On the geometry of infinite cyclic subgroups

In this paper we construct an example of a word metric on an infinite cyclic subgroup. This example shows that subexponential distortion does not obstruct non-trivial growth of connected radii. This answers a question of Gromov [6]. The constructed metric has other pathological properies. Specifically, its asymptotic cone depends on the choice of ultrafilter and scaling sequence. The work has been partially supported by the Swiss National Science Foundation.     

Dubrovin Valuation Skew Group Rings

Some equivalent characterizations for a skew group ring to be a Dubrovin valuation ring are given. Among them all the prime ideals of a Dubrovin valuation skew group ring are characterised. Received June 8, 1999, Revised June 4, 2001, Accepted July 20, 2001     

On a Delay Reaction-Diffusion Difference Equation of Neutral Type

In this paper, we first consider a delay difference equation of neutral type of the form: Δ(y _n + py _n−k + q _n y _n−l = 0 for n∈ℤ⁺(0) (1*) and give a different condition from that of Yu and Wang (Funkcial Ekvac, 1994, 37(2): 241–248) to guarantee that every non-oscillatory solution of (1*) with p = 1 tends to zero as n→∞. Moreover, we consider a delay reaction-diffusion difference equation of neutral type of the form: Δ₁(u _n,m + pu _n−k,m ) + q _n,m u _n−l,m = a ²Δ² ₂ u _{n +1, m−1} for (n,m) ∈ℤ⁺ (0) ×Ω, (2*) study various cases of p in the neutral term and obtain that if p≥−1 then every non-oscillatory solution of (2*) tends uniformly in m∈Ω to zero as n→∞; if p = −1 then every solution of (2*) oscillates and if p < −1 then every non-oscillatory solution of (2*) goes uniformly in m∈Ω to infinity or minus infinity as n→∞ under some hypotheses. Received July 14, 1999, Revised August 10, 2000, Accepted September 30, 2000     

Preparation and dielectric properties of the lead-free BaFe<Subscript>1/2</Subscript>Nb<Subscript>1/2</Subscript>O<Subscript>3</Subscript> ceramics obtained from mechanically triggered powder

In the paper the influence of mechanical activation of the powder on the final dielectric properties lead-free Ba(Fe_1/2Nb_1/2)O₃ (BFN) ceramic was examined. The BFN ceramics were obtained by 3-steps route. Firstly, the substrates were pre-homogenized in a planetary ball mill. Than, the powder was activated in vibratory mill (the shaker type SPEX 8000 Mixer Mill) for different duration between 25 h and 100 h. The influence of the milling time on the BFN powder was monitored by X-ray diffraction. The diffraction data confirmed that the milling process of the starting components is accompanied by partial synthesis of the BFN materials. The longer of the high-energy milling duration the powders results in increasing the amount of amorphous/nanocrystalline content. The mechanically activated materials were sintered in order to obtain the ceramic samples. During this temperature treatment the final crystallisation of the powder appeared what was confirmed by XRD studies. The performed dielectric measurements have revealed the reduction of the dielectric loss of the BFN ceramics compared to materials obtained by classic methods.     

Extended s-wave pairing symmetry on the triangular lattice heavy fermion system

We investigate the pairing symmetry of the Kondo-Heisenberg model on triangular lattice, which is believed to capture the core competition of Kondo screening and local magnetic exchange interaction in heavy electron compounds. On the dominant background of the heavy fermion state, the introduction of the Heisenberg antiferromagnetic interaction (J _H ) leads to superconducting pairing instability. Depending on the strength of the interactions, it is found that the pairing symmetry favours an extended s-wave for small J _H and high conduction electron density but a chiral \(d_{x^2 - y^2 } + id_{xy}\)-wave for large J _H and low conduction electron density, which provides a phase diagram of pairing symmetry from the calculations of the ground-state energy. The transition between these two pairing symmetries is found to be first-order. Furthermore, we also analyze the phase diagram from the pairing strengths and find that the phase diagram obtained is qualitatively consistent with that based on the ground-state energy. In addition, we propose an effective single-band BCS Hamiltonian, which is able to describe the low-energy thermodynamic behaviors of the heavy fermion superconducting states. These results further deepen the understanding of the antiferromagnetic interaction which results in a geometric frustration for the model studied. Our work may provide a possible scenario to understand the pairing symmetry of the heavy fermion superconductivity, which is one of active issues in very recent years.     

