Fixed point theorems under the interior condition

We show a fixed point theorem for condensing mappings under a new condition of the Leray-Schauder type. We call it the Interior Condition. We also discuss examples that demonstrate the independence of these two conditions.

     

A NOVEL METHOD FOR FABRICATING COMPOSITE MOSAIC MEMBRANE WITH UNIQUE NF SELECTIVITY

A novel method of fabricating composite mosaic membranes was studied on the basis of interracial polymerization （IP） by coating a thin selective layer onto the surface of a micro-porous hollow-fiber membrane, in which, 2,5-diaminobenzene sulfonic acid was used as one monomer of the IP reaction, and a mixture of trimesoyl chloride （TMCI） and 4-（chloromethyl） benzoyl chloride as the other monomer. Through the IP reaction a thin selective layer with negatively charged groups could be first formed on the polyethersulfone （PES） support membrane. Then trimethylamine solution was introduced to modify the IP layer through a quaternization reaction. Thus the selective layer of this composite membrane contained both negatively charged and positively charged groups to perform the mosaic functionality. Characterization of the composite mosaic membranes was carried out through permeation experiments using different inorganic salts and dyes. The experimental results showed that the membranes could permeate both mono- and bi-valent inorganic salts, but reject larger organic molecules. Such a mosaic membrane is potentially useful for the separation of salts from water-soluble organics, especially in dye and textile industries.     

High resolution electronic study of ONO, ONO and ONO: A rovibronic survey covering 11 800-14 380 cm

The 11 800-14 380 cm⁻¹ frequency range has been scanned for rotationally resolved rovibronic transitions in the A²B₂-X²A₁ electronic band system of the symmetric (C_2v) ¹⁶O¹⁴N¹⁶O and ¹⁸O¹⁴N¹⁸O isotopologues and in the corresponding electronic band system of the asymmetric (C_s) ¹⁸O¹⁴N¹⁶O isotopologue. The rotational analysis—reflecting minor differences in mass—in combination with symmetry induced spectral differences allows an identification of 68 ¹⁶O¹⁴N¹⁶O vibronic levels, 26 ¹⁸O¹⁴N¹⁸O vibronic levels and 51 ¹⁸O¹⁴N¹⁶O vibronic levels. The bands are recorded using near infrared fluorescence spectroscopy and a piezo valve based pulsed molecular beam expansion of premixed ¹⁸O₂ and ¹⁴N¹⁶O in Ar. The majority of the observed bands is rotationally assigned and can be identified as transitions starting from the vibrational ground state of one of the isotopologues. Numerous hot bands have also been identified. A comparison of the overall spectroscopic features of C_2v vs. C_s symmetric species provides qualitative information on symmetry dependence of vibronic couplings.     

Simulation of electron bunch generation by an ultrashort-pulse high-intensity laser-driven wakefield

Electron acceleration due to a wakefield excited by a ultrashort-pulse intense laser propagating through a finite-length underdense plasma layer is studied by two-dimensional particle-in-cell simulation. The electron energy distribution is analyzed for moderate to high intensity. For the electron density, where the pulse length is almost half of the plasma wavelength, dramatic changes of the density structure occur with cavity and bunch formation with an increase in the laser intensity, also leading to the appearance of a fast electron component well confined in phase space. The analytical form of the fast electron energy spectrum is also presented.     

Study on anti-emission materials for non-emitting grid applications in microwave power tubes

Hafnium and platinum were deposited onto molybdenum grids by ion-beam assisted deposition method. Electron-emission characteristics from molybdenum grids with Hf and Pt films, which were contaminated by active electron-emission substances (Ba, BaO) of the cathode, were measured using analogous diode method. The surfaces of grids were analyzed by X-ray diffraction. The results revealed that the reaction between BaO and Hf formed BaHfO₃ compound, which greatly reduced the accumulation of BaO on the surface and accordingly decreased grid emission. In contrast, Ba were formed by the decomposition of BaO on the surface of Pt film under high temperature and re-evaporated from its surface, which reduced the active electron-emission substances on the surface of the grid and effectively restrained grid emission. Their mechanisms for grid-emission suppression are discussed and a good method to develop new grid-coating materials is suggested.     

Transformation and shift of a Gaussian light beam upon reflection from a resonant medium

The specific features of the transformation and shift of a Gaussian beam reflected from a resonant absorbing medium are analyzed numerically. The study is based on the expansion of the field of the incident Gaussian beam into plane-wave components by using the Fourier integral transform. The calculations are performed for a frequency range covering the resonance region. The conditions for the splitting of the profile of the reflected beam and for its negative shift are established.