94,193 research outputs found
A Distinguished Subgroup of Compact Abelian Groups
No full textHere “group” means additive abelian group. A compact group G contains δ role= presentation style= box-sizing: border-box; max-height: none; display: inline; line-height: normal; font-size: 13.2px; text-align: left; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3eδ–subgroups, that is, compact totally disconnected subgroups Δ role= presentation style= box-sizing: border-box; max-height: none; display: inline; line-height: normal; font-size: 13.2px; text-align: left; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3eΔ such that G/Δ role= presentation style= box-sizing: border-box; max-height: none; display: inline; line-height: normal; font-size: 13.2px; text-align: left; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3eG/Δ is a torus. The canonical subgroup Δ(G) role= presentation style= box-sizing: border-box; max-height: none; display: inline; line-height: normal; font-size: 13.2px; text-align: left; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3eΔ(G) of G that is the sum of all δ role= presentation style= box-sizing: border-box; max-height: none; display: inline; line-height: normal; font-size: 13.2px; text-align: left; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3eδ–subgroups of G turns out to have striking properties. Lewis, Loth and Mader obtained a comprehensive description of Δ(G) role= presentation style= box-sizing: border-box; max-height: none; display: inline; line-height: normal; font-size: 13.2px; text-align: left; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3eΔ(G) when considering only finite dimensional connected groups, but even for these, new and improved results are obtained here. For a compact group G, we prove the following: Δ(G) role= presentation style= box-sizing: border-box; max-height: none; display: inline; line-height: normal; font-size: 13.2px; text-align: left; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3eΔ(G) contains tor(G) role= presentation style= box-sizing: border-box; max-height: none; display: inline; line-height: normal; font-size: 13.2px; text-align: left; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3etor(G), is a dense, zero-dimensional subgroup of G containing every closed totally disconnected subgroup of G, and G/Δ(G) role= presentation style= box-sizing: border-box; max-height: none; display: inline; line-height: normal; font-size: 13.2px; text-align: left; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3eG/Δ(G) is torsion-free and divisible; Δ(G) role= presentation style= box-sizing: border-box; max-height: none; display: inline; line-height: normal; font-size: 13.2px; text-align: left; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3eΔ(G) is a functorial subgroup of G, it determines G up to topological isomorphism, and it leads to a “canonical” resolution theorem for G. The subgroup Δ(G) role= presentation style= box-sizing: border-box; max-height: none; display: inline; line-height: normal; font-size: 13.2px; text-align: left; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3eΔ(G) appeared before in the literature as td(G) role= presentation style= box-sizing: border-box; max-height: none; display: inline; line-height: normal; font-size: 13.2px; text-align: left; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3etd(G) motivated by completely different considerations. We survey and extend earlier results. It is shown that td, as a functor, preserves proper exactness of short sequences of compact groups
FAT DELTA 2: FUNCTORIAL SUBGROUPS OF TOPOLOGICAL ABELIAN GROUPS
No full textIn the predecessor [16] of this paper the canonical subgroup (Fat Delta) ∆(G) of a compact abelian group G was studied. It is the sum of all closed disconnected subgroups of G and it appeared before in the literature (see [28]) as td(G), defined for arbitrary topological groups and motivated by completely different considerations. We introduce and compare further functorial subgroups of general topological groups and study their relationships with ∆(G) and td(G)
Band structure related wave-function symmetry of amphoteric Si dopants in GaAs
No full textAutocompensated Si-doped GaAs is studied with cross-sectional scanning tunnelling spectroscopy (X-STS). The local electronic contrasts of substitutional Si(Ga) donors and Si(As) acceptors under the (110) cleavage plane are imaged with high resolution. Si(Ga) donor atoms exhibit radially symmetrical contrasts. Si(As) acceptors have anisotropic features. The anisotropic acceptor contrasts are traced back to a tunnel process at the valence band edge. They reflect the probability density distribution of the localized acceptor hole state. (C) 2008 Elsevier Ltd. All rights reserved
Asymmetry of acceptor wave functions caused by surface-related strain and electric field in InAs
