Kolmogorov–Sinaj Entropy on MV-Algebras

There is given a construction of the entropy of a dynamical system on arbitrary MV-algebra M. If M is the MV-algebra of characteristic functions of a σ-algebra (isomorphic to the σ-algebra), then the construction leads to the Kolmogorov–Sinaj entropy. If M is the MV-algebra (tribe) of fuzzy sets, then the construction coincides with the Maličky modification of the Kolmogorov–Sinaj entropy for fuzzy sets (Maličky and Riečan, 1986; Riečan and Mundici, 2002; Riečan and Neubrunn, 1997).     

Remarks on Chern–Simons Invariants

The perturbative Chern–Simons theory is studied in a finite-dimensional version or assuming that the propagator satisfies certain properties (as is the case, e.g., with the propagator defined by Axelrod and Singer). It turns out that the effective BV action is a function on cohomology (with shifted degrees) that solves the quantum master equation and is defined modulo certain canonical transformations that can be characterized completely. Out of it one obtains invariants.     

Remarks on 2–q-bit states

We distinguish six classes of families of locally equivalent states in a straightforward scheme for classifying all 2–q-bit states; four of the classes consist of two subclasses each. The simple criteria that we stated recently for checking a given state’s positivity and separability are justified, and we discuss some important properties of Lewenstein–Sanpera decompositions. An upper bound is conjectured for the sum of the degree of separability of a 2–q-bit state and its concurrence. Received: 17 July 2000 / Published online: 6 December 2000     

More on the dilatonic Einstein–Gauss–Bonnet gravity

Einstein–Gauss–Bonnet gravity coupled to a dynamical dilaton is examined from the viewpoint of Einstein’s equivalence principle. We point out that the usual frame change that applies to the action without curvature correction does not cure the problem of nonminimal couplings by the dynamical nature of a dilaton field. Thus a modification of the Einstein frame is required. It is proposed that the kinetic term of a dilaton should be brought to a canonical form, which completely fixes the additional terms associated with the frame transformation.     

Some remarks on the Dirac–Witten operator on pseudo-Riemannian manifolds

In this paper, we get optimal lower bounds for the eigenvalues of the Dirac–Witten operator. These estimates are given in terms of the intrinsic and extrinsic curvature expressions. In the limiting case, we prove that the spacelike submanifold is Einstein if the normal bundle is flat.     

Plasmonic modulator based on gain-assisted metal–semiconductor–metal waveguide

We investigate plasmonic modulators with gain material to be implemented as ultra-compact and ultra-fast active nanodevices in photonic integrated circuits. We analyze metal–semiconductor–metal (MSM) waveguides with InGaAsP-based active material layers as ultra-compact plasmonic modulators. The modulation is performed by changing the gain of the core, that results in different transmittance through the waveguides. A MSM waveguide enables high field localization and therefore high modulation speed. Bulk semiconductor, quantum wells and quantum dots, arranged in either horizontal or vertical layout, are considered as the core of the MSM waveguide. Dependences on the waveguide core size and gain values of various active materials are studied. The designs consider also practical aspects like n- and p-doped layers and barriers in order to obtain close to reality results. The effective propagation constants in the MSM waveguides are calculated numerically. Their changes in the switching process are considered as a figure of merit. We show that a MSM waveguide with electrical current control of the gain incorporates compactness and deep modulation along with having a reasonable level of transmittance.     

Gauss–Bonnet term on vacuum decay

We study the effect of the Gauss–Bonnet term on vacuum decay process in the Coleman–De Luccia formalism. The Gauss–Bonnet term has an exponential coupling with the real scalar field, which appears in the low energy effective action of string theories. We calculate numerically the instanton solution, which describes the process of vacuum decay, and obtain the critical size of bubble. We find that the Gauss–Bonnet term has a nontrivial effect on the false vacuum decay, depending on the Gauss–Bonnet coefficient.     

Fabry–Perot effect on dimer nanoantennas

In this work, we investigate the interaction between a single quantum emitter and dimer nanoantennas through a Fabry–Perot structure composed of an appropriate combination of two dielectric layers. This type of dielectric configuration is well known in the microwave region to increase the antenna performance, such as directivity, radiation efficiency, and radiation resistance. Here, the Fabry–Perot concept is transposed to the optical domain. The single emitter couples to the antenna through the dielectric structure, giving rise to a wide aperture field on top of the dielectrics with the same polarization of the emitter. This purely polarized aperture field can be used to excite one or more conveniently spaced nanoantennas. We demonstrate by 3D numerical calculations that the directivity and excitation rate of a single dimer is highly increased. Also, we show that multiple dimers arranged in an array configuration can be enhanced due to the wide aperture field generated by a single emitter.     

Yang–Mills on Quantum Heisenberg Manifolds

In the noncommutative geometry program of Connes, there are two variations of the concept of the Yang–Mills action functional. We show that for the quantum Heisenberg manifolds for generic parameter values they agree.     