Effect of rotation in lubrication problems: Existence of more fundamental solutions

A generalized Reynolds equation is derived in the present paper by taking into account the effect of rotation in lubrication problems. The existence of certain fundamental solutions is shown in this extended framework which is not allowed in the classical Reynolds theory. Results concerning the pressure and the load capacity of the resulting bearing system are obtained and interpreted in the respective cases when the film thickness is a linear or an exponential functions of the coordinate along the bearing length. One of the important results is that while the load capacity decreases with increasing values of α for an exponentially inclined slider in the classical Reynolds theory, it increases with increasing values of α in the present context.     

Gravitational phase transitions with an exclusion constraint in position space

We discuss the statistical mechanics of a system of self-gravitating particles with anexclusion constraint in position space in a space of dimension d. Theexclusion constraint puts an upper bound on the density of the system and can stabilize itagainst gravitational collapse. We plot the caloric curves giving the temperature as afunction of the energy and investigate the nature of phase transitions as a function ofthe size of the system and of the dimension of space in both microcanonical and canonicalensembles. We consider stable and metastable states and emphasize the importance of thelatter for systems with long-range interactions. For d ≤ 2, there is nophase transition. For d > 2, phase transitions can take place betweena “gaseous” phase unaffected by the exclusion constraint and a “condensed” phase dominatedby this constraint. The condensed configurations have a core-halo structure made of a“rocky core” surrounded by an “atmosphere”, similar to a giant gaseous planet. For largesystems there exist microcanonical and canonical first order phase transitions. Forintermediate systems, only canonical first order phase transitions are present. For smallsystems there is no phase transition at all. As a result, the phase diagram exhibits twocritical points, one in each ensemble. There also exist a region of negative specificheats and a situation of ensemble inequivalence for sufficiently large systems. We showthat a statistical equilibrium state exists for any values of energy and temperature inany dimension of space. This differs from the case of the self-gravitating Fermi gas forwhich there is no statistical equilibrium state at low energies and low temperatures whend ≥ 4. By a proper interpretation of the parameters, our results haveapplication for the chemotaxis of bacterial populations in biology described by ageneralized Keller-Segel model including an exclusion constraint in position space. Theyalso describe colloids at a fluid interface driven by attractive capillary interactionswhen there is an excluded volume around the particles. Connexions with two-dimensionalturbulence are also mentioned.     

Effect of incommensurate potential on the resonant tunneling through Majorana bound states on the topological superconductor chains

We study the transport through the Kitaev chain with incommensurate potentials coupled to two normal leads by the numerical operator method. We find a quantized linear conductance of e ² / h, which is independent to the disorder strength and the gate voltage in a wide range, signaling the Majorana bound states. While the incommensurate potential suppresses the current at finite voltage bias, and then narrows the linear response regime of the I-V curve which exhibits two plateaus corresponding to the superconducting gap and the band edge, respectively. The linear conductance abruptly drops to zero as the disorder strength reaches the critical value 2g _s + 2Δ with Δ the p-wave pairing amplitude and g _s the hopping between neighbor sites, corresponding to the transition from the topological superconducting phase to the Anderson localized phase. Changing the gate voltage also causes an abrupt drop of the linear conductance by driving the chain into the topologically trivial superconducting phase, whose I-V curve exhibits an exponential shape.     

Evaluation of Activation Energies for Pairwise and Non-Pairwise Hydrogen Addition to Propyne Over Pd/Aluminosilicate Fiberglass Catalyst by Parahydrogen-Induced Polarization (PHIP)

Hydrogenation of propyne to propene over Pd/aluminosilicate fiberglass catalyst in the temperature range 175–350 °C was investigated with the use of parahydrogen-induced polarization (PHIP) technique. Activation energies for both pairwise and non-pairwise H₂ addition routes were estimated. It was found that at 175–275 °C the activation energies for hydrogen addition to the triple bond of propyne have similar values (about 60–70 kJ/mol) for both routes of hydrogen addition. At higher temperatures (275–350 °C), the rate constant for pairwise hydrogen addition reaches a maximum value while the rate constant for non-pairwise hydrogen addition continues to increase with increasing temperature.