No full textThe spatial distribution of the local density of states at Mn acceptors near the (110) surface of p-doped InAs is investigated by scanning tunneling microscopy. The shapes of the acceptor contrasts for different dopant depths under the surface are analyzed. Acceptors located within the first ten subsurface layers of the semiconductor show a lower symmetry than expected from theoretical predictions for the bulk acceptor wave function. They exhibit a (001) mirror asymmetry. The degree of asymmetry depends on the acceptor atoms' depths. The measured contrasts for acceptors buried below the tenth subsurface layer closely match the theoretically derived shape. Two effects are able to cause the observed symmetry reduction, i.e., the strain field of the surface relaxation and the tip-induced electric field. While both effects induce similar asymmetries, a comparison of their relative strengths indicates that surface-related strain is the dominant effect for Mn in InAs
Band Bending, Tunneling Paths and Wave Functions
No full textDiese Arbeit befasst sich mit der Untersuchung einzelner Dotieratome mittels Rastertunnelmikroskopie (STM1) und ortsaufgelöster I(V)-Spektroskopie (STS2) [8]. Das Verständnis der lokalen elektronischen Struktur von Dotieratomen ist dabei für Grundlagenforschung und Halbleiterindustrie gleichermaßen von Inte-resse: Innerhalb der nächsten fünf Jahre werden Transistoren, die primären Schaltelemente in jedem gewöhnlichen Computer, auf Strukturgrößen von 15nm geschrumpft sein [1]. Sie sind dann mit der Ausdehnung der quantenmechani-schen Wellenfunktion einzelner Dotieratome vergleichbar. Der typische Durchmesser einer Akzeptorwellenfunktion in Silizium liegt bei 4nm und die Ausdehnung einer Donatorwellenfunktion beträgt bis zu 10nm [2-5]. In naher Zukunft wird nicht nur die genaue Verteilung der Dotieratome in einem Bauele-ment wichtig sein, sondern auch ihre räumliche elektronische Struktur [6, 7]. In diesem Zusammenhang geben Akzeptoren in III-V Verbindungshalbleitern bis heute Rätsel auf. Die Querschnitts-Rastertunnelmikroskopie (X-STM) ermög-licht es, vergrabene Defekte und Heterostrukturen mit dem STM abzubilden [9, 14-16]. Dabei wird eine Halbleiterprobe gezielt entlang einer bevorzugten {110} Bruchrichtung gespalten, so dass ein atomar glatter Querschnitt durch die Struk-tur zugänglich wird. Im STM erscheinen flache Akzeptoren, die knapp unter der Spaltfläche vergraben sind, als dreieckige Bereiche erhöhter Leitfähigkeit [11, 22]. Für tiefe Akzeptoren dagegen wurden bisher flügelförmige Kontraste beobachtet [23]. Obwohl dieses Erscheinungsbild seit einiger Zeit bekannt ist, entziehen sich die beobachteten Akzeptorkontraste bisher einer theoretischen Beschreibung, da sie nicht der Symmetrie der zugrundeliegenden Bandstruktur (c2V) entsprechen. Das Ziel der vorliegenden Arbeit ist das experimentelle Verständnis der zugrundeliegenden Prozesse. In Kapitel 4 wird gezeigt, dass die anisotropen Kontraste von Tunnelprozessen nahe der Valenzbandkante herrühren. Zwei ver-schiedene Tunnelprozesse können identifiziert werden, die anisotrope Leitfähigkeitsverteilungen aufweisen.This thesis reports measurements of single dopant atoms in III-V semiconduc-tors with low temperature Scanning Tunneling Microscopy (STM) and Scanning Tunneling Spectroscopy (STS). It investigates the anisotropic spatial distribution of acceptor induced tunneling processes at the {110} cleavage planes. Two dif-ferent tunneling processes are identified: conventional imaging of the squared acceptor wave function and resonant tunneling at the charged acceptor. A thor-ough analysis of the tip induced space charge layers identifies characteristic bias windows for each tunnel process. The symmetry of the host crystal s band struc-ture determines the spatial distribution of the tunneling paths for both processes. Symmetry reducing effects at the surface are responsible for a pronounced asymmetry of the acceptor contrasts along the principal [001] axis. Uniaxial strain fields due to surface relaxation and spin orbit interaction of the tip induced elec-tric field are discussed on the basis of band structure calculations. High-resolution STS studies of acceptor atoms in an operating p-i-n diode confirm that an electric field indeed changes the acceptor contrasts. In conclusion, the aniso-tropic contrasts of acceptors are created by the host crystal s band structure and concomitant symmetry reduction effects at the surface
Author Correction: Community-wide hackathons to identify central themes in single-cell multi-omics (Genome Biology, (2021), 22, 1, (220), 10.1186/s13059-021-02433-9)
No full textFollowing publication of the original article [1], the authors identified that author Dario Righelli had erroneously been omitted from the author panel. The author group above has been updated and the original article [1] has been corrected
Dispelling the Myths Behind First-author Citation Counts
No full textWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
Author, publisher and bookseller : a tripartite synergy in Nigerian book industry
No full textThis work is about the roles of Author, Publisher and Bookseller in Book development in
Nigeria. The paper started by delving into the history of Book Publishing in Nigeria after
which it proceeded by defining who an author, a publisher, and a bookseller is and
expatiated on the indispensable roles of these key actors in Nigerian Book Industry and in
the emerging Information Society. Furthermore, the various constraints to book
development were identified while the paper advised on how the Book Industry can be
further promoted in Nigeria. However, the paper concluded and made recommendations
on how the Book sector can help in enhancing scholarship in the country
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