Minimal immersions of closed surfaces in hyperbolic three-manifolds

We study minimal immersions of closed surfaces (of genus $g \ge 2$) in hyperbolic 3-manifolds, with prescribed data $(\sigma, t\alpha)$, where $\sigma$ is a conformal structure on a topological surface $S$, and $\alpha dz^2$ is a holomorphic quadratic differential on the surface $(S,\sigma)$. We show that, for each $t \in (0,\tau_0)$ for some $\tau_0 > 0$, depending only on $(\sigma, \alpha)$, there are at least two minimal immersions of closed surface of prescribed second fundamental form $Re(t\alpha)$ in the conformal structure $\sigma$. Moreover, for $t$ sufficiently large, there exists no such minimal immersion. Asymptotically, as $t \to 0$, the principal curvatures of one minimal immersion tend to zero, while the intrinsic curvatures of the other blow up in magnitude.Comment: 16 page

Weblog patterns and human dynamics with decreasing interest

Weblog is the fourth way of network exchange after Email, BBS and MSN. Most bloggers begin to write blogs with great interest, and then their interests gradually achieve a balance with the passage of time. In order to describe the phenomenon that people's interest in something gradually decreases until it reaches a balance, we first propose the model that describes the attenuation of interest and reflects the fact that people's interest becomes more stable after a long time. We give a rigorous analysis on this model by non-homogeneous Poisson processes. Our analysis indicates that the interval distribution of arrival-time is a mixed distribution with exponential and power-law feature, that is, it is a power law with an exponential cutoff. Second, we collect blogs in ScienceNet.cn and carry on empirical studies on the interarrival time distribution. The empirical results agree well with the analytical result, obeying a special power law with the exponential cutoff, that is, a special kind of Gamma distribution. These empirical results verify the model, providing an evidence for a new class of phenomena in human dynamics. In human dynamics there are other distributions, besides power-law distributions. These findings demonstrate the variety of human behavior dynamics.Comment: 8 pages, 1 figure

Preparation of Au Nanostructure Arrays for Fluorometry and Biosensors Applications

The paper describes the fabrication of random and ordered gold nanostructure arrays (NSA) of different morphology using island film thermal annealing and nanoimprint lithography techniques. Structural parameters of obtained NSA were investigated using atomic force microscopy method. Spectral characteristics of obtained NSA were studied in air atmosphere, and NSA light extinction spectra exhibited an expressed plasmon peak. Spectral position of localized surface plasmon resonance can be tuned depending on geometrical parameters of nanostructures, which is an important factor for resonant investigation methods of various types of molecular structures. Proposed technological approaches can be used to implement the resonance fluorometry in electromagnetic field of nanostructures (surface-enhanced fluorescence) method and in chemical and biosensors based on localized surface plasmon resonance. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3496

Hilbert Expansion from the Boltzmann equation to relativistic Fluids

We study the local-in-time hydrodynamic limit of the relativistic Boltzmann equation using a Hilbert expansion. More specifically, we prove the existence of local solutions to the relativistic Boltzmann equation that are nearby the local relativistic Maxwellian constructed from a class of solutions to the relativistic Euler equations that includes a large subclass of near-constant, non-vacuum fluid states. In particular, for small Knudsen number, these solutions to the relativistic Boltzmann equation have dynamics that are effectively captured by corresponding solutions to the relativistic Euler equations.Comment: 50 page

Phase Transition in a Vlasov-Boltzmann Binary Mixture

There are not many kinetic models where it is possible to prove bifurcation phenomena for any value of the Knudsen number. Here we consider a binary mixture over a line with collisions and long range repulsive interaction between different species. It undergoes a segregation phase transition at sufficiently low temperature. The spatially homogeneous Maxwellian equilibrium corresponding to the mixed phase, minimizing the free energy at high temperature, changes into a maximizer when the temperature goes below a critical value, while non homogeneous minimizers, corresponding to coexisting segregated phases, arise. We prove that they are dynamically stable with respect to the Vlasov-Boltzmann evolution, while the homogeneous equilibrium becomes dynamically unstable

Acclimation responses of gill ionocytes of red tilapia (Oreochromis mossambicus × O. niloticus) to water salinity and alkalinity

