Problème inverse de la théorie du potentiel logarithmique pour les lemniscates

The paper is related to the question of uniqueness in the inverse logarithmic potential problem. This question is to find the conditions on which two domains D ₁ and D ₂ producing the same external potential must coincide. Assuming the general hypothesis of regularity and an additional condition of connectivity of (D₁D₂)_c, we prove a theorem of uniqueness in the case when one of the domains is a lemniscate. The main tool is one lemma for Cauchy's potential due to M. Sakai. We give a simple proof of its extension to Newtonian potential.

     

Macdonald polynomials from Sklyanin algebras: A conceptual basis for thep-adics-quantum group connection

We establish a previously conjectured connection betweenp-adics and quantum groups. We find in Sklyanin's two parameter elliptic quantum algebra and its generalizations, the conceptual basis for the Macdonald polynomials, which interpolate between the zonal spherical functions of related real andp-adic symmetric spaces. The elliptic quantum algebras underlie theZ _n -Baxter models. We show that in then limit, the Jost function for the scattering offirst level excitations in the 1+1 dimensional field theory model associated to theZ _n -Baxter model coincides with the Harish-Chandra-likec-function constructed from the Macdonald polynomials associated to the root systemA ₁. The partition function of theZ ₂-Baxter model itself is also expressed in terms of this Macdonald-Harish-Chandrac-function, albeit in a less simple way. We relate the two parametersq andt of the Macdonald polynomials to the anisotropy and modular parameters of the Baxter model. In particular thep-adic regimes in the Macdonald polynomials correspond to a discrete sequence of XXZ models. We also discuss the possibility of q-deforming Euler products.Work supported in part by the NSF: PHY-9000386     

Iodine photodissociation laser system Perun II

A construction and exploitation of a medium size iodine photodissociation laser system Perun II is reported. This laser produced pulses of infrared light (=1.315m) up to 50 J in energy and 300 ps in duration. The diameter of the beam is 82 mm. The beam divergence is about 4×10^–4 rad. The laser beam can be focused in a focal spot of a power density exceeding 10¹⁴ W/cm². The resuls of measurements of basic plasma parameters on an Al foil target are also presented. A recent improvement of the system includes a conversion to the second harmonic by a DKDP crystal.Presented at bilateral international seminar of High Temperature Laser Plasma and High Gain Iodine Lasers held on 4 July 1991 in the Inst. of Physics, Czechosl. Acad. Sci., in Prague (organized by Division of Optics of the Inst. of Physics, Czechosl. Acad. Sci., and Physical Section (Plasma Division) of the Union of Czech Mathematicians and Physicists.     

Electroproduction of strangeness

Formalism for the electroproduction of strange particles based on the one photon exchange approximation and the Feynman diagrams representation of hadron current is reviewed. Different photoproduction models are compared with available photo and electroproduction data. New experiments are proposed that may resolve existing uncertainties and inconsistencies. The formation of hypernuclei via kaon electroproduction is investigated theoretically and compared with other reactions involving purely hadronic processes.     

Distribution of the values of multiplicative functions modulo a prime number

One investigates the distributions of the values of the modified sum of divisors being a real character mod Q, relative to nonzero residue classes mod , 3 being a prime number. One considers in more detail the case of the function 2^–2r₂(n), where r₂(n) is the number of representations of n by a sum of two squares.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 93, pp. 218–224, 1980.     

MPT versus: A manifestly covariant presentation of motion reversal and particle-antiparticle exchange

We show that particle-antiparticle exchange and covariant motion reversal are two physically different aspects of the same mathematical transformation, either in the prequantal relativistic equation of motion of a charged point particle, in the general scheme of second quantization, or in the spinning wave equations of Dirac and of Petiau-Duffin-Kemmer. While, classically, charge reversal and rest mass reversal are equivalent operations, in the wave mechanical case mass reversal must be supplemented by exchange of the two adjoint equations, implying .Denoting by M the rest mass reversal, P the parity reversal, T the Racah time reversal, and Z the exchange, the connection with the usual scheme of charge conjugation, parity reversal, and Wigner motion reversal, is with, of course,     

Interaction of antiprotons with deuterons at low energies

Approximate methods of solving the few-body problem are applied to describe the interaction of anti-protons with the deuteron. In cases available the results are compared with calculations based on solving the Faddeev equations.Submitted to the symposium Mesons and Light Nuclei, Liblice, Czechoslovakia, June 1981.     

Kinetics of the hydrogen electrode reactions of platinum in the NaHSO4 + KHSO4 eutectic melt

The kinetics of the hydrogen electrode reactions on Pt in the NaHSO₄ + KHSO₄ melt at ca. 185°C is studied. Under potentiodynamic conditions both the anodic and cathodic processes can be interpreted with the hydrogen electrode reaction mechanism already known. At potentials more negative than 0.1 V (vs. Ag/Ag⁺ (0.06 M)) the mechanism of the cathodic reaction changes because of a sulphide species formed on the electrode which is produced by a reduction of the melt components.     

Mass spectra of pyrrolo [1,2-a]benzimidazole and imidazo[1,2-a]benzimidazole derivatives

The closeness of the electronic structures of the ions formed in the first act of disintegration of the ions is responsible for the monotypic character of the subsequent fragmentation of pyrrolo[1,2-a]benzimidazole and imidazo[1,2-a]benzimidazole derivatives. The mass-spectrometric disintegration of the investigated systems has something in common with the fragmentation of thiazolo[3,2-a]benzimidazole derivatives.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 8, 1124–1127, August, 1975.     

Genäherte Lösung der Hartree-Fock-Gleichungen wechselwirkender Moleküle im Bereich der geringen Überlappung

A perturbational approach has been developed in order to determine the interaction energy of two molecules in the region of small overlap in an attempt to obtain some information upon reactivity. The total wavefunction of the interacting molecules is set up as a single determinantal wavefunction, whose basisfunctions are constructed as linear combinations of all occupied and unoccupied molecular orbitals. The coefficients are determined by an approximate solution of the Hartree-Fock-Roothaan equations of the total system. The SCF-iteration is performed analytically until all first and second order terms are included in the expression for the interaction energy. Due to the analytical procedure of the SCF-cycle the interaction energy contains no numerically iterated quantities. The interaction between a molecule with an open shell and a molecule with a closed shell is treated in the framework of the unrestricted Hartree-Fock-approximation. The interaction energy in the molecular orbital basis is transformed into an atomic orbital basis by using the LCAO-MO-approximation and introducing approximations for several integrals. Useful expressions for calculations are also derived, which contain only quantities of the isolated molecules, together with interatomic distances and overlap integrals. These formulae for the interaction energy are suitable for detailed interpretation of the different interaction terms and reveal the role of the interacting centres.