Global saddle-point duality for quasi-concave programs

General and quasi-concave non-differentiable cases of the maximization of the minimun between two functions are considered. With the aid of duality theory for mathematical programming involving conjugate-like operators and by defining a bifunction we construct a new Lagrangian and generate a class of perturbations. New saddle-point theorems are presented, and equivalence is proved between the existence of a saddle-point and the existence of a certain cone-supporting property of the perturbation function. These results suggest possible improvements in multiplier methods.This work was partially supported by a grant from Control Data.     

Meson distributions in photoproduction

Extension of the nova model is applied to γ + p → π + anything. The concept of a photon is motivated from vector dominance, and the parameters describing the production of photon novas are estimated from hadron results. The model is essentially without arbitrary parameters. We compare with inclusive and exclusive data at 9.3 GeV/c, where we find excellent agreement. Predictions for 20 GeV/c are also presented.     

Neutron scattering by anharmonic crystals and the effect of sublattice displacements

A theory has been given for the scattering of neutrons by anharmonic crystals, for which terms of the typeV ⁽³⁾ (k _1j1; —k _1j1;o _j) which contribute to the sublattice displacements are not neglected. Using the standard perturbation theory in the interaction picture or Green’s function method, an expression has been derived for the differential scattering cross-section which brings in the shift and the width of the phonons in one-phonon energy exchange processes. It is shown that the sublattice displacements will modify the phase factor arising from the scattering by any atom in the unit cell, and the Debye-Waller factor also gets altered both by the sublattice displacements as well as by higher order terms arising from anharmonicity. It is shown that the differential scattering cross-section contains a term linearly depending on the third order anharmonicity coefficientV ⁽³⁾ (k _1j1;k _2j2;k _3j3) and neutron scattering by crystals should provide a useful method for evaluating the third order anharmonicity coefficients.     

Grüneisen parameter and thermal expansion of V3Si and V3Ge

The Grüneisen parameter and lattice thermal expansion of the A-15 compounds V₃Si and V₃Ge at room temperature are evaluated on the basis of the method due to Brugger and Fritz [1] from the third order elastic constants reported earlier [2]. The calculated values are compared with available experimental values and are found to fit satisfactorily.     

BIOLOGISCHE WIRKUNGEN PHOTOCHEMISCHER WASSERSTOFFPEROXYDBILDUNG:

Abstract— As previously demonstrated, there is a considerable increase in the photodynamic activity of anthraquinone-sulphonic acid on the addition of ethylene glycol, glycerol and sugars in concentrations of the order of 0.4 M . This system exhibits cytostatic activity. With H₂O₂ at higher concentrations there is also formation of aldehydes in approximately equivalent yields as follows:
R.CH₂OH+Q → QH₂+R.CHO
QH₂+O₂→ Q+H₂O₂
In accordance with the recent results of Warburg this accounts for the fundamental importance of glyceraldehyde in cancer research.
Our results on the irradiation of Proteus vulgaris SG2 in buffered medium with the addition of glycerin to anthraquinone-sulphonic acid show the existence of a similar cytostatic effect. One hour's irradiation with visible light reduces the cell count by about 50 per cent.     

Azulenes and related substances—XII A new azulene synthesis—guaiazulene and Se-Guaiazulene

The new method of azulene synthesis, described in the preceding communication, has been extended to the synthesis of guaiazulene and Se-guaiazulene.     

Influence of substitution pattern on the benzenoid transitions: Quantitative evaluation of the electronic and vibrational components from new experimental polarization data

The influence of substitution on the benzenoid ¹L_b, ¹L_a and ¹B transitions is studied by the technique of linear dichroism in stretched polyethylene films.The total intensity of the ¹L_b system is resolved into induced and vibrational components and the influence of various substitution patterns on the magnitude and polarization of both components is analyzed quantitatively. As expected from theoretical considerations, the vibrational components like the induced intensity are found to be strongly affected by the substituent strength and the symmetry of substitution pattern. The previously accepted assumption, according to which the vibrational intensity is regarded as a constant, appears to be completely unrealistic when dealing with cases of strong substituents. A satisfactory quantitative treatment of both weak and strong substituents using the same simple theoretical approach seems possible only if the systematic variations observed in the vibrational intensity are not neglected.A qualitative analysis is given for the ¹L_a, and ¹B systems. The results are compared with available theoretical predictions and previous experimental data.Practical implications of the present new experimental information to the study of aromatic optical activity are discussed.     

Experimental charge density of a potential DHO synthetase inhibitor: dimethyl-trans-2-oxohexahydro-pyrimidine-4,6-dicarboxylate

The experimental charge density distribution of dimethyl-trans-2-oxohexahydro-pyrimidine-4,6-dicarboxylate 1 has been determined using single-crystal X-ray diffraction data measured at 100 K, in terms of the rigid-pseudoatom formalism. Multipole refinement converged at R(F) = 0.034 for 7283 reflections with I > 3 sigma (I) and sin theta/lambda < or = 1.13 A(-1). Covalent and hydrogen bonding interactions are analyzed using a topological analysis of the Laplacian of the charge density. The experimentally derived electrostatic potential mapped onto the reactive surface of the molecule reveals the potential binding sites of 1.     

Amination of ethers using chloramine-T hydrate and a copper(I) catalyst

Amination of C-H bonds activated by ether oxygen atoms is facile with chloramine-T as nitrene source and copper(I) chloride in acetonitrile as catalyst. For cyclic ethers the hemiaminal products are generally stable and can be isolated pure. For acyclic ethers, the hemiaminal products, as expected, fragment with elimination of alcohol to yield imines. When activation of benzylic positions is remote through a conjugated system, stable benzylamine derivatives are isolated. Mechanistic studies are consistent with concerted insertion of an electrophilic nitrenoid into the C-H bond in the rate-determining step, though in an asynchronous manner with a more activated substrate.