196,781 research outputs found
Moduli of spherical tori with one conical point
No full textWe determine the topology of the moduli space MS1;1(v) of surfaces of genus one with a Riemannian metric of constant curvature 1 and one conical point of angle 2 pi v. In particular, for v is an element of (2m-1, 2m + 1) nonodd, MS1,1(v) is connected, has orbifold Euler characteristic -1/12m(2), and its topology depends on the integer m > 0 only. For v= 2m + 1 odd, MS1,1(v) has 1/6 m(m + 1) connected components. For v= 2m even, MS1,1(v) has a natural complex structure and it is biholomorphic to H-2/G(m) for a certain subgroup Gm of SL(2, Z) of index m(2), which is nonnormal for m > 1
Rational maps with real multipliers
No full textLet f be a rational function such that the multipliers of all repelling periodic points are real. We prove that the Julia set of such a function belongs to a circle. Combining this with a result of Fatou we conclude that whenever J(f) belongs to a smooth curve, it also belongs to a circle. Then we discuss rational functions whose Julia sets belong to a circle
Some Lower Bounds in the B. and M. Shapiro Conjecture for Flag Varieties
No full textThe B. and M. Shapiro conjecture stated that all solutions of the Schubert Calculus problems associated with real points on the rational normal curve should be real. For Grassmannians, it was proved by Mukhin, Tarasov, and Varchenko. For flag varieties, Sottile found a counterexample and suggested that all solutions should be real under certain monotonicity conditions. In this paper, we compute lower bounds on the number of real solutions for some special cases of the B. and M. Shapiro conjecture for flag varieties, when Sottile's monotonicity conditions are not satisfied. © 2010 Springer Science+Business Media, LLC.BROWDER F, 1976, P S PURE MATH AM MAT, V28; Degtyarev A. I., 2000, USP MAT NAUK, V55, P129; Eremenko A, 2002, ANN MATH, V155, P105, DOI 10.2307-3062151; EREMENKO A, 2005, ELEMENTARY PROOF B M; Eremenko A, 2002, DISCRETE COMPUT GEOM, V28, P331, DOI 10.1007-s00454-002-0735-x; Eremenko A, 2006, P AM MATH SOC, V134, P949, DOI 10.1090-S0002-9939-05-08048-2; FULTON W, 1984, CBMS REGIONAL C SERI, V54; GOLDBERG LR, 1991, ADV MATH, V85, P129, DOI 10.1016-0001-8708(91)90052-9; Hodge W., 1952, METHODS ALGEBRAIC GE, V2; Itenberg I, 2003, INT MATH RES NOTICES, P2639; Mikhalkin G, 2003, CR MATH, V336, P629, DOI 10.1016-S1631-073X(03)00104-3; Mukhin E, 2009, ANN MATH, V170, P863; Pandharipande R, 2008, J AM MATH SOC, V21, P1169, DOI 10.1090-S0894-0347-08-00597-3; Petersen TK, 2009, J ALGEBR COMB, V30, P19, DOI 10.1007-s10801-008-0150-3; Purbhoo K, 2010, ADV MATH, V224, P827, DOI 10.1016-j.aim.2009.12.013; Ruffo J, 2006, EXP MATH, V15, P199, DOI 10.1080-10586458.2006.10128954; Schubert H., 1979, KALKUL ABZAHLENDEN G; SOLOMON J, 2006, ARXIVMATH0606429V1; Soprunova E, 2006, ADV MATH, V204, P116, DOI 10.1016-j.aim.2005.05.016; SOTTILE F, 2010, ARXIVMATH0609829V2; Sottile F, 1997, DUKE MATH J, V87, P59, DOI 10.1215-S0012-7094-97-08703-2; Sottile F, 2000, EXP MATH, V9, P161; Sottile F, 2010, B AM MATH SOC, V47, P31; Stanley R.P., 1999, ENUMERATIVE COMBINAT, V2; Welschinger J. Y., 2010, ARXIV10032707V1; Welschinger JY, 2003, CR MATH, V336, P341, DOI 10.1016-S1631-073X(03)00059-112
Tropospheric Ozone Monitoring with IASI/MetOP Using a Self-Adapting Regularization Method
No full textTropospheric ozone retrieval from thermal infrared nadir satellite measurements: Towards more adaptability of the constraint using a self-adapting regularization
