Multi-fuzzy sets: An extension of fuzzy sets

In this paper we propose a method to construct more general fuzzy sets using ordinary fuzzy sets as building blocks. We introduce the concept of multi-fuzzy sets in terms of ordered sequences of membership functions. The family of operations T, S, M of multi-fuzzy sets are introduced by coordinate wise t-norms, s-norms and aggregation operations. We define the notion of coordinate wise conjugation of multifuzzy sets, a method for obtaining Atanassov’s intuitionistic fuzzy operations from multi-fuzzy sets. We show that various binary operations in Atanassov’s intuitionistic fuzzy sets are equivalent to some operations in multi-fuzzy sets like M operations, 2-conjugates of the T and S operations. It is concluded that multi-fuzzy set theory is an extension of Zadeh’s fuzzy set theory, Atanassov’s intuitionsitic fuzzy set theory and L-fuzzy set theory.     

Enhanced switching law for synchronized switch damping on inductor with bimodal excitation

Piezoelectric shunt damping is an emerging field of research. In recent years, a multitude of different electrical circuits have been developed aiming to increase the damping performance and robustness. Synchronized switch damping on inductor (SSDI) is a semi-active control technique that utilizes a passive inductance to build-up a voltage on the piezoceramics that is synchronized with the mechanical vibration. For a single mode excitation the voltage inversion should occur at the moments of maximum deformation, but for multimodal vibrations such a switching law may not be optimal.In this paper a novel switching law for bimodal vibrations is presented using a modal observer. An enhanced voltage build-up is generated by utilizing the vibration energy of the second mode. The amplification of dissipated energy is calculated in an analytical way using normalized parameters, yielding a general result which includes the influence of the frequency and amplitude ratio of the excitation signal. Measurements on a clamped beam test rig are conducted in order to validate the proposed method. An increase of nearly 350 percent in energy dissipation compared to the classical SSDI has been achieved. Furthermore, the increase in energy dissipation is higher than for a previously suggested, comparable switching law.     

Option Pricing in Subdiffusive Bachelier Model

The earliest model of stock prices based on Brownian diffusion is the Bachelier model. In this paper we propose an extension of the Bachelier model, which reflects the subdiffusive nature of the underlying asset dynamics. The subdiffusive property is manifested by the random (infinitely divisible) periods of time, during which the asset price does not change. We introduce a subdiffusive arithmetic Brownian motion as a model of stock prices with such characteristics. The structure of this process agrees with two-stage scenario underlying the anomalous diffusion mechanism, in which trapping random events are superimposed on the Langevin dynamics. We find the corresponding fractional Fokker-Planck equation governing the probability density function of the introduced process. We construct the corresponding martingale measure and show that the model is incomplete. We derive the formulas for European put and call option prices. We describe explicit algorithms and present some Monte-Carlo simulations for the particular cases of α-stable and tempered α-stable distributions of waiting times.     

Coherent interaction of a single fermion with a small bosonic field

We have experimentally studied few-body impurity systems consisting of a single fermionic atom and a small bosonic field on the sites of an optical lattice. Quantum phase revival spectroscopy has allowed us to accurately measure the absolute strength of Bose-Fermi interactions as a function of the interspecies scattering length. Furthermore, we observe the modification of Bose-Bose interactions that is induced by the interacting fermion. Because of an interference between Bose-Bose and Bose-Fermi phase dynamics, we can infer the mean fermionic filling of the mixture and quantify its increase (decrease) when the lattice is loaded with attractive (repulsive) interspecies interactions.     

Theory of light amplification in active fishnet metamaterials

We establish a theory that traces light amplification in an active double-fishnet metamaterial back to its microscopic origins. Based on ab initio calculations of the light and plasmon fields we extract energy rates and conversion efficiencies associated with gain and loss channels directly from Poynting's theorem. We find that for the negative refractive index mode both radiative loss and gain outweigh resistive loss by more than a factor of 2, opening a broad window of steady-state amplification (free of instabilities) accessible even when a gain reduction close to the metal is taken into account.     

Surface interactions of molecular C60 and impact on Ni(100) and Co(0001) film growth: A scanning tunneling microscopy study

Here, the interactions of C₆₀ at the surface of pseudomorphic Ni/Cu(100) and Co/Ru(0001) thin films and its effect on film growth and morphology were determined using in-situ scanning tunneling microscopy (STM) and Auger electron spectroscopy (AES). The novel development of C₆₀-metallic based nanosystems, such as C₆₀ molecular junction transistors, hinges on our ability to understand the factors governing structural stability in these nanosystems and the nature of the bond interactions at the C₆₀–metal interface. In this study, C₆₀ deposited onto the Ni(100) film surface is observed to be fairly immobile and uniformly distributed across the Ni surface. On the Co(0001) film surface however, C₆₀ mobility is observed to be severely limited in some regions and highly mobile in others dependent upon Co film surface reconstruction, resulting in a non-uniform distribution of C₆₀ across the Co film surface. Despite the presence of C₆₀ on the Ni surface, there is no obvious influence of the C₆₀ on further Ni film growth. In contrast, during Co film growth, islands only nucleate and grow from step edges or locally around C₆₀ molecules. The strength of the Co–C₆₀ bond interaction appears stronger than the Co–Co bond on Co film terrace. Generally, the Ni and Co films both continue epitaxial film growth in the presence of molecular C₆₀. AES results indicate the C₆₀ molecules maintain their chemical integrity during growth.     

High-efficiency frequency doubling of continuous-wave laser light

We report on the observation of high-efficiency frequency doubling of 1550?nm continuous-wave laser light in a nonlinear cavity containing a periodically poled potassium titanyl phosphate crystal (PPKTP). The fundamental field had a power of 1.10?W and was converted into 1.05?W at 775?nm, yielding a total external conversion efficiency of 95±1%. The latter value is based on the measured depletion of the fundamental field being consistent with the absolute values derived from numerical simulations. According to our model, the conversion efficiency achieved was limited by the nonperfect mode matching into the nonlinear cavity and by the nonperfect impedance matching for the maximum input power available. Our result shows that cavity-assisted frequency conversion based on PPKTP is well suited for low-decoherence frequency conversion of quantum states of light.     

In vitro reconstitution of eukaryotic ion channels using droplet interface bilayers

The ability to routinely study eukaryotic ion channels in a synthetic lipid environment would have a major impact on our understanding of how different lipids influence ion channel function. Here, we describe a straightforward, detergent-free method for the in vitro reconstitution of eukaryotic ion channels and ionotropic receptors into droplet interface bilayers and measure their electrical activity at both the macroscopic and single-channel level. We explore the general applicability of this method by reconstitution of channels from a wide range of sources including recombinant cell lines and native tissues, as well as preparations that are difficult to study by conventional methods including erythrocytes and mitochondria.     

Observations of PDDTT subject to thermal treatment: correlation between performance and order

We show that polybis(thienyl)thienodia-thiazolethiophene (PDDTT), a high-performance semiconducting polymer for photodetectors and field-effect transistors, has strong performance dependence on annealing temperature. An unprecedented increase of 3 orders of magnitude is observed in both transistor and photoconductive properties. XRD and AFM evidence points to increased ordering in PDDTT films with annealing. This correlation highlights the importance that order has in determining performance in PDDTT and has possible implications in the design of polymers.