A general stability result for the semilinear viscoelastic wave model under localized effects

Our main goal in the present work is to address an integro-differential model under localized viscoelastic and frictional effects arising in the Boltzmann theory of viscoelasticity. More precisely, we consider a general version in the history context of the pioneer localized viscoelastic problem approached by Cavalcanti and Oquendo (2003) in the null history scenario, and more recently by Cavalcanti et al. (2018) in the history framework. By means of a new observability inequality, we prove a general stability result to the model under a weaker assumption on the localized frictional damping and a slower condition on the decreasing memory kernel (of polynomial type) than the previously mentioned works. To achieve such stability results, we still work in a general setting by removing the assumption on complementary damping mechanisms and show, in some reasonable situations concerning the density coefficient, that the localized viscoelastic effect is enough to ensure the general stability (of polynomial type) to the problem.     

Imine‐linked porous organic polymers showing mesoporous microspheres architectures with tunable surface roughness

Different kinds of porous organic polymers (POPs) bearing 4,4‐difluoro‐4‐bora‐3a,4a‐diaza‐s‐indacene (BDP) fluorophores have been developed to generate singlet oxygen upon light illumination. Herein, four imine‐linked POPs were prepared by copolymerization of amine and aldehyde with different ratios of di‐aldehyde A1 and A2. The POPs were investigated by a combination of techniques such as solid ¹³C NMR, FTIR, and nitrogen absorption–desorption isotherms and electronic microscopy. The results demonstrated that these POPs were prone to form hierarchical porous architectures. Scanning electron microscopy and transmission electron microscopy images revealed that the spherical morphologies showed different roughness, that is, BDP‐POPs with more BDP aldehyde A2 presented rougher surface. Finally, these POPs were used to generate singlet oxygen (¹O₂) monitored by 1,3‐diphenylisobenzofuran and bioimaging in HeLa cells. Our results indicated that the ability to generate ¹O₂ is dependent on the amount of BDP. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 319–327     

Magnetic field dependence ofT c and temperature dependence ofH c2 in layered superconductors with open normal state Fermi surface

A theoretical framework for treating the effects of magnetic fieldH on the pairing theory of superconductivity is considered, where the field is taken in an arbitrary direction with respect to crystal axes. This is applicable to closed, as well as open normal state Fermi surface (FS), including simple layered metals. The orbital effects of the magnetic field are treated semiclassically while retaining the full anisotropic paramagnetic contribution. Explicit calculations are presented in the limits |H| → |H _c2(T)|,T ∼ 0 andT →T _c(|H|), |H| ∼ 0. Effects of weak nonmagnetic impurity scattering, without vertex corrections, have also been taken into account in a phenomenological way. The final results for the case of open FS and layered materials are found to differ considerably from those of the closed FS. For example, an important parameter,h(T=0)=|H_c2(0)|/[-Tδ|H _c2 T|δT]_T{s0} for the case of a FS open ink _z-direction with thek _z-bandwidth, 4t ₃, very small compared to the Fermi energy,E _F, is close to 0.5906, compared to 0.7273 for the closed FS, in the clean limit. Analytical results are given for the magnetic field dependence ofT _c and the temperature dependence of H _c2 for a model of layered superconductors with widely open FS. For a set of band structure parameters for YBa₂Cu₃O₇ used elsewhere, we find reasonable values for the upper critical fieldH _c2(0), the slope (dH _c2/dT)_{T c0}, anisotropic coherence lengths ζ_i(T=0),i=x, y, z, and (dT _c/d|H|)_{|H| → 0}.     

Superhydrophobic surfaces fabricated by microstructuring of stainless steel using a femtosecond laser

Fabrication of superhydrophobic surfaces induced by femtosecond laser is a research hotspot of superhydrophobic surface studies nowadays. We present a simple and easily-controlled method for fabricating stainless steel-based superhydrophobic surfaces. The method consists of microstructuring stainless steel surfaces by irradiating samples with femtosecond laser pulses and silanizing the surfaces. By low laser fluence, we fabricated typical laser-induced periodic surface structures (LIPSS) on the submicron level. The apparent contact angle (CA) on the surface is 150.3°. With laser fluence increasing, we fabricated periodic ripples and periodic cone-shaped spikes on the micron scale, both covered with LIPSS. The stainless steel-based surfaces with micro- and submicron double-scale structure have higher apparent CAs. On the surface of double-scale structure, the maximal apparent CA is 166.3° and at the same time, the sliding angle (SA) is 4.2°.     

