Balancedness conditions for exact games

We provide two new characterizations of exact games. First, a game is exact if and only if it is exactly balanced; and second, a game is exact if and only if it is totally balanced and overbalanced. The condition of exact balancedness is identical to the one of balancedness, except that one of the balancing weights may be negative, while for overbalancedness one of the balancing weights is required to be non-positive and no weight is put on the grand coalition. Exact balancedness and overbalancedness are both easy to formulate conditions with a natural game-theoretic interpretation and are shown to be useful in applications. Using exact balancedness we show that exact games are convex for the grand coalition and we provide an alternative proof that the classes of convex and totally exact games coincide. We provide an example of a game that is totally balanced and convex for the grand coalition, but not exact. Finally we relate classes of balanced, totally balanced, convex for the grand coalition, exact, totally exact, and convex games to one another.     

Coherent thermal radiation

The radiation emitted by a heated body is generally quoted as a typical example of incoherent radiation, in distinction to laser radiation. One is nearly isotropic, the other highly directional; one is spectrally broad, the other quasi-monochromatic. It may come as a surprise that the thermal radiation of a large number of substances is coherent, both in space and time, when it is observed at a distance from the body that is shorter than the wavelength. This behaviour can be understood within an electromagnetic approach to thermal emission. Several recent experiments have confirmed these unexpected properties.     

Etude des fragmentations en spectrographie de masse de dithiannes-1,3 substitués en 2 par des groupements insaturés

The mass spectra of the title compounds always show an intense molecular ion. Some fissions involve loss of the ethylenic group, while others are related to cleavage of the dithiane ring, eventually followed by recyclizations involving the ethylenic chain stabilized by the resonance possibilities. If a phenyl group is present in the ethylenic chain, the spectra are modified by the formation of the very stable benzothiopyrylium ion.     

Apurinic DNA reactivity: Modelisation of apurinic DNA breakage with phenylhydrazine and formation of a pyrazole adduct

We have elucidated the exact mechanism of apurinic oligodeoxynucleotide d(Tp[AP]pT) cleavage by phenylhydrazine and shown that the final isolated product is in fact a 3-substituted derivative of 1-phenyl-pyrazole.     

Etude en RMN du carbone 13 de dicoumarols substitués

The ¹³C n.m.r. spectrum of the bridge substituted dicoumarols are interpreted in order to obtain structural information for quantitative structure-activity relationships. The results are in agreement with those obtained by ¹H n.m.r. These dicoumarols exhibit double restricted rotation around both bridge bonds.     

Rearrangement thermique des adduits du tetracyanoethylene de 2H-pyrannes

The addition of tetracyanotehylene to 2H-pyrans 1 results in a mixture of two isomeric adducts 6. The thermal decomposition of the compounds 6 gives rise to both a small percentage of the retro Diels-Alder, and a new mode of evolution leading to a mixture of furans (E+Z) 7. A detailed interpretation of the ¹³C spectra of the compounds 7 was established by comparison with the ¹³C spectra of 2,5-diphenylfuran and trans-stilbene. The structure 7 is confirmed by chemical degradation.     

Carbon-13 spin–lattice relaxation in some polyfluoroaromatic compounds

Carbon-13 chemical shifts, spin-lattice relaxation times and nuclear Overhauser enhancement factors are reported for five polyfluoroaromatic compounds at 28°C. In all cases the relaxation of the fluorine bearing carbon is predominantly dipolar. Effective correlation times are smaller than those of the analogous benzene derivatives by a factor of 3–4, in qualitative agreement with predictions from the Stokes–Einstein diffusion theory. The T₁ values for the para-carbon of monosubstituted fluorobenzenes is clearly shorter than the T₁ values for the ortho- and meta-carbons. This phenomenon was traced to anisotropic tumbling, and D∥ and D⊥ diffusion coefficients were computed using Woessner's equations for molecules assumed to behave like symmetric rotors about their C₂ in-plane principal symmetry axis. Equal tumbling ratios, D∥/D⊥, were found in this way for toluene and perfluorotoluene.     

Synthesis,Electrochemical, and Optical Properties of New Fluorescent,Substituted Thieno[3,2-b][1]Benzothiophenes

The synthesis, electrochemical and optical properties of three fluorescent substituted thieno[3,2-b][1]benzothiophenes (TBT) derivatives, including 3-methoxythieno[3,2-b][1]benzothiophene (3-MeO-TBT), 2,3-dimethylthieno[3,2-b][1]benzothiophene (2,3-diMe-TBT), and 6-methoxythieno[3,2-b][1]benzothiophene-2-carboxylate (6-MeO-TBT-2-COOMe), were investigated. The oxidation potential values varied between 1.40 and 1.20 V/SCE according to the electronic substituent effect, and electropolymerization attempts, performed in 0.1 M LiClO₄ acetonitrile solution, led to the formation of very thin films of poly(3-MeO-TBT) and poly(2,3-di-Me-TBT). Electronic absorption spectra, fluorescence excitation and emission spectra, fluorescence quantum yields (Φ_F) , lifetimes (τ_F), and other photophysical parameters of the three new TBT derivatives were measured in DMSO solutions at room temperature. For the methyl-and methoxy-substituted TBT derivatives, the fluorescence emission peak were slightly red shifted relative to that of unsubstituted TBT (Δλ_em = 1–12 nm) whereas, in the case of 6-MeO-TBT-2-COOMe, a rather strong red-shift (Δλ_em = 73 nm) was attributed to the existence of a “push-pull” electronic interaction of the MeO and COOMe groups. All Φ_F values were rather high, varying between 0.11 and 0.35, according to the substituent effect. Fluorescence decays were mono-exponential and τ_F values were very short, ranging between 0.11 and 0.30 ns for the substituted TBT derivatives until study.