Compatibility and Marginality

We present a way of introducing joint distibution function and its marginal distribution functions for non-compatible observables. Each such marginal distribution function has the property of commutativity. Models based on this approach can be used to better explain some classical phenomena in stochastic processes.     

Low noise optical receiver with multi-octave bandwidth

Optical and Quantum Electronics - A new approach for the design and construction of low noise broadband optical receivers is presented utilizing distributed amplification based on hybrid integrated...     

Gradient- and Sensitivity-Enhanced TOCSY Experiments

A pulsed field gradient version of the sensitivity-enhanced 2D TOCSY experiment is proposed which yields high-quality spectra with improved sensitivity and a minimum of two scans pert₁increment. For rapid acquisition of 1D TOCSY spectra, the 1D DPFGSE–TOCSY experiment was modified to include phase-encoded multiple-selective excitation followed by a simple spectral editing. Combination of these two building blocks is used in a sensitivity-enhanced 2D analog of the 3D TOCSY–TOCSY experiment which provides an efficient tool for resolving severely overlapped signals of oligomers in short experimental time.     

The surface electronic structure of Ag8Au4 superlattice

We present the calculations of electronic structure and photoemission spectra for a lattice-matched Ag-Au(111) superlattice. The selfconsistent band structure exhibits a superlattice gap at about 1 eV below the Fermi level. A surface state is found in this gap and its dispersion properties are investigated. Its energy location is varied with location of surface terminating plane within the superlattice period. The calculated normal photoemission spectra explain well available experimental data.     

Newtonian limits of warp drive spacetimes

We find a class of warp drive spacetimes possessing Newtonian limits, which we then determine. The same method is used to compute Newtonian limits of the Schwarzschild solution and spatially flat Friedmann-Robertson-Walker cosmological models. This work was partially supported by FCT/POCTI/FEDER.     

Zeroth and second laws of thermodynamics simultaneously questioned in the quantum microworld

A new and rather trivial model is suggested with mechanism that implies simultaneous violation of the zeroth and the second laws of thermodynamics. Mathematically rigorous quantum theory reduces to a trivial application of the Golden rule formula. It yields exciton on-energy-shell diffusion caused by bath-nonassisted excitation hopping between tails of different exciton site levels ε₁ < ε₂ broadened by bath-assisted finite life-time effects. The elastic character of the hopping implies 1 ↔ 2-symmetric transfer rate W. Thus the net diffusion exciton flow W(P ₁ - P ₂) and also, as argued, the net energy flow are possible due to different near-to-equilibrium exciton populations P ₁ > P ₂. As the sites are provided with two different baths, the population imbalance and the flows survive even for slightly different local bath temperatures T ₁ < T ₂ < T ₁ε₂/ε₁. Thus spontaneous exciton and also energy flows against temperature step become possible, in contradiction with the Clausius form of the second law. Violations of both the laws disappear in the high-temperature, i.e. classical limit Received 16 May 2001 and Received in final form 20 September 2001     

On the Cartan–Jacobson Theorem

The well-known Cartan–Jacobson theorem claims that the Lie algebra of derivations of a Cayley algebra is central simple if the characteristic is not 2 or 3. In this paper we have studied these two cases, with the following results: if the characteristic is 2, the theorem is also true, but, if the characteristic is 3, the derivation algebra is not simple. We have also proved that in this last case, there is a unique nonzero proper seven-dimensional ideal, which is a central simple Lie algebra of type A₂, and the quotient of the derivation algebra modulo this ideal turns out to be isomorphic, as a Lie algebra, to the ideal itself. The original motivation of this work was a series of computer-aided calculations which proved the simplicity of derivation algebras of Cayley algebras in the case of characteristic not 3. These computations also proved the existence of a unique nonzero proper ideal (which turns out to be seven-dimensional) in the algebra of derivations of split Cayley algebras in characteristic 3.     

A multivalued version of Sharkovskiĭ’s theorem holds with at most two exceptions

A multivalued version of Sharkovskiĭ’s theorem is formulated for M-maps on linear continua and, more generally, for triangular M-maps on a Cartesian product of linear continua. This improves the main result of [AP1] in the sense that our multivalued analogue holds with at most two exceptions. A further specification requires some additional restrictions. For instance, 3- orbits of m-maps imply the existence of k-orbits for all k ? \mathbbNk \in {\mathbb{N}} , except possibly for k ?k \in {4, 6}. It is also shown that, on every connected linearly ordered topological space, an M-map with orbits of all periods can always be constructed. This demonstrates that Baldwin’s classification of linear continua in terms of admissible periods [Ba] is useless for multivalued maps.     

Problems of an additional experiment

In some situations estimates of unknown parameters must be corrected by additional measurements. It is in principle no problem to calculate the corrected estimates, however, it is of more interest to find formulae for correction itself. The formulae enable us to design an additional experiment and to judge its usefulness. The aim of the paper is to find such formulae for several situations. Supported by the grant of the Council of Czech Government MSM 6 198 959 214.