No full textWe developed a Self-Adapting Constraint Retrieval Scheme (SACRS) to retrieve ozone profiles from nadir infrared satellite measurements. In this algorithm, the constraint is variable in altitude and adapted automatically for each individual measurement. The algorithm is tested on synthetic observations representing the future IASI-NG satellite observations and considering either ozonesonde measurements or chemistry-transport model ozone simulations to represent the true ozone (pseudo-reality). The ozone retrievals are evaluated mainly for the troposphere with a specific focus on the lower troposphere between the surface and 6 km. Compared to a previous algorithm based on a fixed constraint retrieval scheme (FCRS), the biases, correlation and error estimates are improved with the SACRS. The bias is reduced by 40% and the correlation coefficient increases from 0.72 to 0.80. The SACRS algorithm also leads to an enhanced sensitivity in the lower troposphere with degrees of freedom for signal up to 0.83, increased by 11% compared to the FCRS. The SACRS performs especially well where current algorithms usually fail, namely for polar and tropical air masses. The bias is reduced from 8.6% to 0.5% in the troposphere (surface-9 km) when considering polar cases and from 24.4% to 10.1% in the upper troposphere - lower troposphere column (12–18 km) in the tropics
Dr. Duane M. Jackson, Morehouse College, July 2011
No full textThis video is a conversation with Dr. Duane M. Jackson. Dr. Jackson talks about his paper, "Recall and the Serial Position Effect: The Role of Primacy and Recency on Accounting Students' Performance." Jackie Daniel, AUC Woodruff Library, is the interviewer
"Reflections on the subject of Emigration from Europe with a view to Settlement in the United States" By M. Carey.
No full text"Reflections on the subject of Emigration from Europe with a view to Settlement in the United States: containing bried sketches of the moral and political character of those states.
By M. Carey, member of the American philosophical, and of the American Antiquarian Society, and author of The Olive Branch, Cindiciae Hibernicae, essays on banking, on political economy, and on internal improvement.
To which are now added the English editor's comments on the subject; together with Important Advice to Emigrants, and Cautions Against Impositions Practiced in the Outports
Über Funktionen in der Speiser-Klasse mit einem Trakt
No full textLet f be a transcendental entire map. A complex number w is called critical value of f if there exists a complex number z such that f'(z)=0 and f(z)=w. A complex number b is called an asymptotic value of f if there exists a curve \gamma with \gamma(t)\to\infty as t\to\infty but f(\gamma(t))\to b as t\to\infty. The singular set of f is the set consisting of all critical and asymptotic values of f. The set B of all transcendental entire functions with a bounded singular set is called Eremenko-Lyubich class. The Speiser class S consists of all functions in class B where the singular set is not only bounded but finite.
These classes have been thoroughly studied, notably, in complex dynamics, which deals with the behaviour of an entire or rational map f under iteration. Of particular interest is the construction of functions in classes B and S with prescribed behaviour. One method to obtain maps in class B is using so-called Cauchy integrals. Gwyneth Stallard used this method to prove that for any d\in(1,2) there exists a function in class B whose Julia set has Hausdorff dimension equal to d. It is the shape of the tracts of her maps which yields the desired Hausdorff dimension. Here, a tract is a connected component of the set where the modulus of the function is large.
The question arises whether Stallard's result also holds for maps in class S. While we are not able to answer this question, we show that there exist functions in class S whose tracts are in some sense similar to the tracts used by Stallard. The method of Cauchy integrals does generally not generate maps in class S. An alternative construction method is quasiconformal folding, which was recently introduced by Christopher Bishop.
