On L2L^2 -functions with bounded spectrum

We consider the class $PW(\mathbb R^n)$ of functions in $L^2(\mathbb R^n)$, whose Fourier transform has bounded support. We obtain a description of continuous maps $\varphi : \mathbb R^m\rightarrow\mathbb R^n$ such that $f\circ\varphi\in PW(\mathbb R^m)$ for every function $f\in PW(\mathbb R^n)$. Only injective affine maps $\varphi$ have this property

Spatial statistics of passive scalar in two-dimensional shear flow with fluctuations

We examine statistical properties of the passive scalar field advected by the flow consisting of the regular shear flow and of irregular flow fluctuations. We consider the particular case of two-dimensional flow where the shear flow is dominating and the random flow is smooth. We examine both the decaying case and the case of the permanent supply of the passive scalar fluctuations. In both cases the passive scalar possesses strong intermittence, that can be characterized via the single-point moments and correlation functions, calculated in our work. We reveal features of the correlation functions related to the strong anisotropy of the flow. Our qualitative results are universal. Some quantitative results are obtained in the framework of the model where the flow fluctuations are short correlated in time.Comment: 14 pages, 2 figure

Symmetries and Interaction coefficients of Kelvin waves

We considered symmetry restriction on the interaction coefficients of Kelvin waves and demonstrated that linear in small wave vector asymptotic is not forbidden, as one can expect by naive reasoning.Comment: 4 pages, submitted to J. of Low Temp. Phy

Who are you, Griselda? A replacement name for a new genus of the Asiatic short-tailed shrews (Mammalia, Eulipotyphla, Soricidae): molecular and morphological analyses with the discussion of tribal affinities

The first genetic study of the holotype of the Gansu short-tailed shrew, Blarinella griselda Thomas, 1912, is presented. The mitochondrial analysis demonstrated that the type specimen of B. griselda is close to several recently collected specimens from southern Gansu, northern Sichuan and Shaanxi, which are highly distinct from the two species of Asiatic short-tailed shrews of southern Sichuan, Yunnan, and Vietnam, >B. quadraticauda and B. wardi. Our analysis of four nuclear genes supported the placement of B. griselda as sister to B. quadraticauda / B. wardi, with the level of divergence between these two clades corresponding to that among genera of Soricinae. A new generic name, Parablarinella, is proposed for the Gansu short-tailed shrew. Karyotypes of Parablarinella griselda(2n = 49, NFa = 50) and B. quadraticauda (2n = 49, NFa = 62) from southern Gansu are described. The tribal affinities of Blarinellini and Blarinini are discussed.Copyright Anna A. Bannikova et al. This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. The attached file is the published version of the article

Clinically relevant morphological structures in breast cancer represent transcriptionally distinct tumor cell populations with varied degrees of epithelial-mesenchymal transition and CD44+CD24- stemness

Intratumor morphological heterogeneity in breast cancer is represented by different morphological structures (tubular, alveolar, solid, trabecular, and discrete) and contributes to poor prognosis; however, the mechanisms involved remain unclear. In this study, we performed 3D imaging, laser microdissection-assisted array comparative genomic hybridization and gene expression microarray analysis of different morphological structures and examined their association with the standard immunohistochemistry scorings and CD44+CD24- cancer stem cells. We found that the intratumor morphological heterogeneity is not associated with chromosomal aberrations. By contrast, morphological structures were characterized by specific gene expression profiles and signaling pathways and significantly differed in progesterone receptor and Ki-67 expression. Most importantly, we observed significant differences between structures in the number of expressed genes of the epithelial and mesenchymal phenotypes and the association with cancer invasion pathways. Tubular (tube-shaped) and alveolar (spheroid-shaped) structures were transcriptionally similar and demonstrated co-expression of epithelial and mesenchymal markers. Solid (large shapeless) structures retained epithelial features but demonstrated an increase in mesenchymal traits and collective cell migration hallmarks. Mesenchymal genes and cancer invasion pathways, as well as Ki-67 expression, were enriched in trabecular (one/two rows of tumor cells) and discrete groups (single cells and/or arrangements of 2-5 cells). Surprisingly, the number of CD44+CD24- cells was found to be the lowest in discrete groups and the highest in alveolar and solid structures. Overall, our findings indicate the association of intratumor morphological heterogeneity in breast cancer with the epithelial-mesenchymal transition and CD44+CD24- stemness and the appeal of this heterogeneity as a model for the study of cancer invasion

Nonmonotonic Decay of Nonequilibrium Polariton Condensate in Direct-Gap Semiconductors

Time evolution of a nonequilibrium polariton condensate has been studied in the framework of a microscopic approach. It has been shown that due to polariton-polariton scattering a significant condensate depletion takes place in a comparatively short time interval. The condensate decay occurs in the form of multiple echo signals. Distribution-function dynamics of noncondensate polaritons have been investigated. It has been shown that at the initial stage of evolution the distribution function has the form of a bell. Then oscillations arise in the contour of the distribution function, which further transform into small chaotic ripples. The appearance of a short-wavelength wing of the distribution function has been demonstrated. We have pointed out the enhancement and then partial extinction of the sharp extra peak arising within the time interval characterized by small values of polariton condensate density and its relatively slow changes.Comment: 20 pages, LaTeX 2.09; in press in PR

ISOTOPIC COMPOSITION OF LIGHT NUCLEI IN COSMIC RAYS: RESULTS FROM AMS-01

The variety of isotopes in cosmic rays allows us to study different aspects of the processes that cosmic rays undergo between the time they are produced and the time of their arrival in the heliosphere. In this paper, we present measurements of the isotopic ratios [superscript 2]H/[superscript 4]He, [superscript 3]He/[superscript 4]He, [superscript 6]Li/[superscript 7]Li, [superscript 7]Be/([superscript 9]Be+[superscript 10]Be), and [superscript 10]B/[superscript 11]B in the range 0.2-1.4 GeV of kinetic energy per nucleon. The measurements are based on the data collected by the Alpha Magnetic Spectrometer, AMS-01, during the STS-91 flight in 1998 June.United States. Dept. of EnergyMassachusetts Institute of Technolog