A characterization of strong measure zero sets

We show that a setXυR has strong measure zero iff for every closed measure zero setFυR,F+X has measure zero. Supported by KBN grant PB 2 1017 91 01.     

Non-linear electrical effect in graded-electron concentration silicon

A gradient of carrier concentration in semiconductors can create a double-frequency internal electric field which is parallel to this gradient and perpendicular to the applied a.c. field. This warm-carrier effect was measured in silicon specimens with a gradient of electron concentration, at 77 and 300 K, under applied fields from 1 to 10 V m^-1 and within the frequency range of 0.3–20 kHz. A comparison between experimental data and a theoretical model is discussed.     

Two stars

The authors investigate an operation * on the subsets of ${\mathcal{P}(\mathbb{R})}$ . It is connected with Borel’s strong measure zero sets as well as strongly meager. The results concern the behaviour of the family of countable sets when * is applied.     

The electronic absorption study of imide anion radicals in terms of time dependent density functional theory

The absorption spectra of the N-(2,5-di-tert-butylphenyl) phthalimide (1-), N-(2,5-di-tert-butylphenyl)-1,8-naphthalimide (2-) and N-(2,5-di-tert-butylphenyl)-perylene-3,4-dicarboximide (3-) anion radicals are studied in terms of time dependent density functional theory (TDDFT). For these anion radicals a large number electronic states (from 30 to 60) was found in the visible and near-IR regions (5000-45,000 cm(-1)). In these regions the TD/B3LYP treatment at the 6-1+G* level is shown to reproduce satisfactorily the empirical absorption spectra of all three anion radicals studied. The most apparent discrepancies between purely electronic theory and the experiment could be found in the excitation region corresponding to D0-->D1 transitions in the 2- and 3- molecules. For these species we argue that the structures seen in the lowest energy part of the absorptions of the 2- and 3- species are very likely due to Franck-Condon (FC) activity of the totally symmetric vibrations not studied in this Letter.     

Hypochromic and hyperchromic effects on the vibronic structure of molecular crystal spectra. The dimer model

It is shown on model calculations that crystal-field mixing of Frenkel excition states in molecular crystals lead not only to a redistribution of their relative intensities but also to changes in the vibrational structure of weak exciton bands.     

On sums of Darboux and nowhere constant continuous functions

We show that the property

(P)

for every Darboux function there exists a continuous nowhere constant function such that is Darboux

follows from the following two propositions:

(A)

for every subset of of cardinality there exists a uniformly continuous function such that ,

(B)

for an arbitrary function whose image contains a non-trivial interval there exists an of cardinality such that the restriction of to is uniformly continuous,

which hold in the iterated perfect set model.

     

On the cofinalities of Boolean algebras and the ideal of null sets

We will show that if the cofinality of the ideal of Lebesgue measure zero sets is equal to then there exists a Boolean algebra B of cardinality which is not a union of strictly increasing -sequence of its subalgebras. This generalizes a result of Just and Koszmider who showed that it is consistent with that such an algebra exists. Received November 21; accepted in final form April 12, 2001.     

State mixing and cd spectra of chiral molecules consisting of two identical chromophores

A study is reported of the effect of electronic state mixing on circular dichroism spectra of chiral molecules containing two identical chromophores. The CD spectrum of dimethyl-1,1'-bianthry1-2,2' dicarboxylate is intepreted in terms of such mixing between the ¹L_a and ¹B_b states of the anthracene moicty.     

Direct and indirect optical transitions in Zn3P2

Absorption measurements were made on single crystals of Zn₃P₂ at temperatures of 300, 80 and 5 K, and photo-voltage spectral responses-were measured at 300 K for Au- and In---Zn₃P₂ contacts. Interband absorption was interpreted as a process involving three mechanisms: (1) indirect transitions from the valence band at the Γ point, (2) either excitations from acceptor level to the conduction band at the Γ point, or second indirect transitions associated with the creation of excitons, and (3) band-to-band direct transitions at the Γ point. The effect of the lighting configuration on spectral PV plots is also discussed, and the origin of two peaks of PV responses is interpreted as being in accordance with optical data. The indirect energy gap has been estimated as 1.315eV at 300 K and 1.335 eV at 80 and 5 K, and the direct one as 1.505, 1.645 and 1.685 eV at 300, 80 and 5 K, respectively.