A multifractal analysis of equilibrium measures for conformal expanding maps and Moran-like geometric constructions

In this paper we establish the complete multifractal formalism for equilibrium measures for Hölder continuous conformal expanding maps andexpanding Markov Moran-like geometric constructions. Examples include Markov maps of an interval, beta transformations of an interval, rational maps with hyperbolic Julia sets, and conformal toral endomorphisms. We also construct a Hölder continuous homeomorphism of a compact metric space with an ergodic invariant measure of positive entropy for which the dimension spectrum is not convex, and hence the multifractal formalism fails.     

A new rapid micro-method for the molecular-chemical characterization of rhizodeposits by field-ionization mass spectrometry

Time-consuming investigation of rhizodeposit composition by leaching, freeze-drying of leachate, and pyrolysis-field ionization mass spectrometry (Py-FIMS) of solid samples was replaced by direct Py-FIMS of a 5 microL liquid rhizodeposit sample which was evaporated overnight in the quartz tube of a mass spectrometer inlet system. Application of this new rapid technique to a set of 14 liquid rhizodeposit samples from maize (Zea mays L.), leached twice with a time lag of 80 min, unequivocally showed the effect of soil texture on the chemical composition of the rhizodeposits. Irrespective of leaching time, a partial least-squares analysis separated the Py-FI mass spectra of the maize rhizodeposits leached from a soil from those leached from a soil + quartz sand-mixture (prepared by addition of 50% w/w quartz sand to the original soil). The signals which had the strongest discrimination power and were significantly enriched in leachates from the soil + quartz sand were assigned to sugars, peptides and polyamines. Mass signals of putrescine and cadaverine, a priori not expected in the rhizodeposits, were indicators of modified root environment and rhizosphere processes in the soil + quartz sand. In conclusion, the new rapid mass spectrometric profiling method is suitable for rhizosphere research because it requires very small sample volumes, is fast and highly sensitive to detect and quantify a wide range of a priori expected and unexpected organic substances.     

Strongly convergent approximations to fixed points of total asymptotically nonexpansive mappings

In this work we prove a new strong convergence result of the regularized successive approximation method given by yn＋1 = qnz0 ＋ （1 - qn）T^nyn, n = 1, 2,…,where lim n→∞ qn = 0 and ∞∑n=1 qn=∞ for T a total asymptotically nonexpansive mapping, i.e., T is such that
││T^n x - T^n y││ ≤ x - y ││ ＋ kn^（1）φ（││x - y││） ＋ kn^（2）,where kn^1 and kn^2 are real null convergent sequences and φ：R^＋→R^＋ is continuous such that φ（0）=0 and limt→∞φ（t）/t≤ C for a certain constant C 〉 0.
Among other features, our results essentially generalize existing results on strong convergence for T nonexpansive and asymptotically nonexpansive. The convergence and stability analysis is given for both self- and nonself-mappings.     

Direct AFM measurements of adhesion forces between calcium oxalate monohydrate and kidney epithelial cells in the presence of Ca2+ and Mg2+ ions

Adhesion forces between the calcium oxalate monohydrate (COM, whewellite) crystal and the layer of the epithelial kidney cells have been directly measured under buffer solutions by using atomic force microscope (AFM). Two renal epithelial lines, MDCK (a collecting duct line) and LLC-PK1 (a proximal tubular line), were used. All experiments were conducted in buffer solutions containing additional Ca(2+) and Mg(2+) ions in the various concentrations. For MDCK-cells, the obtained values of the adhesion force were in the range 0.12-0.51 nN and 0.12-0.20 nN for Ca(2+) and Mg(2+), respectively. No adhesion force (larger than 0.05 nN) has been found for LLC-PK1 cells. The "critical" concentrations of ions, near which the adhesion force (for MDCK-cells) was maximal, were found to be 100 mM. The "critical" concentration of ions and the tendency of the adhesion forces with the changing ions concentration, confirm earlier results of Lieske et al. [J.C. Lieske, G. Farell, S. Deganello, Urol. Res. 32 (2004) 117-123], in which the affinity (rather than the adhesion force) between the COM micro-crystals and the layer of the MDCK-cells were measured, calculating the radioactive signal of radioactive (14)C COM-crystals stuck to the cells. We believe that the aggregation of the COM crystals does not occur in the bulk urine due to short travel time through the nephron. If so, the kidney stone formation is determined by COM-seeding on the tubules walls. The further growth of the stone on the seed can take practically unlimited time because the COM crystal is practically is not soluble in water or urine solutions. The value of the adhesion force can be useful for evaluation of the adhesion energy or probability of the COM-aggregates to stick to the kidney epithelium under the urine flow. This probability is calculated taking into account the adhesion force, F(ad), and hydrodynamic driving force of the flow. This probability reflects the opportunity of the small aggregates to grow and form the kidney stones.     

Geometric approach to parabolic induction

In this paper we construct a “restriction” map from the cocenter of a reductive group G over a local non-archimedean field F to the cocenter of a Levi subgroup. We show that the dual map corresponds to parabolic induction and deduce that parabolic induction preserves stability. We also give a new (purely geometric) proof that the character of normalized parabolic induction does not depend on the parabolic subgroup. In the appendix, we use a similar argument to extend a theorem of Lusztig–Spaltenstein on induced unipotent classes to all infinite fields. We also prove a group version of a theorem of Harish-Chandra about the density of the span of regular semisimple orbital integrals.     

Contact orderability up to conjugation

We study in this paper the remnants of the contact partial order on the orbits of the adjoint action of contactomorphism groups on their Lie algebras. Our main interest is a class of noncompact contact manifolds, called convex at infinity.     

Charge ordering in amorphous WOx films

We report on the observation of highly anisotropic viscous electronic conducting phase in amorphous WO_1.55 films that occurs below a current (I)- and frequency (f  )-dependent temperature T^∗(I,f)$T^{\ast }(I,f)$. At T<T^∗(I,f)$T<T^{\ast }(I,f)$ the rotational symmetry of randomly disordered electronic background is broken leading to the appearance of mutually perpendicular metallic- and insulating-like states. A rich dynamic behavior of the electronic matter occurring at T<T^∗(I,f)$T<T^{\ast }(I,f)$ provides evidence for an interplay between pinning effects and electron–electron interactions. The results suggest a dynamic crystallization of the disordered electronic matter, viz. formation of sliding Wigner crystal, as well as the occurrence of quantum liquid-like crystal or stripe phase at low drives.