Fixed point theorems and convergence theorems for generalized nonspreading mappings in Banach spaces

In this paper, we first prove a general fixed point theorem for nonlinear mappings in a Banach space. Then we prove a nonlinear mean convergence theorem of Baillon??s type and a weak convergence theorem of Mann??s type for 2-generalized nonspreading mappings in a Banach space.     

Regularizing Effect and Local Existence for the Non-Cutoff Boltzmann Equation

The Boltzmann equation without Grad’s angular cutoff assumption is believed to have a regularizing effect on the solutions because of the non-integrable angular singularity of the cross-section. However, even though this has been justified satisfactorily for the spatially homogeneous Boltzmann equation, it is still basically unsolved for the spatially inhomogeneous Boltzmann equation. In this paper, by sharpening the coercivity and upper bound estimates for the collision operator, establishing the hypo-ellipticity of the Boltzmann operator based on a generalized version of the uncertainty principle, and analyzing the commutators between the collision operator and some weighted pseudo-differential operators, we prove the regularizing effect in all (time, space and velocity) variables on the solutions when some mild regularity is imposed on these solutions. For completeness, we also show that when the initial data has this mild regularity and a Maxwellian type decay in the velocity variable, there exists a unique local solution with the same regularity, so that this solution acquires the C ^∞ regularity for any positive time.     

Initial testing of a high-repetition-rate electron-beam-pumped KrF laser amplifier

The initial test results of the high-repetition-rate (rep-rate) electron-beam (e-beam) pumped KrF laser amplifier under development in our laboratory are reported. This amplifier is aimed at producing a laser energy of 20 J per pulse at a rep rate of 1 Hz. Thus far, 700 consecutive e-beampulses (250 kV, 270 J/pulse) were generated at a rep rate of 1 Hz. The laser gas was repetitively pumped by the e-beams injected through the water-cooled diaphragm foils. Received: 5 February 2001 / Published online: 21 March 2001     

Estimation of the latent track size of CR-39 using atomic force microscope

As a frame work of the study for the latent track size measurement using atomic force microscope, we have measured the minute etch pits and the extremely small amount of bulk etch of CR-39 at the beginning of chemical etching, and obtained its growth curves in nanometer dimensions. The pieces of CR-39 were exposed to 6 MeV/nC and Fe ions with normal incidence angle and were etched in 70°C 7 N NaOH solution for 0.5,1,2,3,5 min. The diameters of latent track were estimated to be 17 nm for Fe ions and 8 nm for C ions, respectively. These values are comparable to the experimental data on the average ‘track core diameters’ that have been obtained by various experimental techniques.     

Preparation and reactions of pyridinyl tellurides

Tellurium‐metal exchange reaction of n‐butyl 2‐pyridinyl telluride derivatives with n‐butyllithium or dilithium dimethylcyanocuprate proceeded smoothly to give the corresponding 2‐pyridinylmetal derivatives, which are important intermediates for functionalization of pyridines.     

Theoretical prediction of vertical transition energies of diaminosilylenes and aminosubstituted disilenes

Vertical electronic transition energies of diaminosilylenes and their dimers (disilenes and nitrogen‐bridged) were investigated by ab initio and density functional calculations. A good linear correlation was found between the observed UV transition energies of various silylenes and disilenes and those of model compounds calculated using the CIS and TD–DFT methods. On the basis of these computations the experimental UV absorption maximum observed for the dimer of (i‐Pr₂N)₂Si: (λ_max 439 nm at 77 K), could be assigned to an Si? Si bonded dimer with an unusually long Si? Si distance of 2.472 Å, and the isomeric amino‐bridged cyclic dimer could be discarded. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1536–1541, 2001     

