Harnack Inequality and Regularity for a Product of Symmetric Stable Process and Brownian Motion

In this paper, we consider a product of a symmetric stable process in $\mathbb{R}^d$ and a one-dimensional Brownian motion in $\mathbb{R}^+$. Then we define a class of harmonic functions with respect to this product process. We show that bounded non-negative harmonic functions in the upper-half space satisfy Harnack inequality and prove that they are locally H\"older continuous. We also argue a result on Littlewood-Paley functions which are obtained by the $\alpha$-harmonic extension of an $L^p(\mathbb{R}^d)$ function.Comment: 23 page

Regenerative capacity in newts is not altered by repeated regeneration and ageing

The extent to which adult newts retain regenerative capability remains one of the greatest unanswered questions in the regeneration field. Here we report a long-term lens regeneration project spanning 16 years that was undertaken to address this question. Over that time, the lens was removed 18 times from the same animals, and by the time of the last tissue collection, specimens were at least 30 years old. Regenerated lens tissues number 18 and number 17, from the last and the second to the last extraction, respectively, were analysed structurally and in terms of gene expression. Both exhibited structural properties identical to lenses from younger animals that had never experienced lens regeneration. Expression of mRNAs encoding key lens structural proteins or transcription factors was very similar to that of controls. Thus, contrary to the belief that regeneration becomes less efficient with time or repetition, repeated regeneration, even at old age, does not alter newt regenerative capacity

High frequency diffraction of an electromagnetic plane wave by an imperfectly conducting rectangular cylinder

Copyright @ 2011 IEEEWe shall consider the the problem of determining the scattered far wave field produced when a plane E-polarized wave is incident on an imperfectly conducting rectangular cylinder. By using the the uniform asymptotic solution for the problem of the diffraction of a plane wave by a right-angled impedance wedge, in conjunction with Keller's method, the a high frequency far field solution to the problem is given

Emergence of non-centrosymmetric topological insulating phase in BiTeI under pressure

The spin-orbit interaction affects the electronic structure of solids in various ways. Topological insulators are one example where the spin-orbit interaction leads the bulk bands to have a non-trivial topology, observable as gapless surface or edge states. Another example is the Rashba effect, which lifts the electron-spin degeneracy as a consequence of spin-orbit interaction under broken inversion symmetry. It is of particular importance to know how these two effects, i.e. the non-trivial topology of electronic states and Rashba spin splitting, interplay with each other. Here we show, through sophisticated first-principles calculations, that BiTeI, a giant bulk Rashba semiconductor, turns into a topological insulator under a reasonable pressure. This material is shown to exhibit several unique features such as, a highly pressure-tunable giant Rashba spin splitting, an unusual pressure-induced quantum phase transition, and more importantly the formation of strikingly different Dirac surface states at opposite sides of the material.Comment: 5 figures are include

Dynamic Analysis of Vascular Morphogenesis Using Transgenic Quail Embryos

Background: One of the least understood and most central questions confronting biologists is how initially simple clusters or sheet-like cell collectives can assemble into highly complex three-dimensional functional tissues and organs. Due to the limits of oxygen diffusion, blood vessels are an essential and ubiquitous presence in all amniote tissues and organs. Vasculogenesis, the de novo self-assembly of endothelial cell (EC) precursors into endothelial tubes, is the first step in blood vessel formation [1]. Static imaging and in vitro models are wholly inadequate to capture many aspects of vascular pattern formation in vivo, because vasculogenesis involves dynamic changes of the endothelial cells and of the forming blood vessels, in an embryo that is changing size and shape. Methodology/Principal Findings: We have generated Tie1 transgenic quail lines Tg(tie1:H2B-eYFP) that express H2B-eYFP in all of their endothelial cells which permit investigations into early embryonic vascular morphogenesis with unprecedented clarity and insight. By combining the power of molecular genetics with the elegance of dynamic imaging, we follow the precise patterning of endothelial cells in space and time. We show that during vasculogenesis within the vascular plexus, ECs move independently to form the rudiments of blood vessels, all while collectively moving with gastrulating tissues that flow toward the embryo midline. The aortae are a composite of somatic derived ECs forming its dorsal regions and the splanchnic derived ECs forming its ventral region. The ECs in the dorsal regions of the forming aortae exhibit variable mediolateral motions as they move rostrally; those in more ventral regions show significant lateral-to-medial movement as they course rostrally. Conclusions/Significance: The present results offer a powerful approach to the major challenge of studying the relative role(s) of the mechanical, molecular, and cellular mechanisms of vascular development. In past studies, the advantages of the molecular genetic tools available in mouse were counterbalanced by the limited experimental accessibility needed for imaging and perturbation studies. Avian embryos provide the needed accessibility, but few genetic resources. The creation of transgenic quail with labeled endothelia builds upon the important roles that avian embryos have played in previous studies of vascular development

Ferromagnetic semiconductors

The current status and prospects of research on ferromagnetism in semiconductors are reviewed. The question of the origin of ferromagnetism in europium chalcogenides, chromium spinels and, particularly, in diluted magnetic semiconductors is addressed. The nature of electronic states derived from 3d of magnetic impurities is discussed in some details. Results of a quantitative comparison between experimental and theoretical results, notably for Mn-based III-V and II-VI compounds, are presented. This comparison demonstrates that the current theory of the exchange interactions mediated by holes in the valence band describes correctly the values of Curie temperatures T_C magnetic anisotropy, domain structure, and magnetic circular dichroism. On this basis, chemical trends are examined and show to lead to the prediction of semiconductor systems with T_C that may exceed room temperature, an expectation that are being confirmed by recent findings. Results for materials containing magnetic ions other than Mn are also presented emphasizing that the double exchange involving hoping through d states may operate in those systems.Comment: 18 pages, 8 figures; special issue of Semicon. Sci. Technol. on semiconductor spintronic

Control of intestinal stem cell function and proliferation by mitochondrial pyruvate metabolism.

Most differentiated cells convert glucose to pyruvate in the cytosol through glycolysis, followed by pyruvate oxidation in the mitochondria. These processes are linked by the mitochondrial pyruvate carrier (MPC), which is required for efficient mitochondrial pyruvate uptake. In contrast, proliferative cells, including many cancer and stem cells, perform glycolysis robustly but limit fractional mitochondrial pyruvate oxidation. We sought to understand the role this transition from glycolysis to pyruvate oxidation plays in stem cell maintenance and differentiation. Loss of the MPC in Lgr5-EGFP-positive stem cells, or treatment of intestinal organoids with an MPC inhibitor, increases proliferation and expands the stem cell compartment. Similarly, genetic deletion of the MPC in Drosophila intestinal stem cells also increases proliferation, whereas MPC overexpression suppresses stem cell proliferation. These data demonstrate that limiting mitochondrial pyruvate metabolism is necessary and sufficient to maintain the proliferation of intestinal stem cells

Ferromagnetism in semiconductors and oxides: prospects from a ten years' perspective

Over the last decade the search for compounds combining the resources of semiconductors and ferromagnets has evolved into an important field of materials science. This endeavour has been fuelled by continual demonstrations of remarkable low-temperature functionalities found for ferromagnetic structures of (Ga,Mn)As, p-(Cd,Mn)Te, and related compounds as well as by ample observations of ferromagnetic signatures at high temperatures in a number of non-metallic systems. In this paper, recent experimental and theoretical developments are reviewed emphasising that, from the one hand, they disentangle many controversies and puzzles accumulated over the last decade and, on the other, offer new research prospects.Comment: review, 13 pages, 8 figures, 109 reference