First and second order optimality conditions for optimal control problems of state constrained integral equations

This paper deals with optimal control problems of integral equations, with initial-final and running state constraints. The order of a running state constraint is defined in the setting of integral dynamics, and we work here with constraints of arbitrary high orders. First and second-order necessary conditions of optimality are obtained, as well as second-order sufficient conditions

Polarized triplet production by circularly polarized photons

A process of the pair production by a circularly polarized photon in the field of unpolarized atomic electron has been considered in the Weizaecker-Williams approximation. The degree of longitudinal polarization of positron and electron has been calculated. An exclusive cross-section as well as a spectral distribution are obtained. We estimate the accuracy of our calculations at the level of a few percent. We show the identity of the positron polarization for considered process and for process of pair production in the screened Coulomb field of nucleus.Comment: 9 pages, 3 picture

Cross-relaxation and phonon bottleneck effects on magnetization dynamics in LiYF4:Ho3+

Frequency and dc magnetic field dependences of dynamic susceptibility in diluted paramagnets LiYF$_4$:Ho$^{3+}$ have been measured at liquid helium temperatures in the ac and dc magnetic fields parallel to the symmetry axis of a tetragonal crystal lattice. Experimental data are analyzed in the framework of microscopic theory of relaxation rates in the manifold of 24 electron-nuclear sublevels of the lowest non-Kramers doublet and the first excited singlet in the Ho$^{3+}$ ground multiplet $^5I_8$ split by the crystal field of S$_4$ symmetry. The one-phonon transition probabilities were computed using electron-phonon coupling constants calculated in the framework of exchange charge model and were checked by optical piezospectroscopic measurements. The specific features observed in field dependences of the in- and out-of-phase susceptibilities (humps and dips, respectively) at the crossings (anti-crossings) of the electron-nuclear sublevels are well reproduced by simulations when the phonon bottleneck effect and the cross-spin relaxation are taken into account

Dissymmetrization of crystals: Theory and experiment

The distribution of Cu2+ impurities in ZnSeO4·6H2O and Na2Cd(SO4)2·2H2O crystals was investigated by electron paramagnetic resonance. The tangential selectivity by sectors in pyramid growth was revealed. Dissymmetrization, i.e., decrease of point group symmetry, is explained by tangential selectivity occupying impurities and formation defects. An analysis by group theory is presented to explain dissymmetrization of crystals. The connection between the distribution of point defects in a crystal and the growth process is discussed. © 1980 Springer-Verlag

Possible Method for Measuring the Proton Form Factors in Processes with and without Proton Spin Flip

The ratio of the squares of the electric and magnetic proton form factors is shown to be proportional to the ratio of the cross sections for the elastic scattering of an unpolarized electron on a partially polarized proton with and without proton spin flip. The initial proton at rest should be polarized along the direction of the motion of the final proton. Similar results are valid for both radiative $ep$ scattering and the photoproduction of pairs on a proton in the Bethe--Heitler kinematics. When the initial proton is fully polarized in the direction of the motion of the final proton, the cross section for the $ep \to ep$ process, as well as for the $ep \to ep \gamma$ and $\gamma p \to e \bar e p$ processes, without (with) proton spin flip is expressed only in terms of the square of the electric (magnetic) proton form factor. Such an experiment on the measurement of the cross sections without and with proton spin flip would make it possible to acquire new independent data on the behavior of $G_E^2(Q^2)$ and $G_M^2(Q^2)$, which are necessary for resolving the contradictions appearing after the experiment of the JLab collaboration on the measurement of the proton form factors with the method of polarization transfer from the initial electron to the final proton.Comment: 7 pages, revtex

Electron paramagnetic study of fe3+ and gd3+ in na2zn(S04)24h20

The epr of Fe3- and Gd3- in single crystals of Na2Zn(S04)24H20 was studied at liquid nitrogen temperature using a Q band spectrometer. For each ion, two spectra superimposed in the (010) plane and along b were observed. The spectra were described by the most general spin Hamiltonian, the constants of which were obtained for both ions. Analysing the pseudo-symmetry of the fourth-order term of the spin Hamiltonian, it is found that Fe3- only modifies the orientation of the local structure slightly and that the charge defect is probably balanced by a Na- vacancy. It is shown that the local structure around Gd3- is very different from the one around Fe3-. © 1986 The Institute of Physics

One-dimensional Model of a Gamma Klystron

A new scheme for amplification of coherent gamma rays is proposed. The key elements are crystalline undulators - single crystals with periodically bent crystallographic planes exposed to a high energy beam of charged particles undergoing channeling inside the crystals. The scheme consists of two such crystals separated by a vacuum gap. The beam passes the crystals successively. The particles perform undulator motion inside the crystals following the periodic shape of the crystallographic planes. Gamma rays passing the crystals parallel to the beam get amplified due to interaction with the particles inside the crystals. The term `gamma klystron' is proposed for the scheme because its operational principles are similar to those of the optical klystron. A more simple one-crystal scheme is considered as well for the sake of comparison. It is shown that the gamma ray amplification in the klystron scheme can be reached at considerably lower particle densities than in the one-crystal scheme, provided that the gap between the crystals is sufficiently large.Comment: RevTeX4, 22 pages, 4 figure

Local environment of Gd3+ in MgF2

The electron paramagnetic resonance (EPR) of Gd3+ in MgF2 reveals that Gd3+ has two different environments in the lattice. One of them has D2h symmetry, the EPR spectrum is characterized by a large zero field splitting [B2 0= 968.10-4 cm-1; B2 2= 357.10-4 cm-1] and the fourth order term of the spin Hamiltonian is axial; it is assumed that one Gd3+ substitutes two Mg2+. The other Gd3+ center has only monoclinic symmetry. From the analysis of the fourth order term of the spin Hamiltonian of the corresponding spectrum it is seen that one Gd3+ substitutes one Mg2+ and that this substitution produces a large local distortion of the lattice. © 1990 Springer-Verlag

EPR of Gd3+ in Na2Cd(SO4) 22H2O, comparison with previous results obtained for Fe3+

An EPR experiment on Gd3+ in a single crystal of Na 2Cd(SO4)22H2O (CdK) was carried out at Q band frequency and nitrogen temperature. Two spectra related by symmetry were observed. All spin Hamiltonian constants have been calculated. The pseudosymmetries of the fourth-order term of the spin Hamiltonian are compared to those of Fe3+. It is observed that the substitution of Gd 3+ for Cd2+ induced a very important local distortion of the host lattice, which is discussed. © 1985 American Institute of Physics

Study of the environment of Fe3+ in Na2Cd(SO 4)2 2H2O by EPR

An EPR experiment on Fe3+ in a single crystal of Na 2Cd(SO4)2 2H2O was carried out at Q band frequency and nitrogen temperature. The angular dependencies of the spectra were studied in the three crystallographic planes. In order to have a very precise orientation of the crystal, the experiment was done with a twinned crystal (superposition of two spectra in all three planes). The zero-field splitting of Fe3+ is of the same order of magnitude as the quantum hv, so that many ΔM=2 transitions were observed. All spin-Hamiltonian parameters (20) were calculated using observed ΔM=1 and ΔM=2 transitions for 30 different orientations of the magnetic field. The pseudosymmetries of the fourth-order term of the spin Hamiltonian of Fe 3+ are compared to those we calculated using the superposition model. It is seen that Fe3+ is substituted for Cd2+ and that the orientation of the ocatahedral environment of Fe3+ does not differ much in orientation from that of Cd2+. Differences between the distortions of the Cd-O6 and Fe-O6 octahedra are discussed. © 1985 American Institute of Physics