Thermoluminescence kinetic study of binary lead-silicate glasses

This paper describes a detailed experimental study of the thermoluminescence (TL) properties of four binary lead-silicate glasses, with PbO concentrations ranging from 32% to 62% in mole percent. The TL glow peaks between room temperature and 300 °C were analyzed using a systematic thermal cleaning technique. The T_max-T_stop and E-T_stop methods of analysis were used to identify the number of peaks under the glow curves, and to obtain the activation energy E for each TL trap. A computerized glow curve fitting analysis is used to fit the experimental data to four first-order peaks with maxima at temperatures of 54, 80, 110 and 210 °C, as measured with a heating rate of 2 °C/s. The kinetic parameters of the glow-peak at 210 °C were confirmed by using phosphorescence decay methods of analysis. The TL traps associated with the low-temperature TL peak at 54 °C are found to depend strongly on the PbO concentration of the samples, while the higher-temperature TL peaks show a behavior independent of the PbO concentration. The activation energy E and frequency factor s of the low-temperature TL trap associated with the peak at 54 °C are consistent with a trap involving a delocalized transition through the conduction band. However, the activation energies and frequency factors for the higher-temperature TL traps are consistent with traps involving localized transitions via an excited state below the conduction band. The data suggest that these higher-temperature TL traps are associated with the common silicate matrix in these binary silicate glasses.     

ON THE BOREL DIRECTION OF K-QUASIMEROMORPHIC MAPPINGS

For the K-quasimeromorphic mappings, a precise fundamental inequality for the angular domain is established. From this, the Borel direction of the K-quasimeromorphic mappings of zero order is derived.     

Some sufficient conditions for tunnel numbers of connected sum of two knots not to go down

In this paper, we show the following result: Let K _i be a knot in a closed orientable 3-manifold M _i such that (M _i ,K _i ) is not homeomorphic to (S ₂ ×S ₁, x ₀ ×S ₁), i = 1, 2. Suppose that the Euler Characteristic of any meridional essential surface in each knot complement E(K _i ) is less than the difference of one and twice of the tunnel number of K _i . Then the tunnel number of their connected sum will not go down. If in addition that the distance of any minimal Heegaard splitting of each knot complement is strictly more than 2, then the tunnel number of their connected sum is super additive.     

有理曲线和曲面的分片多项式逼近

本文利用摄动的思想,以摄动有理曲线（曲面）的系数的无穷模作为优化目标,给出了用多项式曲线（曲面）逼近有理曲线（曲面）的一种新方法．同以前的各种方法相比,该方法不仅收敛而且具有更快的收敛速度,并且可以与细分技术相结合,得到有理曲线与曲面的整体光滑、分片多项式的逼近．     

Effect of high gamma dose on the PADC properties

The effect of the properties of PADC nuclear track detectors after exposure to high doses of gamma absorbed doses up to 5×10⁵ Gray (50 Mrad) were studied. The gamma source was a 9.03 PBq (244 KCi), Co-60 source. Results indicate that each of the bulk etch rate (V_b), the tracks etch rate (V_t) and the sensitivity (V) of the detectors increases with the high gamma absorbed dose, but there is a drop in these parameters at the low gamma absorbed dose. Signs of surface roughness were observed by increasing the gamma absorbed doses and changes in color observed for doses larger than 2×10⁵ Gray. The temperature of detectors during irradiation time reached 41°C. The fission fragment tracks (from Cf-252 source) disappeared quickly within the etching time (minutes) for total absorbed doses greater than 3×10⁵ Gray due to their high bulk etch rate.     

K3 surfaces,Picard numbers and Siegel disks

If a K3 surface admits an automorphism with a Siegel disk, then its Picard number is an even integer between 0 and 18. Conversely, using the method of hypergeometric groups, we are able to construct K3 surface automorphisms with Siegel disks that realize all possible Picard numbers. The constructions involve extensive computer searches for appropriate Salem numbers and computations of algebraic numbers arising from holomorphic Lefschetz-type fixed point formulas and related Grothendieck residues.