Melt rheology and structure of silicone resins

Rheological investigation and X-ray analysis of silicone resins have been performed to get a fundamental understanding of the relationship between melt rheology and structure. Rheological properties of the melts of silicone resins were characterized by dynamic shear measurements. Samples were a series of silicone resins having different side groups, such as methyl, phenyl, methylphenyl, and propylphenyl. A time-temperature superposition based on the WLF rule was successfully applicable. The free volume fraction at the glass transition temperature and the free volume expansion coefficient were estimated from the C₁ and C₂ values of the WLF-equation. The loss modulus G′′ was found to be proportional to the angular frequency in a double-logarithmic plot over a wide frequency range. However, the storage modulus G′ exhibited a bending in a intermediate frequency region for all silicone resins. The shape of the G′ curve is unexpected from the results of gel permeation chromatography (GPC) and differential scanning calorimeter (DSC), which demonstrate that the silicone resins are amorphous polymers of relatively low molecular weight. To get more insight into the rheological properties of the silicone resins which indicate a heterogeneous structure, X-ray analysis was carried out. The X-ray measurement displayed two peaks, one broad peak around 4.5?Å of d-spacing which corresponds to a random amorphous structure, and the other higher intensity peak from 8.5?Å to 12?Å. This peak strongly depends on the size of organic side groups. From the rheological characterization and the X-ray analysis, it can be concluded that the silicone resins consist of two components; one of them shows a random amorphous and the other a regular structure even in the molten stage.     

Uniaxial elongational viscosity of PS/a small amount of UHMW-PS blends

A series of polystyrene (PS) and a small amount of ultra high molecular weight (UHMW) PS blends have been prepared by using tetrahydrofuran (THF). Matrix PS has an M_w of 423,000 (M_w/M_n= 2.36) and UHMW-PS has either an M_w of 3,220,000 (M_w/M_n= 1.05) or 15,400,000 (M_w/M_n=1.30) in the range of concentration from 0 wt% to 1.5 wt%. The influence of a small amount of UHMW on dynamic viscoelasticity was investigated. At the frequency lower than 0.001 rad/s, the enhancement of G′ was observed by the incorporation of a small amount of UHMW. And the degree of enhancement was in the order of M_w of UHMW and its concentration. The measurement of uniaxial elongational viscosity for the blends was performed and the effects of UHMW on strain-hardening properties were analyzed at equal strain-rate conditions. The concentration of UHMW where the strain-hardening becomes substantially stronger was determined. To get more insight into the cause of enhancement of strain-hardening at a certain concentration, the damping function from step-shear stress relaxation was measured. The influence of a small amount of UHMW on the damping function was found to be small. It was interpreted, from time- and strain-dependency points, that the enhancement of strain-hardening by a small amount of UHMW was governed by the long relaxation time. Received: 6 September 2000 Accepted: 11 January 2001     

DTμ Physics and Its Application

A high-intensity neutron source that is highly correlated spatially and with time and will be used for neutron scattering experiments can be obtained by dt m catalyzed fusion by enhancing the formation rate of dtμ molecules using a high-intensity pulsed laser to dtμ gas. This paper considers the use of dtμ fusion for fast ignition of inertial confinement fusion, and the possibility of ensuring energy balance in energy production. dt fusion can be quickly ignited by depositing dtμ fusion energy into a smaller space than is done in other methods, such as Z-pinch or heavy-ion fusion. Space propulsion can be obtained with a light fuel mass rather than by a fission repulsion system using the muons produced by annihilation of the anti-protons stored in liquid superfluid of condensed He. Using an extremely highly compressed target can create a source of high luminosity muons for muon–muon collider- and neutrino-oscillation experiments. This approach can eliminate the need for a super-conducting solenoidal for capturing the beam of pions and muons generated in a large target, and then these pions and muons can be manipulated by a laser beam instead of by employing RF manipulation. This revised version was published online in August 2006 with corrections to the Cover Date.     

Synthesis of Benzopyran-4-Amides Potassium Channel Openers Via Palladium-Catalyzed Amidation

The novel potassium channel openers benzopyran-4-amides have been synthesized via palladium-catalyzed amidation of 4-bromobenzopyrans under an atmoshere in the presence of an equivalent of potassium iodide.