Interference inspection of the aspherical components of an objective for nanolithography

Methods and schemes to inspect the EUV mirror shape are developed on the basis of a point diffraction interferometer with computer processing of interferograms. A measurement accuracy to within 0.001 of a wavelength in the visual range is achieved.     

Hard collisions of spinning protons: Past,present and future

There will be a review of the history of polarized proton beams, and a discussion of the unexpected and still unexplained large transverse spin effects found in several high-energy proton-proton spin experiments at the ZGS, AGS and Fermilab. Next, there will be a discussion of present and possible future experiments on the violent elastic collisions of polarized protons at IHEP-Protvino's 70GeV U-70 accelerator in Russia and the new high-intensity 50GeV J-PARC facility being built at Tokai in Japan.     

A note on strongly π-regular rings

Let R be an associative ring with unit and let N(R) denote the set of nilpotent elements of R. R is said to be stronglyπ-regular if for each x∈R, there exist a positive integer n and an element y∈R such that x ⁿ=x ^{n +1} y and xy=yx. R is said to be periodic if for each x∈R there are integers m,n≥ 1 such that m≠n and x ^m=x ⁿ. Assume that the idempotents in R are central. It is shown in this paper that R is a strongly π-regular ring if and only if N(R) coincides with the Jacobson radical of R and R/N(R) is regular. Some similar conditions for periodic rings are also obtained. This revised version was published online in June 2006 with corrections to the Cover Date.     

Left, right, and inner socles of associative systems

We investigate the basic properties of the different socles that can be considered in not necessarily semiprime associative systems. Among other things, we show that the socle defined as the sum of minimal (or minimal and trivial) inner ideals is always an ideal. When trivial inner ideals are included, this inner socle contains the socles defined in terms of minimal left or right ideals. This revised version was published online in June 2006 with corrections to the Cover Date.     

On α-I-continuous and α-I-open functions

Montgomery and Vaughan improved a theorem of Erd?s and Fuchs for an arbitrary sequence. Sárközy extended this theorem of Erd?s and Fuchs for two arbitrary sequences which are "near" in a certain sense. Using the idea of Jurkat (differentiation of the generating function), we will extend similarly the result of Montgomery and Vaughan for "sufficiently near" sequences.     

The variation of the density functions on chaotic spheres in chaotic space-like Minkowski space time

In this article we introduce types of chaotic spheres in chaotic space-like Minkowski space time Mⁿ⁺¹. The variations of the density functions under the folding of these chaotic spheres are defined. The foldings restriction imposed on the density function are also discussed. The relations between the folding of geometry and pure chaotic manifolds are deduced. Some theorems concerning these relations are presented.     

Nonclassical pseudospectral method for the solution of brachistochrone problem

In this paper, nonclassical pseudospectral method is proposed for solving the classic brachistochrone problem. The brachistochrone problem is first formulated as a nonlinear optimal control problem. Properties of nonclassical pseudospectral method are presented, these properties are then utilized to reduce the computation of brachistochrone problem to the solution of algebraic equations. Using this method, the solution to the brachistochrone problem is compared with those in the literature.     

Amine‐blocked polyisocyanates. I. Synthesis of novel N‐methylaniline‐blocked polyisocyanates and deblocking studies using hot‐stage fourier transform infrared spectroscopy

A series of substituted N‐methylaniline‐blocked polyisocyanates based on 4,4′‐methylenebis(phenyl isocyanate) and poly(tetrahydrofuran) were prepared and characterized thoroughly with FTIR, ¹H NMR, and ¹³C NMR spectroscopy methods. Compared with unsubstituted N‐methylaniline, a blocking agent with an electron‐releasing substituent at the para position took a shorter time, whereas those with an electron‐releasing substituent at the ortho position or an electron‐withdrawing substituent at the ortho and para positions took longer times for the blocking reaction. The thermal dissociation reactions of blocked polyisocyanates were carried out with an FTIR spectrophotometer attached to hot‐stage accessories under dynamic and isothermal conditions. The dynamic method was used to determine the deblocking temperature, and the isothermal method was used to calculate the deblocking kinetics and activation parameters. The cure times of blocked polyisocyanates with hydroxyl‐terminated polybutadiene were also determined. The deblocking temperatures, the results of cure‐time studies, and the kinetic parameters revealed that the thermal dissociation of the N‐methylaniline‐blocked polyisocyanates was retarded by electron‐donating substituents and facilitated by electron‐withdrawing substituents. The action of N‐methylanilines as blocking agents for isocyanate was explained by the formation of a four‐center, intramolecularly hydrogen‐bonded ring structure during the thermal dissociation of the blocked polyisocyanates. The formation of such a hydrogen‐bonded ring structure was confirmed and supported by variable‐temperature ¹H NMR studies and entropy parameters, respectively. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1557–1570, 2007     

Calculation of the Radiating Characteristics of a Thermodynamically Nonuniform Gas Medium

Passive methods of remote analysis of waste gases of industrial enterprises and aircrafts engines and gases ejected in eruptions of volcanos, in fires, and in other processes disturbing the atmosphere are now of limited utility because of the lack of well-developed mathematical techniques for solving the inverse problems of gas analysis. However, the advantage of these methods is obvious, since the equipment is limited to a receiving device and the gas medium serves as a radiator. At the same time, in modern techniques, the interpretation of measurements of emissivities of gases is performed using a phenomenological approach such that experimental data on radiation characteristics of various objects are approximated by simple polynomial relations whose coefficients are determined by minimization methods. This approach does not allow one to investigate the mechanism of the processes occurring in a radiating medium and gives no way of solving the inverse problem of monitoring the composition and thermodynamic parameters of a medium which disturbs the atmosphere by thermal effects. In elaborating theoretical methods of gas analysis, the elaboration of the direct problem of calculation of radiating characteristics of gases is of importance, since it is not clear how the emissivity of a gas medium depends on its thermodynamic parameters. This paper is devoted to the above problem. Here, the error is estimated that arises in modeling a nonuniform gas medium with an actual temperature distribution, which linearly depends on coordinate, by a uniform gas layer. It is shown that the difference between the radiation intensities calculated for uniform and nonuniform media can be significant in the practically important case where the recording device is in a zone of normal temperatures. This implies that the error of reconstruction of the spectroscopic and molecular parameters of gaseous compounds from high-temperature measurements of the radiating and absorbing characteristics should take into account the thermodynamic nonuniformity of the medium.