Automatic continuity and representation of group homomorphisms defined between groups of continuous functions

Let C(X,G) be the group of continuous functions from a topological space X into a topological group G with pointwise multiplication as the composition law, endowed with the uniform convergence topology. To what extent does the group structure of C(X,G) determine the topology of X? More generally, when does the existence of a group homomorphism H between the groups C(X,G) and C(Y,G) implies that there is a continuous map h of Y into X such that H is canonically represented by h? We prove that, for any topological group G and compact spaces X and Y, every non-vanishing C-isomorphism (defined below) H of C(X,G) into C(Y,G) is automatically continuous and can be canonically represented by a continuous map h of Y into X. Some applications to specific groups and examples are given in the paper.     

Extension of the range of resonator scanning spectrometer into submillimeter band and some perspectives of its further developments

Extension of the working frequency of modern resonator spectrometers into submillimeter wave range is described. Experimental record of atmospheric absorption spectrum covering 45-370 GHz range is demonstrated for the first time, and measured water vapor J′_{ka′, kc′}-J_{ka, kc} = 5_1,5-4_2,2 at 325 GHz line parameters are presented. For the first time pressure lineshift for the 325-GHz water vapor line is measured. Further extension of working range is discussed. New estimations of physical limits of time needed for measurements of absorption in the whole Backward Wave Oscillator (BWO) range are given for phase continuous synthesizer regime. Basic schemes of fast broadband continuous phase synthesized sources are discussed. Verification of the previous measurements of water vapor 3_1,3-2_2,0 at 183 GHz line parameters is presented. Comparisons with ringdown resonator spectrometers are given.     

Efficient domain partitioning algorithms for global optimization of rational and Lipschitz continuous functions

A domain partitioning algorithm for minimizing or maximizing a Lipschitz continuous function is enhanced to yield two new, more efficient algorithms. The use of interval arithmetic in the case of rational functions and the estimates of Lipschitz constants valid in subsets of the domain in the case of others and the addition of local optimization have resulted in an algorithm which, in tests on standard functions, performs well.     

Quotient normed cones

Given a normed cone (X, p) and a subconeY, we construct and study the quotient normed cone (X/Y,p) generated byY. In particular we characterize the bicompleteness of (X/Y, ‖·‖ ^p ,p) in terms of the bicompleteness of (X, p), and prove that the dual quotient cone ((X/Y)^*, || · ‖·‖^p,p) can be identified as a distinguished subcone of the dual cone (X ^*, || · ||_{p, u}). Furthermore, some parts of the theory are presented in the general setting of the spaceCL(X, Y) of all continuous linear mappings from a normed cone (X, p) to a normed cone (Y, q), extending several well-known results related to open continuous linear mappings between normed linear spaces.     

The Role of a Specific Response of Media in the Vavilov-Cherenkov Effect

It is shown that the condition υ > υ_p (ω), which is necessary in order to trigger the Vavilov-Cherenkov effect, determines the interval of radiated frequencies and it alone cannot establish a strong restriction to the velocity of the particle. It is exhibited that it is possible to define a general lower bound for the velocity of the particle, which does not depend on the frequency when both, a specific response of the medium is taken into account and the mentioned condition is considered. The minimum value of the phase velocity of light in the medium determines the existence of such general lower bound.     

利用莫尔条纹的准正弦特性的三维轮廓术

分析了两个矩形光栅迭合产生的莫尔条纹的光强分布特性，通过选择适当的光栅参数，可得到一个近似的正弦分划板，并把它用于三维面形测量中，实验结果表明，这种方法简单，易于自动处理，有广泛的实用价值。     

Precise lattice parameter measurements in CsCl-Br solid solutions between room temperature and 90°K by powder x-ray diffraction

Solid solutions of CsCl-Br in five different concentrations were prepared in sealed quartz tubes by heating the mixture to 1123°K for 6–8 hr and quenching to room temperature. X-ray diffractograms were taken at eight different temperatures between room temperature and 90°K for these solid solutions using the YPC50NM powder diffractometer and a continuous flow cryostat. The observed lattice parameters for each sample at each temperature obtained from the powder diffractograms were then extrapolated to give the true lattice parameters using the least square method with Nelson-Riley extrapolation scheme. The values of the true lattice parameters at each concentration and at each temperature were tabulated and the results discussed. It is shown that the lattice parameters vs temperature for some concentrations exhibit an anomalous behaviour. Contribution No. 691     

高抗冲聚丙烯序列结构的综合表征

用高分辨＾１３Ｃ ＮＭＲ、ＦＴＩＲ等手段获得了高抗冲聚丙烯的组成和序列分布等链结构方面的信息。用ＤＳＣ、ＷＡＸＤ等方法研究了它们的结晶行为、熔融转变及晶体结构，多种方法相结合有效地表征了高抗冲聚丙烯的序列结构。     

Reversible addition–fragmentation transfer (RAFT) copolymerization of methyl methacrylate and styrene in miniemulsion

In the reversible addition–fragmentation transfer (RAFT) copolymerization of two monomers, even with the simple terminal model, there are two kinds of macroradical and two kinds of polymeric RAFT agent with different R groups. Because the structure of the R group could exert a significant influence on the RAFT process, RAFT copolymerization may behave differently from RAFT homopolymerization. The RAFT copolymerization of methyl methacrylate (MMA) and styrene (St) in miniemulsion was investigated. The performance of the RAFT copolymerization of MMA/St in miniemulsion was found to be dependent on the feed monomer compositions. When St is dominant in the feed monomer composition, RAFT copolymerization is well controlled in the whole range of monomer conversion. However, when MMA is dominant, RAFT copolymerization may be, in some cases, out of control in the late stage of copolymerization, and characterized by a fast increase in the polydispersity index (PDI). The RAFT process was found to have little influence on composition evolution during copolymerization. The synthesis of the well‐defined gradient copolymers and poly[St‐b‐(St‐co‐MMA)] block copolymer by RAFT miniemulsion copolymerization was also demonstrated. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 6248–6258, 2004     

On accurate boundary conditions for a shape sensitivity equation method

This paper studies the application of the continuous sensitivity equation method (CSEM) for the Navier–Stokes equations in the particular case of shape parameters. Boundary conditions for shape parameters involve flow derivatives at the boundary. Thus, accurate flow gradients are critical to the success of the CSEM. A new approach is presented to extract accurate flow derivatives at the boundary. High order Taylor series expansions are used on layered patches in conjunction with a constrained least‐squares procedure to evaluate accurate first and second derivatives of the flow variables at the boundary, required for Dirichlet and Neumann sensitivity boundary conditions. The flow and sensitivity fields are solved using an adaptive finite‐element method. The proposed methodology is first verified on a problem with a closed form solution obtained by the Method of Manufactured Solutions. The ability of the proposed method to provide accurate sensitivity fields for realistic problems is then demonstrated. The flow and sensitivity fields for a NACA 0012 airfoil are used for fast evaluation of the nearby flow over an airfoil of different thickness (NACA 0015). Copyright © 2005 John Wiley & Sons, Ltd.