Minimal genus problem for pseudo-real Riemann surfaces

A Riemann surface is said to be pseudo-real if it admits an antiholomorphic automorphism but not an antiholomorphic involution (also known as a symmetry). The importance of such surfaces comes from the fact that in the moduli space of compact Riemann surfaces of given genus, they represent the points with real moduli. Clearly, real surfaces have real moduli. However, as observed by Earle, the converse is not true. Moreover, it was shown by Seppälä that such surfaces are coverings of real surfaces. Here we prove that the latter may always be assumed to be purely imaginary. We also give a characterization of finite groups being groups of automorphisms of pseudo-real Riemann surfaces. Finally, we solve the minimal genus problem for the cyclic case.     

Decay of mass for nonlinear equation with fractional Laplacian

The large time behavior of non-negative solutions to the reaction–diffusion equation ?_t u=-(-D)^a/2u - u^p{\partial_t u=-(-\Delta)^{\alpha/2}u - u^p}, ${(\alpha\in(0,2], \;p > 1)}${(\alpha\in(0,2], \;p > 1)} posed on \mathbbR^N{\mathbb{R}^N} and supplemented with an integrable initial condition is studied. We show that the anomalous diffusion term determines the large time asymptotics for p > 1 + α/N, while nonlinear effects win if p ≤ 1 + α/N.     

Blowup of solutions to generalized Keller–Segel model

The existence and nonexistence of global in time solutions is studied for a class of equations generalizing the chemotaxis model of Keller and Segel. These equations involve Lévy diffusion operators and general potential type nonlinear terms.     

Uniqueness of minimal Fourier-type extensions in L_1-spaces

We give a characterization of uniqueness of finite rank Fourier-type minimal extensions in $L_1$ -norm. This generalizes the main result obtained by Lewicki (Proceedings of the Fifth International Conference on Function Spaces, Lecture Notes in Pure and Applied Mathematics, vol. 213, pp. 337–345, 1998) to the case of $n$ -circular sets in $\mathbb{C }^n$ .     

Influence of a strontium-enriched intergranular cluster network on the electrical conductivity of In2O3-SrO ceramics

A metastable hexagonal R-phase is revealed in polycrystalline In₂O₃-SrO samples, which has the form of a network made up of mesoscopic clusters (60–180 Å in size). The clusters arise from strontium-enriched regions near grain boundaries in the main cubic structure of indium oxide. It is shown that annealing in oxygen at T _a ? 300°C saturates dangling bonds between the R-phase and the matrix and makes the system metastable. This state shows up in the presence of (i) solitary diffuse maxima from the R-phase imposed on Debye lines from the main phase in the X-ray diffraction pattern and (ii) the electron cyclotron resonance (ECR) line with g = 1.875. In addition, the sample in this state acquires a high resistivity (ρ ～ 10⁶ Ω cm). Relaxation at T ? 300°C after annealing at T _a > 300°C disrupts bonds between the strontium-enriched clusters of the R-phase and the indium oxide matrix. This causes spatial separation of the clusters, disruption of their coherent bonds with the matrix structure, and escape of excess oxygen from the sample along grain boundaries. As a result, a new stable state forms, which is characterized by (i) a series of diffuse maxima from the R-phase imposed on lines assigned to the main phase, (ii) the presence of the ECR line with g = 2 with the line with g = 1.875 retained, and (iii) the transition of the sample to a low-resistivity state (ρ ～ 100 Ω cm).     

Statistical approach to multiple-q modulated structures: average Patterson analysis

Using a statistical approach, the average unit cells have been constructed for modulated structures with different types of modulation, from simple sinusoidal to square-wave functions. The obtained unit cells fully describe diffraction intensities of the main reflections and their satellites. A universal distribution, valid for different lengths of the modulation vector, has been found. Average Patterson functions have been constructed and used to distinguish between different types of modulation.     

Helical twisting power of antiferroelectric chiral terphenyls in different matrices

To determine the influence of chemical structure on the Helical Twisting Power (HTP), we tested four optically active dopants having a terphenyl rigid core and the same chiral centre but differing in the length of nonchiral terminal chain and the substitution of benzene rings with fluorine atoms. The compounds were added to different achiral liquid crystalline matrices: nematic and smectic C. It was found that HTP as well as its temperature variation depends on the kind of used matrices. It gives a conclusion that information about HTP obtained in one matrix cannot be uncritically transferred to another one.