4,502 research outputs found
Over convergent de Rham-Witt complex
No full textThesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2009.Includes bibliographical references (p. 83-84).We define the overconvergent de Rham-Witt complex ... for a smooth affine variety over a perfect field in characteristic p. We show that, after tensoring with Q, its cohomology agrees with Monsky-Washnitzer cohomology. If dim C 2.by Christopher Davis.Ph.D
On the Witt vector Frobenius
No full textWe study the kernel and cokernel of the Frobenius map on the p-typical Witt vectors of a commutative ring, not necessarily of characteristic p. We give many equivalent conditions to surjectivity of the Frobenius map on both finite and infinite length Witt vectors. In particular, surjectivity on finite Witt vectors turns out to be stable under certain integral extensions; this provides a clean formulation of a strong generalization of Faltings’s almost purity theorem from p-adic Hodge theory, incorporating recent improvements by Kedlaya–Liu and by Scholze
p-adic points of rational Witt spaces
No full textDiese Dissertation untersucht wie rationale Wittvektoren verwendet werden können, um die Menge der Ring-wertigen Punkte eines Schemas X zu erweitern. Dabei schränken wir uns auf Punkte mit Werten in einem Rang eins Bewertungsring von gemischter Charakteristik ein. Für X affin zeigen wir, wie diese Punkte als Untilts des Tilts des Bewertungsrings über X interpretiert werden können. Dies geschieht unter Zuhilfenahme perfektoider Techniken, unter anderem Diamanten, und ist eine Verallgemeinerung eines vorangegangenen Resultats von Deninger für höhere Dimensionen. Des Weiteren wird gezeigt, dass die Elemente des infinitesimalen Periodenrings des Schemas X injektiv als Funktionen auf der neuen Menge von Punkten wirken. Hierfür werden Sätze über das Anheben von Punkten und der Satz über reduzierte Fasern verwendet. Außerdem wird in der kommutativen Algebra eine Bijektion bewiesen, welche Morphismen mit einer Gruppenwirkung auf dem Definitionsbereich in Verbindung setzt.In these thesis we explore how rational Witt vectors can be used to refine and extend the ring-valued points of a scheme X. Our primary goal is to understand the behaviour of such points valued in a mixed characteristic rank one valuation ring. When X is affine we show how these points can be interpreted as untilts of the tilt of the valuation ring lying over X. This is done using perfectoid techniques and diamonds, generalising a previous result of Deninger to higher dimensional X. Additionally, it is shown that the elements of the infinitesimal period ring defined by the scheme act injectively as functions on the new set of points set. This result uses lifting theorems and the reduced fibre theorem. Furthermore, in commutative algebra a bijection is proven relating morphisms with a group action on the domain
Compositional dependence of physical properties in nickel-manganese-gallium polycrystals
No full textThesis (B.S.)--Massachusetts Institute of Technology, Dept. of Materials Science and Engineering, 1997.Includes bibliographical references (leaf 36).by Christopher Kantner.B.S
Aristoxenus Elements of rhythm: text, translation, and commentary with a translation and commentary on POxy 2687
No full textAristoxenus of Tarentum makes productive use of Aristotelian concepts and methods in developing his theory of musical rhythm in his treatise Elements of Rhythm. He applies the Aristotelian distinction between form and material and the concept of hypothetical necessity to provide an explanation for why musical rhythm is manifested in the syllables of song, the notes of melody, and the steps of dance. He applies the method of formulating differentiae, as described in Aristotle's Parts of Animals, to codify the formal properties of rhythm.
Aristoxenus' description of the rhythmic foot presents several interpretive challenges. Our text is fragmentary, and we lack Aristoxenus' definitions of several key terms. This study seeks to establish the meanings of these terms on the basis of a close examination of the structure of Aristoxenus' argument. Parallel passages in Aristides Quintilianus' On Music are considered in detail for their consistency or lack thereof with Aristoxenian usage. Parallel passages in POxy 2687 are cited as illustrations for several rhythmic constructions and principles Aristoxenus mentions; because these involve original interpretations of some points in POxy 2687, they are supported by a thorough presentation of POxy 2687 in a separate chapter.
