Wave attenuation model for dephasing and measurement of conditional times

Inelastic scattering induces dephasing in mesoscopic systems. An analysis of previous models to simulate inelastic scattering in such systems is presented and a relatively new model based on wave attenuation is introduced. The problem of Aharonov-Bohm (AB) oscillations in conductance of a mesoscopic ring is studied. We show that the conductance is symmetric under flux reversal and the visibility of AB oscillations decays to zero as a function of the incoherence parameter, signaling dephasing. Further the wave attenuation model is applied to a fundamental problem in quantum mechanics, that of the conditional (reflection/transmission) times spent in a given region of space by a quantum particle before scattering off from that region.     

Qualitative properties of modified equations

Suppose that a consistent one-step numerical method of orderr is applied to a smooth system of ordinary differential equations.Given any integer m 1, the method may be shown to be of orderr + m as an approximation to a certain modified equation. Ifthe method and the system have a particular qualitative propertythen it is important to determine whether the modified equationsinherit this property. In this article, a technique is introducedfor proving that the modified equations inherit qualitativeproperties from the method and the underlying system. The techniqueuses a straightforward contradiction argument applicable toarbitrary one-step methods and does not rely on the detailedstructure of associated power series expansions. Hence the conclusionsapply, but are not restricted, to the case of Runge-Kutte methods.The new approach unifies and extends results of this type thathave been derived by other means: results are presented forintegral preservation, reversibility, inheritance of fixed points.Hamiltonian problems and volume preservation. The techniquealso applies when the system has an integral that the methodpreserves not exactly, but to order greater than r. Finally,a negative result is obtained by considering a gradient systemand gradient numerical method possessing a global property thatis not shared by the associated modified equations.     

How Fast can a Subharmonic Function Decay Along a Ray?

Much is known about the connection between the growth and decayof subharmonic functions. The results indicate that there isa general principle: asubharmonic function cannot decay ‘toofast’ relative to its growth.Three theorems are provedwhich, together with work previously published elsewhere, givea fairly complete account of how this principle works out fora subharmonic function having extremal decay along a ray. 1991Mathematics Subject Classification: 30D20, 31A05.     

Chemical analysis on the microgram scale. II

Summary The separation and identification of lead, mercurous mercury, silver and tungstate on the microgram scale are described, these ions being treated as Group II of a non-H₂S schematic analysis.

---

Zusammenfassung Trennung und Nachweis der Elemente Blei, Quecksilber(I), Silber und Wolfram werden für die Ausführung im Mikrogramm-Maßstab beschrieben. Diese Ionen werden als 2. Gruppe eines Analysenganges behandelt, der nicht dem Schwefelwasserstoffgang entspricht.

---

Résumé On décrit la séparation et l'identification du plomb, du mercure mercureux, de l'argent et du tungstène à l'échelle du microgramme, ces ions étant considérés comme formant le groupe II d'une analyse schématique sans H₂S.

     

Design, synthesis, and antimicrobial activity of fused triheterocyclic nitrogen systems involving tetrazolo[1,5-b][1,2,4]triazines [1]

Dehydrogenative cyclization of the 6-substituted 7-arylidenehydrazinotetrazolo[1,5-b][1,2,4]triazines derived from 6-methyl and 6-phenyl derivatives of 7-hydrazinotetrazolo[1,5-b][1,2,4]triazines and aromatic aldehydes gave the corresponding 6-substituted 9-aryl-[1,2,4]triazolo[4,3-d]tetrazolo-[1,5-b][1,2,4]triazines. The latter compounds were also obtained by an alternative route involving dehydrative cyclization of 6-methyl and 6-phenyl derivatives of 7-chlorotetrazolo[1,5-b][1,2,4]triazines with aromatic hydrazides through the isolable aroylhydrazino intermediates. Also, the triazolotetrazolotriazine rings were accomplished by one-pot cyclization of cyclic amidrazones with aromatic acid chlorides. The ditetrazolo[1,5-b:1′,5′-d][1,2,4]triazine systems were synthesized by cyclization of the former cyclic amidrazones with nitrous acid, or cyclic imidoyl chlorides with sodium azide. The bis-triazolotetrazolotriazine derivatives were synthesized by cyclization of two equivalents of each cyclic imidoyl chloride with acid dihydrazides through the isolable bis-hydrazide products. The antimicrobial activity of representative compounds was studied.