We use Bishop's method to construct quasiregular maps which only grow in one parabola shaped tract which is symmetric to the real axis and are bounded otherwise. Furthermore, we prove that for each constructed quasiregular map g there exists an entire function f in class S such that g=f\circ\phi for some quasiconformal homeomorphism \phi. Thus, the tract of f, which is still symmetric to the real axis, is the quasiconformal image of the tract of g. Moreover, the quasiconformal map involved is asymptotically conformal at infinity. We use this to prove that the maximum modulus M(r,f) of f on the circle with radius r is bounded below by a function which depends on the shape of the tract. In particular, we prove that there exists an entire map f in the class S with only one tract, which is symmetric to the real axis, such that \log\log M(r,f) is bounded below by d\cdot\sqrt{r} for some d>0.Sei f eine ganz transzendente Funktion. Eine komplexe Zahl w heißt kritischer Wert der Funktion f, falls es eine kpomplexe Zahl z mit f'(z)=0 und f(z)=w gibt. Eine komplexe Zahl b heißt asymptotischer Wert von f, falls es eine Kurve \gamma mit \gamma(t)\to\infty für t\to\infty gibt, so dass f(\gamma(t))\to b gilt. Die Menge sing(f^{-1}) ist die Menge der Singularitäten der Umkehrfunktion von f und besteht aus allen kritischen und allen asymptotischen Werten von f. Die Menge B aller ganz transzendenter Funktionen derart, dass sing(f^{-1}) beschränkt ist, heißt Eremenko-Lyubich-Klasse. Die Speiser-Klasse S besteht aus allen Funktionen der Klasse B, deren Menge der Singularitäten der Umkehrfunktion sogar endlich ist.
Insbesondere in der komplexen Dynamik, die sich mit dem Verhalten einer ganzen oder rationalen Funktion unter Iteration befasst, wurden diese Funktionenklassen ausgiebig untersucht. Die Konstruktion von Funktionen in den Klassen B und S mit vorgeschriebenem Verhalten ist von besonderem Interesse. Eine Möglichkeit, Funktionen der Klasse B zu konstruieren, sind sogenannte Cauchyintegrale. Gwyneth Stallard nutzte diese Methode, um zu beweisen, dass es für jedes d\in(1,2) eine Funktion in der Klasse B gibt, deren Juliamenge Hausdorff-Dimension d hat. Die Form der Trakte ihrer Funktionen bestimmt dabei die Hausdorff-Dimension. Dabei ist ein Trakt eine Zusammenhangskomponente der Menge, auf welcher der Absolutbetrag der Funktion groß ist.
Es ergibt sich die Frage, ob Stallards Resultat auch für Funktionen der Klasse S gilt. Auch wenn wir diese Frage nicht beantworten können, so zeigen wir, dass es Funktionen in der Klasse S gibt, deren Trakte in gewissem Sinne den von Stallard genutzten Trakten ähneln. Im Allgemeinen sind Funktionen, die mithilfe von Cauchyintegralen konstruiert wurden, nicht in der Klasse S. Eine alternative Konstruktionsmethode ist die quasikonforme Faltung, die kürzlich von Christopher Bishop vorgestellt wurde.
Wir nutzen Bishops Methode, um quasireguläre Funktionen zu konstruieren, die nur in einem parabelförmigen, zur reellen Achse symmetrischen Trakt wachsen und ansonsten beschränkt sind. Des Weiteren beweisen wir, dass es zu jeder so konstruierten quasiregulären Funktion g eine ganze Funktion f in der Klasse S gibt, so dass g=f\circ\phi für eine quasikonforme Abbildung \phi gilt. Somit ist der Trakt von f, welcher ebenfalls symmetrisch zur reellen Achse ist, ein quasikonformes Bild des Traktes von g. Ferner ist die hierbei genutzte quasikonforme Abbildung asymptotisch konform bei unendlich. Wir nutzen dieses, um zu zeigen, dass der Maximalbetrag M(r,f) von f auf dem Kreis mit Radius r von unten durch eine Funktion beschränkt ist, die von der Form des Traktes abhängt. Insbesondere beweisen wir, dass es eine ganze Funktion f in der Klasse S gibt, die nur einen Trakt hat, der ferner symmetrisch zur reellen Achse ist, so dass \log\log M(r,f) von unten durch d\cdot\sqrt{r} für ein d>0 beschränkt ist
Tropospheric Ozone Measurements with IASI/MetOp-A: Improvement of the Retrieval for the Lower Troposphere and Validation
No full textDispelling 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
- …
