Fixed Point Tehorems in Fuzzy Inner Product Spaces

In this paper, we obtain some new fixed point theorems in fuzzy-Banach spaces by considering the t-norms of h-type and a linear mapping of weakly demicompact.     

Two new electronic transitions of Bi2

The absorption spectra of Bi₂ molecule has been obtained in the region 3166–3380 Å in the second order of a 3.4 m Ebert Spectrograph with a reciprocal dispersion of 2.6 Å/mm. The bands obtained are found to belong to two new systems named G-X and J-X. Vibrational analysis is performed and computer methods have been used to determine the molecular constants.     

Dynamics of laser-induced cavitation in liquid

This paper presents an analysis of the rate of bubble expansion and an estimate of maximum bubble diameter and bubble lifetime prior to collapse. Such data are needed for the optimization of system parameters for elemental analysis in water by laser-induced breakdown spectroscopy (LIBS). Two techniques were used for this study: pump-probe beam deflection and high-speed photography. Plasma in the water bulk was generated by a focussed laser pulse with energy of 140 mJ and pulse duration of 10 ns, operating at the fundamental Nd:YAG laser wavelength (1064 nm). Reasonable agreement on the value of maximum bubble diameter was obtained between the photographic and probe beam deflection results. Reasonable agreement for the total duration of the oscillating cavitation bubble was also obtained for the two techniques, with a mean value of ∼800 μs. A comparison between empirical results and predictions based on the Rayleigh equation is also presented.     

Electrical Resistance of the Low Dimensional Critical Branching Random Walk

We show that the electrical resistance between the origin and generation n of the incipient infinite oriented branching random walk in dimensions d < 6 is O(n ^1-α ) for some universal constant α > 0. This answers a question of Barlow et al. (Commun Math Phys 278:385–431, 2008).     

Slightly subcritical hypercube percolation

We study bond percolation on the hypercube {0,1}^m in the slightly subcritical regime where p = p_c(1 ? ε_m) and ε_m = o(1) but ε_m ? 2^?m/3 and study the clusters of largest volume and diameter. We establish that with high probability the largest component has cardinality , that the maximal diameter of all clusters is , and that the maximal mixing time of all clusters is . These results hold in different levels of generality, and in particular, some of the estimates hold for various classes of graphs such as high‐dimensional tori, expanders of high degree and girth, products of complete graphs, and infinite lattices in high dimensions.     

Wirelessly powered dielectrophoresis of metal oxide particles using spark-gap Tesla coil

Wirelessly powered dielectrophoresis (DEP) of metal oxide particles was performed using a spark-gap Tesla coil (TC). The main contribution of this work is the simplification of the conventional DEP setup that requires attaching wires directly to the electrodes. Wireless power from the TC generates a high output frequency and voltage, which corresponds to that used for the DEP. Therefore, a spark-gap TC was built and utilized to conduct the DEP process. Metal oxides (ZnO and Fe₂O₃) were used as targets for the assembly. The results showed that the wirelessly powered DEP technique via a TC was successful in assembling the metal oxide particles. Positive and negative DEP phenomena were observed. Positive DEP occurred during ZnO assembly, making particles chain grow 0.92 mm toward the sparks within 60 s. Negative DEP was observed during Fe₂O₃ assembly, where the repulsion of particles formed a void around the sparks with a 1.45 mm radius. The mechanism of this wireless DEP system is discussed.     

Divergence of Geodesics in Teichmüller Space and the Mapping Class Group

We show that both Teichmüller space (with the Teichmüller metric) and the mapping class group (with a word metric) have geodesic divergence that is intermediate between the linear rate of flat spaces and the exponential rate of hyperbolic spaces. For every two geodesic rays in Teichmüller space, we find that their divergence is at most quadratic. Furthermore, this estimate is shown to be sharp via examples of pairs of rays with exactly quadratic divergence. The same statements are true for geodesic rays in the mapping class group. We explicitly describe efficient paths “near infinity” in both spaces.     

Kinetics and thermodynamics of adsorption of congo red on cellulose

Thermodynamics and kinetics of adsorption of congo red (CR) on cellulose are studied at 308–328 K. In the used concentration range of CR, interaction of CR with cellulose is exothermic and CR molecules adsorb chemically on cellulose surface. The effects of contact time, temperature and initial concentration of CR on kinetics of its adsorption on cellulose were investigated. The process proceeds according to the pseudo-second-order equation. Initial adsorption rate of adsorption is first-order in CR and the intraparticle diffusion of CR molecules within cellulose is identified as the main rate-limiting step.