To understand the acclimation strategies of red tilapia to different environments, this study aimed to evaluate different responses of red tilapia (O. mossambicus × O. niloticus) to salinity (10-30‰), alkalinity (1-3 gL^-1 NaHCO3) and salinity and alkalinity (10/1-30/3 ‰/gL^-1 NaHCO3) environments. Localization, type, size, and numeration of gill ionocytes were investigated on the same specimens by scanning electron microscopy (SEM) and immunohistochemistry (IHC) with antibodies of Na+/K+-ATPase (NKA), Na+/K+/2Cl-contransporter (NKCC), cystic fibrosis transmembrane conductance regulator (CFTR) and carbonic anhydrase (CA). Ionocytes were only located on filaments conducted by SEM. Four types of ionocytes namely pit, convex, concave and transitory types were determined morphologically by their apical openings of which concave and transitory type were not present in freshwater (FW) and saltwater (SW) fish (10). Both ionocytes size and number increased with elevated stress levels. In comparison to FW, density of ionotypes increased to about 4.75, 3.00 and 3.44 fold in SW (30), AW (3) and S&AW (30/3) respectively. Immunoreactive cells on gill filaments confirmed branchial distribution of ionocytes. Immunoreaction of NKA, NKCC and CA appeared in FW except for CFTR while they all appeared in SW (30), AW (3) and S&AW (30/3)

The Conformal Willmore Functional: a Perturbative Approach

The conformal Willmore functional (which is conformal invariant in general Riemannian manifold $(M,g)$) is studied with a perturbative method: the Lyapunov-Schmidt reduction. Existence of critical points is shown in ambient manifolds $(\mathbb{R}^3, g_\epsilon)$ -where $g_\epsilon$ is a metric close and asymptotic to the euclidean one. With the same technique a non existence result is proved in general Riemannian manifolds $(M,g)$ of dimension three.Comment: 34 pages; Journal of Geometric Analysis, on line first 23 September 201

Reconstructing initial data using observers: error analysis of the semi-discrete and fully discrete approximations

A new iterative algorithm for solving initial data inverse problems from partial observations has been recently proposed in Ramdani et al. (Automatica 46(10), 1616-1625, 2010 ). Based on the concept of observers (also called Luenberger observers), this algorithm covers a large class of abstract evolution PDE's. In this paper, we are concerned with the convergence analysis of this algorithm. More precisely, we provide a complete numerical analysis for semi-discrete (in space) and fully discrete approximations derived using finite elements in space and an implicit Euler method in time. The analysis is carried out for abstract Schrödinger and wave conservative systems with bounded observation (locally distributed)

Pulsating flow and convective heat transfer in a cavity with inlet and outlet sections

This paper deals with the study of 2-D, laminar, pulsating flow inside a heated rectangular cavity with different aspect ratios. The cooling liquid (water with temperature dependent viscosity and thermal conductivity) comes and leaves the cavity via inlet and outlet ports. The flow topology is characterised by the large recirculation regions that exist at inner corners of the cavity. These low velocity regions cause the heat transfer to be small when compared, for instance, to that of a straight channel. We study the effect that a prescribed pulsation at the inlet port has on the cavity heat transfer. This pulsating boundary condition, of the unsteady Poiseuille type, is described by its frequency and the amplitude of the pressure gradient. The time averaged Reynolds number of the flow, based on the hydraulic diameter of the inlet channel, is 100 and we consider that the dimensionless pulsation frequency (Strouhal number) varies in the range from 0.0 to 0.4. We show that the prescribed pulsation enhances heat transfer in the cavity and that the mechanism that causes this enhancement appears to be the periodic change in the recirculation flow pattern generated by the pulsation. Regarding the quantitative extent of heat transfer recovery, we find that appropriate selection of the pulsation parameters allows for the cavity to behave like a straight channel that is the configuration with the highest Nusselt number

Molecular evidence of the haploid origin in wheat (Triticum aestivum L.) with Aegilops kotschyi cytoplasm and whole genome expression profiling after haploidization

Aegiolops kotschyi cytoplasmic male sterile system often results in part of haploid plants in wheat (Triticum aestivum L.). To elucidate the origin of haploid, 235 wheat microsatellite (SSR) primers were randomly selected and screened for polymorphism between haploid (2n = 3x = 21 ABD) and its parents, male-sterile line YM21 (2n = 6x = 42 AABBDD) and male fertile restorer YM2 (2n = 6x = 42 AABBDD). About 200 SSR markers yielded clear bands from denatured PAGE, of which 180 markers have identifiable amplification patterns, and 20 markers (around 8%) resulted in different amplification products between the haploid and the restorer, YM2. There were no SSR markers that were found to be distinguishable between the haploid and the male sterile line YM21. In addition, different distribution of HMW-GS between endosperm and seedlings from the same seeds further confirmed that the haploid genomes were inherited from the maternal parent. After haploidization, 1.7% and 0.91% of total sites were up- and down-regulated exceeding twofold in the shoot and the root of haploid, respectively, and most of the differentially expressed loci were up/down-regulated about twofold. Out of the sensitive loci in haploid, 94 loci in the shoot, 72 loci in the root can be classified into three functional subdivisions: biological process, cellular component and molecular function, respectively