One central conclusion of this study is that Aristoxenus viewed rhythmic feet as musical functions, analogous to the theory of melodic functions he had presented in his Elements of Harmony. Only limited conclusions about the applicability of Aristoxenus' theory to the history of ancient Greek music can be justified. While some of the extant remains of Greek music are in accord with Aristoxenian theory, others contradict it. Much of ancient poetry is more rhythmically complex than what is presented in our text of E.R., but regular poetic forms such as the anapestic dimeter and the stately rhythms of religious hymns may have provided the original starting points for subsequent rhythmic developments Aristoxenus seeks to explain.Ph.D.Includes bibliographical references (296-312)by Christopher C. Marchett
Oregon Justice Reinvestment Initiative: return on investment
No full textsubmitted to: Oregon Criminal Justice Commission ; principal investigator: Mauri Matsuda, Ph.D. ; co-investigators: Christopher Campbell, Ph.D., Christopher Dollar, M.S., Mark Leymon, Ph.D., Brian Renauer, Ph.D.This archived document is maintained by the State Library of Oregon as part of the Oregon Documents Depository Program. It is for informational purposes and may not be suitable for legal purposes.Includes bibliographical references (pages 38-39).Funded by: Oregon Criminal Justice Commission.Mode of access: Internet from the Oregon Government Publications Collection.Text in English
Overconvergent de Rham-Witt cohomology for semistable varieties
No full textThis is the author accepted manuscript. The final version is available from the Mathematisches Institut, Universität Münster via the DOI in this recordWe define an overconvergent version of the Hyodo-Kato complex for semistable
varieties Y over perfect fields of positive characteristic, and prove that its hypercohomology
tensored with Q recovers the log-rigid cohomology when Y is quasi-projective. We then
describe the monodromy operator using the overconvergent Hyodo-Kato complex. Finally,
we show that overconvergent Hyodo-Kato cohomology agrees with log-crystalline cohomology
in the projective semistable cas
Volterra Centennial Meetings - Invited talks given by Christopher Baker at Arlington & Tempe
No full textJune 1996 saw two meetings to mark the centennial of the mathematical work of Vito Volterra, the first being held at the University of Texas at Arlington (organised by Professors Corduneanu and Kanner) and the second at the State University of Arizona at Tempe. In invited talks at each meeting, the first-named author presented joint work that follows, in chronological sequence, in this technical report. Christopher T H Baker & Arslang Tang 2 GENERALIZED HALANAY INEQUALITIES FOR VOLTERRA FUNCTIONAL DIFFERENTIAL EQUATIONS AND DISCRETIZED VERSIONS CHRISTOPHER T.H. BAKER 1 & ARSALANG TANG 2 Department of Pure and Applied Mathematics, The Victoria University of Manchester, England Abstract. Halanay's inequality provides a decreasing bound on a function satisfying a delay-differential inequality, subject to certain conditions, and it has been used by Halanay to analyze asymptotic stability of the zero solution of a certain delay-differential equations with fixed lag. The original ineq..
Pannexin-1 and P2X7-Receptor Are Required for Apoptotic Osteocytes in Fatigued Bone to Trigger RANKL Production in Neighboring Bystander Osteocytes
No full textOsteocyte apoptosis is required to induce intracortical bone remodeling after microdamage in animal models, but how apoptotic osteocytes signal neighboring “bystander” cells to initiate the remodeling process is unknown. Apoptosis has been shown to open pannexin-1 (Panx1) channels to release adenosine diphosphate (ATP) as a “find me” signal for phagocytic cells. To address whether apoptotic osteocytes use this signaling mechanism, we adapted the rat ulnar fatigue-loading model to reproducibly introduce microdamage into mouse cortical bone and measured subsequent changes in osteocyte apoptosis, receptor activator of NF-kB ligand (RANKL) expression and osteoclastic bone resorption in wild-type (WT; C57Bl/6) mice and in mice genetically deficient in Panx1 (Panx1KO). Mouse ulnar loading produced linear microcracks comparable in number and location to the rat model. WT mice showed increased osteocyte apoptosis and RANKL expression at microdamage sites at 3 days after loading and increased intracortical remodeling and endocortical tunneling at day 14. With fatigue, Panx1KO mice exhibited levels of microdamage and osteocyte apoptosis identical to WT mice. However, they did not upregulate RANKL in bystander osteocytes or initiate resorption. Panx1 interacts with P2X7R in ATP release; thus, we examined P2X7R-deficient mice and WT mice treated with P2X7R antagonist Brilliant Blue G (BBG) to test the possible role of ATP as a find-me signal. P2X7RKO mice failed to upregulate RANKL in osteocytes or induce resorption despite normally elevated osteocyte apoptosis after fatigue loading. Similarly, treatment of fatigued C57Bl/6 mice with BBG mimicked behavior of both Panx1 KO and P2X7RKO mice; BBG had no effect on osteocyte apoptosis in fatigued bone but completely prevented increases in bystander osteocyte RANKL expression and attenuated activation of resorption by more than 50%. These results indicate that activation of Panx1 and P2X7R are required for apoptotic osteocytes in fatigued bone to trigger RANKL production in neighboring bystander osteocytes and implicate ATP as an essential signal mediating this process.Peer reviewe
- …
