Almost global existence for Hamiltonian semilinear Klein‐Gordon equations with small Cauchy data on Zoll manifolds

This paper is devoted to the proof of almost global existence results for Klein‐Gordon equations on Zoll manifolds (e.g., spheres of arbitrary dimension) with Hamiltonian nonlinearities, when the Cauchy data are smooth and small. The proof relies on Birkhoff normal form methods and on the specific distribution of eigenvalues of the Laplacian perturbed by a potential on Zoll manifolds. © 2007 Wiley Periodicals, Inc.     

Order conditions for linearly implicit fractional step Runge Kutta methods

^{In this paper, we study the consistency of a variant of fractionalstep Runge–Kutta methods. These methods are designed tointegrate efficiently semi-linear multidimensional parabolicproblems by means of linearly implicit time integration processes.Such time discretization procedures are also related to a splittingof the space differential operator (or the spatial discretizationof it) as a sum of ‘simpler’ linear differentialoperators and a nonlinear term.}     

Electron energy loss spectroscopy; history and related matters

This paper begins with some historical remarks regarding the author’s early interest in the use of electron energy loss spectroscopy to probe dynamical phenomena on crystal surfaces. We then discuss the physical nature of the interactions responsible for vibrational and spin waves losses, with attention to their role in related phenomena. PACS 61.14.-x; 68.35.Ja; 68.49.Jk; 68.49.Uv     

Einstein relation in chemically doped organic semiconductors

Based on the assumption of Gaussian energy distributions of the lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO), analytical expressions of generalized Einstein relation in chemically doped organic semiconductor are developed, by approximation of Coulomb traps with a rectangle potential well. Numerical calculations show that traditional Einstein relations do not hold for chemically doped organic semiconductors. Similar to physical doping, the dependence of diffusion coefficient to mobility D/μ ratio on the carrier concentration has a maximum. An essential difference between chemical doping and physical doping is that, the D/μ ratio in chemically doped organic semiconductors depends not only on carrier concentration and doping concentration, but also on the applied electric field. PACS 71.20.Rv; 72.90.+y; 73.50.-h     

Superconducting magnetis in spectrometers of high-energy particles

This is a retrospective review of superconducting magnets for spectrometers of high-energy particles. The magnets are grouped according to the purpose of the spectrometers and the shape of coils. Data on the thermostatting and electrical protection of the coils are presented. Design features of various-type magnets are described. The first large superconducting solenoids were constructed for hydrogen bubble chambers. Further progress was related to the construction of spectrometers that were designed for experiments at colliders and included solenoids with radiation-transparent walls. Along with solenoids, dipole and toroidal magnets were used in spectrometers; some designs of such magnets are also discussed in the review. A special type of polarizing solenoid is used in polarized targets. Spectrometers with magnets of various coil shapes were created for astrophysical research. As an instance, the original radiation-transparent solenoid and the dipole magnet with a cryocooler are represented. Prospects for the future development of magnets are connected with the use of high-temperature superconductors (HTS). Information on the present situation in engineering the HTS ribbon and solenoids is given.     

Comparative analysis of the twin and heterophase structures in (1−x)Pb(Mg1/3Nb2/3)O3−xPbTiO3 crystals

The specific features of the coexistence of phases in heavily twinned crystals of the (1?x)Pb(Mg_1/3Nb_2/3)O₃?xPbTiO₃ system in the vicinity of the morphotropic phase boundary (0.30≤x≤0.40) are investigated. The phase transformations in crystals at x = const during cooling are considered at electric field strengths E=0 and 0.1 MV/m. The conditions of the formation of interphase boundaries (zero net strain planes) are determined for different first-order phase transitions. The results of calculating the tetragonal-monoclinic M _C and monoclinic-monoclinic (M _C –M _A ) phase transitions are represented in the form of “twin state-interphase boundary” diagrams. The effect of a 90° domain (twin) structure of the tetragonal phase on the heterophase state associated with the presence of monoclinic phases is analyzed.     

Critical parameters of methylbromo-and ethylbromosilanes

Critical parameters of nine methylbromo-and ethylbromosilanes were determined.     

Sorption of Sc(III) on phosphorus-containing cation exchangers

Kinetics of Sc(III) sorption from hydrochloric acid solutions on KRF-20t-60 cation exchanger is studied. The experimental data are analyzed in terms of the gel and film kinetic models. The Sc(III) diffusion coefficient in the resin phase is estimated. Static and dynamic sorption data are obtained on Sc(III) sorption from various process solutions on KRF-20t-60, PA-1, AFI-22 ion exchangers, and also on ion exchangers supported on polyacrylonitrile-based fibrous material. Desorption of Sc(III) from KRF-20t-60 is also studied.     

Algebraic curve in the unit ball in ℂ2 that passes through the origin and all of whose boundary components are arbitrarily short

A negative answer is given to the following question of A.G. Vitushkin: Does there exist a nontrivial lower bound for the length of the maximal component of intersection of the unit sphere and an algebraic curve passing through the origin. Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2006, Vol. 253, pp. 135–157. To the memory of Anatolii Georgievich Vitushkin