Geometric bounds on Kaluza–Klein masses

We point out geometric upper and lower bounds on the masses of bosonic and fermionic Kaluza–Klein excitations in the context of theories with large extra dimensions. The characteristic compactification length scale is set by the diameter of the internal manifold. Based on geometrical and topological considerations, we find that certain choices of compactification manifolds are more favored for phenomenological purposes. Received: 11 August 2000 / Revised version: 30 January 2001 / Published online: 3 May 2001     

Effects of thermal fluctuations on the Kerr–Newman–NUT–AdS black hole

This paper is devoted to studying the impact of thermal fluctuations on thermodynamics of rotating as well as charged anti-de Sitter black holes with the Newman–Unti–Tamburino(NUT)parameter. To this end, we derive the analytic expression of thermodynamic variables, namely the Hawking temperature, volume, angular velocity, and entropy within the limits of extended phase space. These variables meet the first law of thermodynamics as well as the Smarr relation in the presence of new NUT charge. To analyze the effects of quantum fluctuations, we derive the exact expression of corrected entropy, which yields modification in other thermodynamical equations of state. The local stability and phase transition of the considered black hole are also examined through specific heat. It is found that the NUT parameter increases the stability of small black holes, while the logarithmic corrections induce instability in the system.     

Gauss–Bonnet dark energy on Hořava–Lifshitz cosmology

We investigate the Gauss–Bonnet dark energy model and its deformed version on Ho?ava–Lifshitz cosmology, which belongs to the class of cosmologies obtained from the so-called projectable version of Ho?ava–Lifshitz gravity. In particular, we investigate the bulk/boundary interaction in this scenario through the Q function, which we interpret as a measure of the energy transference between the bulk and the spacetime boundary. Then we discuss whether the thermal equilibrium will be stable or not, once it is reached, and the validity of the generalized second law. We show that the Q function can exhibit sign changes along the cosmic evolution and the Universe reaches the thermal equilibrium as a transient phenomenon.     

Investigations on ultrafast welding of glass–glass and glass–silicon

Using ultrafast laser radiation glass substrates are welded with glass and silicon plates. The pump beam is focused by a microscope objective with large NA=0.4 (beam diameter 4 μm) into the glass. After partial absorption of the optical energy, the glass is heated and melted. Procedures for high-quality welding of glass–glass and glass–silicon substrates with high-repetition ultra-fast laser radiation have been derived at the repetition rate 700 kHz. The dependencies of the dimension and geometry of the welding seam on scan velocity, repetition rate and pulse energy have been investigated defining a process window. Adding a noninterferometric technique for quantitative phase detection with the welding setup, the interaction zone of the welding seam for the welding partners glass–glass is detected. A change in refractive index is induced by heating and compression of the glass and has been detected by phase detection up to 2 μs after irradiation with 100 fs time resolution.     

Remarks on Chern–Simons–Dirac Equations in One Space Dimension

We prove global existence of solutions to Chern–Simons–Dirac equations under the gauge condition \({A_1 \equiv 0}\) . We also find a solitary wave solution and derive L ^∞ bound of the solution by applying local form of charge conservation.     

Investigation on bulk Nd–Fe–Al amorphous/nano-crystalline alloy

Cylindrical ingots of bulk amorphous Nd₇₀Fe₂₀Al₁₀ with a diameter of 8 mm were prepared by a copper mold casting method. It was proved experimentally with X-ray diffraction, scanning electron microscopy and differential scanning calorimetry that the as-prepared alloy samples consisted mainly of the amorphous phase with a minute amount of nano-crystalline phase. The onset crystallization temperature (T_x) and the melting temperature (T_m) of the samples were 743 and 823 K, respectively, from DSC results. The temperature interval between T_x and T_m, ΔT=T_m−T_x, is 80 K and the resulting ratio of T_x/T_m is 0.90. Both a high T_x/T_m ratio and a small ΔT are considered the reasons for the good glass-forming ability. The Curie temperature (T_c) of these samples was 525 K from magneto-thermal gravimetric analysis. This measured value is higher than the highest T_c among binary Nd–Fe amorphous alloys. Annealing treatments were carried out for the as-cast samples to obtain dual-phase samples with different volume fractions of nano-crystalline phase. Magnetic measurement results indicated that the hard magnetic behavior is weakest for samples with 40% of nano-crystalline phase. The curve of the measured hysteresis loop area versus the volume fraction of nano-crystalline phase concaves upward, which agrees with what we predicated in our previous simulation results.     

A Riemann–Hilbert Approach to Complex Sharma–Tasso–Olver Equation on Half Line

In this paper, the Fokas unified method is used to analyze the initial-boundary value problem of a complex Sharma–Tasso–Olver(c STO) equation on the half line. We show that the solution can be expressed in terms of the solution of a Riemann–Hilbert problem. The relevant jump matrices are explicitly given in terms of the matrix-value spectral functions spectral functions {a(λ), b(λ)} and {A(λ), B(λ)}, which depending on initial data u_0(x) = u(x, 0) and boundary data g_0(y) = u(0, y), g_1(y) = ux(0, y), g_2(y) = u_(xx)(0, y). These spectral functions are not independent, they satisfy a global relation.     

Euler–Poincaré Reduction on Principal Bundles

Let : P M be an arbitrary principal G-bundle. We give a full proof of the Euler–Poincaré reduction for a G-invariant Lagrangian L: J ¹ P R as well as the study of the second variation formula, the conservations laws, and study some of their properties.     

Structural-colored silk based on Ti–Si bilayer

In this Letter, Ti–Si bilayer was deposited on white silk to achieve coloration of the silk. By controlling the thickness of the Ti layer and Si layer, the saturation and the hue of the color on the silk could be preciously modulated, respectively. The structural colors on the silk could cover the major colors in the International Commission on Illumination 1931 chromaticity diagram, and it exhibits good durability, which is demonstrated by rubbing and stretching treatments. The developed textile coloration method may provide an eco-friendly technology in the silk dyeing industry.