia-form was found to be highly elusive, observed only as a short-lived intermediate in monitoring solvent-free synthesis and not at all from solution. The destabilization of a dense dia-framework relative to a lower dimensionality one is in contrast to the behavior of other imidazolate MOFs, with periodic density functional theory (DFT) calculations showing that it arises from weak interactions, including structure-stabilizing agostic C−H⋅⋅⋅Hg contacts. While providing a new link between MOFs and crystal engineering of organic solids, these findings highlight a possible role for agostic interactions in directing topology and stability of MOF polymorphs.     

A theory of non-radiative transfer of excitation energy in solids

A theory of non-radiative transfer of excitation energy in solids is elaborated for the case of strong interaction of an atom of the sensitizer and an atom of the activator with the oscillations of the whole crystal lattice.     

Ein Detektor Langsamer Neutronen

Zusammenfassung Der Scintilationsdetektor für Thermo-und Resonanzneutronen, der in dieser Arbeit beschrieben wird, wurde aus einem geschmolzenen Gemisch von ZnS(Ag) und ₂₃ hergestellt. Bei optimalem Verhältnis beider Komponenten und optimaler Dicke des Detektors kann für Thermoneutronen eine verhältnismässig grosse Wirksamkeit erzielt werden (bis 25%). Der Detektor kann auch bei starkem Hintergrund von -Strahlung benützt werden, da die Wirksamkeit der -Strahlregistrierung durch passende Einstellung des Diskriminators unter 10^–7% herabgesetzt werden kann, bei einer Wirksamkeit für Thermoneutronen von ungefähr 6%.     

Die Elektrolumineszenz von Einkristallen von ZnO

Zusammenfassung Der Wert der Spannung des Feldes, die quadratische Abhängigkeit des Leuchtens vom Strom, die äu\erst gute übereinstimmung der Abhängigkeiten der Ionisationszahl von der Spannung, welche experimentell wie auch von der Theorie der Multiplikation der Elektronen ausgehend gewonnen wurden, entsprechen somit dem Mechanismus der Sto\ionisation in ZnO. Diese Schlu\folgerung bleibt, wie zusätzliche Nachprüfungen ergeben, auch bei der Aufhebung einiger Vereinfachungen, die bei der Berechnung vorgenommen wurden (z. B. bei der Berücksichtigung schwächerer Abhängigkeiten(t), k(E), der Breite der Sperrzone von der Temperatur usw.) unverändert.Da im Falle der Isolation der Kristalle von den Elektroden die Herkunft der Oberflächensperren dieselbe bleibt, können die Ergebnisse dieser Arbeit auch für die Deutung der Eigenschaften des Destriau-Effektes in ZnO verwertet werden. Sie können anscheinend auch auf das Leuchten homogener Kristalle von ZnS mit ungefähr gleicher elektrischer Leitfähigkeit und der Sperre an der Kathode bezogen werden.

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We observed the same effect on ZnO single crystals as Destriau and Losev. We studied light emission and the electric properties of single crystals with a rectifying contact, which was switched on in the non-transmitting direction. It was found that the dependence of the number of ionizations on each electron, which passes through the contact, on the voltage, which was determined by comparing the experimental results with the diffusion theory of rectification, agrees with the dependence calculated by means of the multiplication theory of electrons in semi-conductors. The conclusion was reached that inelastic collisions play a greater role in ZnO as the excitation mechanism. The calculated voltage dependence of electroluminescence is very close to the measured dependence.

     

Toeplitz Operators and Group Representations

Toeplitz operators on the Bergman space of the unit disc can be written as integrals of the symbol against an invariant operator field of rank-one projections. We consider a generalization of the Toeplitz calculus obtained upon taking more general invariant operator fields, and also allowing more general domains than the disc; such calculi were recently introduced and studied by Arazy and Upmeier, but also turn up as localization operators in time-frequency analysis (witnessed by recent articles by Wong and others) and in representation theory and mathematical physics. In particular, we establish basic properties like boundedness or Schatten class membership of the resulting operators. A further generalization to the setting when there is no group action present is also discussed, and the various settings in which similar operator calculi appear are briefly surveyed.     

Littlewood-Paley inequalities in uniformly convex and uniformly smooth Banach spaces

It is proved that the inequality δX(ε)?cεp, p?2, where δX is the modulus of convexity of X, is sufficient and necessary for the inequality