An eigenform of weight one expressed by meromorphic η-quotients

In this paper, we construct an eigenform of weight one by using meromorphic η-quotients. It is the modular form associated to an irreducible representation r: Gal(L/\mathbb Q)? GL₂(\mathbb C)\rho : {\rm Gal}(L/\mathbb {Q})\rightarrow {\rm GL}_{2}(\mathbb {C}) with L=\mathbb Q(?{-3},³?{3})L=\mathbb {Q}(\sqrt{-3},\sqrt[3]{3}).     

Polymerization process of the silane coupling agent 3-aminopropyltriethoxy silane – H NMR spectra and kinetics of ethanol release

In the 3-aminopropyltriethoxy silane–deuterated ethanol–H₂O system, the rate of release of ethanol from the ethoxy groups, a reaction which occurs during the condensation process, has been followed by use of ¹H NMR spectroscopy at different temperatures. Two separate reaction processes have been identified, and values of the reaction rate constants and thermodynamic parameters (E_a, ΔH^‡ and ΔS^‡) have been calculated.     

Dynamic investigation of a functionally graded layered structure with a crack crossing the interface

The dynamic response of a functionally graded layered structure with a crack crossing the interface is analyzed. The in-plane impact loading condition is considered. By using the Laplace and Fourier integral transforms, singular integral equation method and residue theory, the present problem is reduced to a singular integral equation in the Laplace transform domain. The influences of Young’s modulus ratio, thickness ratio, and crack length and location on the dynamic stress intensity factors (DSIFs) are investigated. Particularly, the DSIFs corresponding to different crack locations are shown in the case when the crack center moves from one layer to another layer through the interface. The peak and static values and overshoot characteristics of the DSIFs are analyzed. It is found that these values typically exhibit kinking behavior when the crack tips arrive at the interface. This study is different from previous other investigations in the following respects: (1) the dynamic response of a crack crossing the interface of a functionally graded structure is studied analytically, which has hardly been done in the past and (2) the present model can be reduced to some important problems, such as a functionally graded coating-substrate structure with a crack in the graded coating or homogeneous substrate or one intersecting the interface.     

On a dendrite generated by a zero-dimensional weak self-similar set

Let S be a zero-dimensional, perfect, compact weak self-similar set generated in dendrite X by a family {f_j} of weak contractions from X to itself. Decomposition space D_f of S due to a continuous mapping f from S onto X is also a dendrite. In the dendrite D_f, there exists a zero-dimensional, perfect, compact weak self-similar set S¹ based on a family each of which is topologically conjugate to f_j. Decomposition space D_f¹ of S¹ due to a continuous mapping f¹ from S¹ onto D_f is again a dendrite. In this manner, through the successive formation of weak self-similar set, we can obtain a sequence X,D_f,D_f¹,… of dendrite any pair in which are mutually homeomorphic.     

On the uniqueness of measuring elastoplastic properties from indentation: The indistinguishable mystical materials

Indentation is widely used to extract material elastoplastic properties from the measured force-displacement curves. One of the most well-established indentation techniques utilizes dual (or plural) sharp indenters (which have different apex angles) to deduce key parameters such as the elastic modulus, yield stress, and work-hardening exponent for materials that obey the power-law constitutive relationship. However, the uniqueness of such analysis is not yet systematically studied or challenged. Here we show the existence of “mystical materials”, which have distinct elastoplastic properties yet they yield almost identical indentation behaviors, even when the indenter angle is varied in a large range. These mystical materials are, therefore, indistinguishable by many existing indentation analyses unless extreme (and often impractical) indenter angles are used. Explicit procedures of deriving these mystical materials are established, and the general characteristics of the mystical materials are discussed. In many cases, for a given indenter angle range, a material would have infinite numbers of mystical siblings, and the existence maps of the mystical materials are also obtained. Furthermore, we propose two alternative techniques to effectively distinguish these mystical materials. The study in this paper addresses the important question of the uniqueness of indentation test, as well as providing useful guidelines to properly use the indentation technique to measure material elastoplastic properties.     

Molecularly intact and dissociative adsorption of water on clean Cu(1 1 0): A comparison with the water/Ru(0 0 1) system

An X-ray photoelectron spectroscopy (XPS) study was undertaken of the water/Cu(1 1 0)-system finding non-dissociative adsorption on clean Cu(1 1 0) at temperatures below 150 K. Thermally induced dissociation of D₂O is observed to occur above 150 K, similar to the H₂O/Ru(0 0 1) system, with an experimentally derived activation barrier of 0.53-0.56 eV which is very close in magnitude to the derived activation barrier for desorption of 0.50-0.53 eV. X-ray and electron induced damage to the water overlayer was quantified and used to rationalize the results of a recent XPS study of the water/Cu(1 1 0)-system where partial dissociation was observed already at 90 K.     

The charge-transfer polymerization of nitroethylene in electron-donating solvents

The anionic polymerization of nitroethylene was studied in N,N-dimethylformamide (DMF) and in dimethyl sulfoxide (DMSO) at 0–40°C. The polymerization proceeds spontaneously when monomer is mixed with solvent in the absence of light. From the observed results of the rate of polymerization, the molecular weight of polymer, the effects of additives and solvents, the copolymerization with acrylonitrile, and the optical absorption spectra it is concluded that the polymerization is initiated by the nitroethylene radical anion generated by the slow dissociation of the electron donor–acceptor (EDA) complexes between the solvent molecule and the monomer. The activation energy for the rate of polymerization was 50 and 29 kJ/mole in DMF and DMSO, respectively, which seems to be determined primarily by the dissociation of the EDA complexes. The significant features of this polymerization are that the initiation proceeds slowly and there is essentially no termination.     

Thermochromism of poly-1-butene gels

Poly-1-butene gels in some solvents of benzene-derivatives show a colouring phenomenon. The colour changes from blue to yellow under irradiation of natural light as the temperature rises from the melting point of the solvent to the sol-gel transition temperature. The colouring phenomenon is due to selective scattering, but not to optical absorption. The apparent characteristics of the phenomenon resemble the thermochromism of cholesteric liquid crystals, although poly-1-butene itself is colourless and has no asymmetric carbons.     

Stability Constants for 1:1 Complexes Formed between2-hydroxypropyl-β-Cyclodextrin with an Average Substitution Degree of 4.4 and Benzene and Alkylbenzenes as Guests by Modified Static Head-Space Gas Chromatography Method

Modified static head-space gas chromatography method (M-SHSGC method) was used to determine the stability constants of benzene and alkylbenzenes with 2-hydroxypropyl-β-cyclodextrin inclusion complexes. The 1:1 stability constants were in agreement with those obtained by conventional SHSGC method. The M-SHSGC method precludes the necessity of the calibration curve by the use of Henry’s law constant of guest. Consequently, it is more advantageous than conventional SHSGC method because the time required to determine the stability constant is markedly reduced.