Isomorphic copies of ℓ1 for m‐homogeneous non‐analytic Bohnenblust–Hille polynomials

We employ a classical result by Toeplitz (1913) and the seminal work by Bohnenblust and Hille on Dirichlet series (1931) to show that the set of continuous m‐homogeneous non‐analytic polynomials on c ₀ contains an isomorphic copy of ℓ₁. Moreover, we can have this copy of ℓ₁ in such a way that every non‐zero element of it fails to be analytic at precisely the same point.     

Statistical mechanics characterization of spatio-compositional inhomogeneity

On the basis of a model system of pillars built of unit cubes, a two-component entropic measure for the multiscale analysis of spatio-compositional inhomogeneity is proposed. It quantifies the statistical dissimilarity per cell of the actual configurational macrostate and the theoretical reference one that maximizes entropy. Two kinds of disorder compete: (i) the spatial one connected with possible positions of pillars inside a cell (the first component of the measure), (ii) the compositional one linked to compositions of each local sum of their integer heights into a number of pillars occupying the cell (the second component). As both the number of pillars and sum of their heights are conserved, an upper limit for a pillar height h_max occurs. If due to a further constraint there is the more demanding limit h?h^∗<h_max, the exact number of restricted compositions can be then obtained only through the generating function. However, at least for systems with exclusive composition degrees of freedom, we show that neglecting the h^∗ is not destructive yet for a nice correlation of the h^∗-constrained entropic measure and its less demanding counterpart, which is much easier to compute. Given examples illustrate a broad applicability of the measure and its ability to quantify some of the subtleties of a fractional Brownian motion, time evolution of a quasipattern [A.M. Rucklidge, M. Silber, SIAM J. Appl. Dyn. Syst. 8 (2009) 298 http://www.maths.leeds.ac.uk/~alastair/papers/RS_qp_siads_abs.html; A.M. Rucklidge, M. Silber, Phys. Rev. E 75 (2007) 055203] and reconstruction of a laser-speckle pattern [Y. Jiao, F.H. Stillinger, S. Torquato, Phys. Rev. E 77 031135, (the II part) (2008); Phys. Rev. E 76 031110 (the I part) (2007)], which are hard to discern.     

Are deformed modes still Raman active for single-wall carbon nanotubes?

Using group theory calculations combined with the force-constant model and molecular-dynamics simulations, whether the deformed modes are Raman active or not for (10,10) and (10,0) single-wall carbon nanotubes under hydrostatic pressure is discussed. With increasing pressure, the tube symmetry lowers from D_20h to D_2h then to C_2h point group. For D_20h, A_1g is changed to A_g, while E_1g and E_2g are split: E_1g→B_2g+B_3g→2B_g and E_2g→A_g+B_1g→2A_g. On the basis of the correlation between D_20h, D_2h, and C_2h point groups, the deformed modes should be still Raman active. The result can help us clarify the essence of the experimental observations.     

二阶奇异Sturm-Liouville边值问题m（λ）函数比较

讨论了二阶奇异Sturm-Liouville边值问题,通过Weyl-Titchmarsh m（λ）理论,得到了在一定条件下不同势函数q（t）所对应的m（λ）函数的比较定理.     

Formation and removal of multi-layered fluorescence patterns in gold-ion doped glass

We report the formation of fluorescence patterns inside gold-doped glass medium by femtosecond-laser fabrication. Strong fluorescence images appeared from the irradiated multi-layered region after low temperature annealing. We removed the images by exposing the glass to an electric furnace or a CO₂ laser beam for high temperature annealing. The method was also applied to recording, reading, and erasing of fluorescence data by a femtosecond laser, a 405-nm laser diode, and a CO₂ laser respectively.     

Decay pathway and high-temperature luminescence of Eu in Ca2Gd8Si6O26

The temperature-dependent luminescence of Eu:Ca₂Gd₈Si₆O₂₆ and its decay pathways are investigated in order to assess the utility of the material as a thermometric phosphor. Non-radiative decays are found to compete with radiative processes even at room temperature. A decay pathway involving decay through charge-transfer states is proposed based on the decay profiles of emissions from ⁵D₁ and ⁵D₀ levels and on the temperature sensitivity of the spectra as observed after excitation by several wavelengths. The implications of this on solid-state lighting are also discussed.     

Strong influence of substrate temperature on the growth of nanocrystalline MoO3 thin films

Nanocrystalline MoO₃ thin films are prepared by electron beam evaporation technique. By using the dry MoO₃ pellets, the films are deposited on quartz substrates at substrate temperatures ranging from 100 °C to 400 °C. A phase structure of β-MoO₃ at the substrate temperature 200 °C is characterized by X-ray diffraction, but α-MoO₃ comes forth at 300 °C and 400 °C. The surface morphology, cross section view and plate form nanostructures have been illustrated from the scanning electron microscope images. The absorption spectra of films show that the energy band Eg decreases with the increasing substrate temperature, due to the increase in oxygen vacancy. The resistances of thin films prepared at various substrate temperatures gradually decrease with the increasing environmental temperatures.     

Introduction of amino groups on the surface of thin photo definable epoxy resin layers via chemical modification

The introduction of amine groups on the surface of dielectric resins improves the adhesion with electrochemically deposited metals. In this work, etched epoxy resin surfaces are modified with aliphatic amines via a two step wet chemical reaction approach. First, cyanuric chloride is introduced on the surface. Next, the remaining reactive sites of cyanuric chloride are used to couple an aliphatic polyamine. Both reaction steps are optimized by variation of reaction parameters such as concentration, chemicals, temperature and time. A detailed surface characterization after each reaction step is provided using following techniques: ATR-IR, SEM-EDS, XPS and AFM.     

Atom in electromagnetic field of near-atomic strength

Ionization and high-harmonics generation in a single hydrogen-like atom driven by a laser pulse of near-atomic field strength is the subject of this paper. We use exact solutions of the eigenvalue problem on particle motion in the cylindrically symmetric field (CSF) as a basis for the wave-function expansion. The superposition of the spherically symmetric intra-atomic field and linearly polarized laser field has the cylindrical symmetry. Hence, the use of the free-atom eigenfunctions as a basis for the wave-function expansion requires an infinitely increasing number of spherical harmonics (i.e., free-atom eigenfunctions) when the laser field strength approaches the intra-atomic field value. The eigenfunctions of the CSF problem depend on the laser field strength; therefore, the appropriate matrix elements show how the spectral width of atomic response and angular selection rules vary with increase in the laser field strength. The introduction gives a phenomenological semiclassical illustration of the problem. Talk presented at the oral issue of J. Russ. Laser Res. dedicated to the memory of Professor Vladimir A. Isakov, Professor Alexander S. Shumovsky, and Professor Andrei V. Vinogradov held in Moscow February 21–22, 2008.     

The further unified theory for modifications of g-closed sets

We introduce a new set called mng-closedwhich is defined on a set with two families of sets satisfying some minimal conditions. This set enables us to unify modifications of g-closed sets due to Levine [19].