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.     

Coherent backscattering of light from saturated atoms

We survey recent progress achieved in understanding the impact of inelastic processes on coherent backscattering of light from cold atoms that are saturated by a powerful laser field.     

On the interpretation of the racemic states of the B 2 phase of banana-shaped mesogens

We show that the racemic states of the B 2 phase of liquid crystals composed of banana-shaped molecules do not satisfy the Curie principle. Thus it is argued that these states cannot exist in bulk samples and the homochiral states constitute the only stable microscopic structures. A reinterpretation of the racemic states with the same macroscopic optical behaviour is proposed in terms of mixtures of the homochiral structures.     

Operational characteristics and power scaling of a transverse flow transversely excited CW CO<Subscript>2</Subscript> laser

Transverse flow transversely excited (TFTE) CO₂ lasers are easily scalable to multikilowatt level. The laser power can be scaled up by increasing the volumetric gas flow and discharge volume. It was observed in a TFTE CW CO₂ laser having single row of pins as an anode and tubular cathode that the laser power was not increasing when the discharge volume and the gas volumetric flow were increased by increasing the electrode separation keeping the gas flow velocity constant. The discharge voltage too remained almost constant with the change of electrode separation at the same gas flow velocity. This necessitated revision of the scaling laws for designing this type of high power CO₂ laser. Experimental results of laser performance for different electrode separations are discussed and the modifications in the scaling laws are presented.     

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.     

Mixing characteristics of motionless mixers

Motionless mixers have found a large range of applications, including blending, reaction, dispersion, heat transfer and mass transfer. Understanding the mixing processes that occur in these diverse systems is essential for predicting many aspects of practical importance. The objective of this study is to perform the experimental investigations of mixing characteristics for three different motionless mixers. The red color dye tracer was mixed in the main stream of green hair styling gel, and then the mixing efficiency was quantified by calculating the percentage area concentration of red color at the outlet cross section using a digital image processing technique. In the Sulzer SMX and YHC mixer, a single element mixes the fluid nearly in two dimensions, and three-dimensional mixing is accomplished by the next elements aligned at 90o to their former one. In the Sulzer SMX mixer, the flow appears to be globally well mixed after 5 elements, while in the YHC and YNU mixers, it is necessary to globally well mix more than 1 and 2 elements.     

First measurement of the ϱ spectral function in nuclear collisions

The NA60 experiment at the CERN SPS has studied low-mass muon pairs in 158 A GeV In–In collisions. A strong excess of pairs is observed above the yield expected from neutral meson decays. The unprecedented sample size close to 400000 events and the good mass resolution of about 2% made it possible to isolate the excess by subtraction of the decay sources. The shape of the resulting mass spectrum shows some non-trivial centrality dependence, but is largely consistent with a dominant contribution from π⁺π^-→ϱ→μ⁺μ^- annihilation. The associated ϱ spectral function exhibits considerable broadening, but essentially no shift in mass. The p_T-differential mass spectra show the excess to be much stronger at low p_T than at high p_T. The results are compared to theoretical model predictions; they tend to rule out models linking hadron masses directly to the chiral condensate. PACS 25.75.-q; 12.38.Mh; 13.85.Qk     

Multi-parton cross sections at hadron colliders

We present an alternative method to calculate cross sections for multi-parton scattering processes in the standard model at leading order. The helicity amplitudes are computed using recursion relations in the number of particles, based on the Dyson–Schwinger equations, whereas the summation over colour and helicity configurations is performed by Monte Carlo methods. The computational cost of our algorithm grows asymptotically as 3ⁿ, where n is the number of particles involved in the process, as opposed to the n!-growth of the Feynman diagram approach. Typical results for the total cross section, the differential distributions of the invariant masses and the transverse momenta of the partons are presented and cross checked by explicit summation over colours.     

Study of interactions of various ionic species with solvents toward the design of receptors

In earlier studies, the interactions of isolated ionic species with various solvents were investigated using ab initio calculations. The ionic species investigated included cations (proton, hydronium, ammonium, and metal cations) and anions (single electron, hydroxide, and halide anions). However in the present study, we investigate the interactions of these ionic species with the solvent in the presence of other competing ionic species. We also elaborate on how the information obtained from these extensive studies have been employed in designing and synthesizing various kinds of novel ionophores and receptors.