The single-mode rate equations for semiconductor lasers with thermal effects

A mathematical model describing the coupling of electrical,optical and thermal effects in semiconductor lasers is introduced.Numerical and asymptotic solutions are derived, including expressionsfor key physical quantities such as the initial time delay,the frequency of spike oscillation and the temperature rise,together with its influence on the photon density, the electronconcentration and the threshold current. The consequences ofthermal effects in reducing efficiency are thus quantified.     

Introducing calculus: an accumulation of teaching ideas?

The accumulation of ideas concerning the teaching of elementary calculus includes recommendations which are still not in widespread use. Research into students’ understanding of calculus suggests that there are many learning difficulties which current teaching methods are not helping students to overcome. The introduction of calculators and microcomputers to school mathematics classes provides us with the illustrative and computational power to practise methods based on practical investigation and intuition which should help to meet the needs of students beginning calculus and lead to greater understanding.     

A line parameter list for the ν2 and ν4 bands of 12CH4 and 13CH4, extended to J′ = 25 and its application to planetary atmospheres

Line parameters (transition frequencies, line strengths, line widths, ground state energies and quantum identifications) for the ν₂ and ν₄ bands of ¹²CH₄ and ¹³CH₄ have been calculated for J'?25 using the simultaneous coupled fitting procedure of Gray and Robiette. Molecular constants for the ν₂ band of ¹³CH₄ were estimated from isotopic shifts from ¹²CH₄ values. Agreement with laboratory spectra, where available, is always well within 1 cm^-1 over the entire spectral range covered by the list. The most serious problem in comparison with laboratory data is the omission of lines belonging to “hot” bands in this spectral region. This list is valuable in remote sensing problems for sorting out lines of trace species from weak methane lines and for determining the atmospheric opacity in relatively transparent spectral regions. Applications of the parameter list are demonstrated for remote sounding of the Jovian atmosphere. The list is available on magnetic tape from the authors.     

SYNTHESIS AND 31P NMR STUDY OF DIHYDRONAPHTHALENO- AND NAPHTHALENO-DERIVATIVES OF PHOSPHOLENE OXIDES

Abstract

Naphthalenophospholenes (dihydrobenzo[e] and [g]-phosphindoles) represent a new heterocyclic type that forms in 65-80% yield on dehydrogenation with Pd–C of the corresponding dihydronaphthaleno derivatives. The latter are readily accessible from hydrolysis of cycloadducts of certain vinyldihydronaphthalenes with P(III) chlorides. Six members of this family, as well as some derived phosphines and phosphonium salts, have been prepared. A phenanthrenophospholene oxide, also a new system, was synthesized similarly. ³¹P nmr chemical shifts were appreciably (5-10 ppm) upfield in aromatized phosphine oxides relative to the dihydro forms. It is proposed that this shift results more from a change in the steric environment about phosphorus, as the carbon beta- to it in the adjacent ring changes from tetrahedral to planar geometry, rather than from a change in the degree of interaction of a carbon p-orbital with phosphorus. The upfield shift was even more pronounced (13 ppm) for a phosphine. Most of the new compounds were characterized also by ¹³C nmr spectroscopy.