scholarly journals Derived Categories and the Analytic Approach to General Reciprocity Laws: Part III

2010 ◽  
Vol 2010 ◽  
pp. 1-19
Author(s):  
Michael C. Berg
Keyword(s):  
Recent Work ◽  
Geometric Phase ◽  
Metric Spaces ◽  
Singularity Analysis ◽  
Derived Categories ◽  
Analytic Approach ◽  
Stability Conditions ◽  
Complex Manifolds ◽  
Reciprocity Laws ◽  
The Way

Building on the scaffolding constructed in the first two articles in this series, we now proceed to the geometric phase of our sheaf (-complex) theoretic quasidualization of Kubota's formalism forn-Hilbert reciprocity. Employing recent work by Bridgeland on stability conditions, we extend our yoga oft-structures situated above diagrams of specifically designed derived categories to arrangements of metric spaces or complex manifolds. This prepares the way for provingn-Hilbert reciprocity by means of singularity analysis.

scholarly journals Derived categories and the analytic approach to general reciprocity laws. Part I

2005 ◽  
Vol 2005 (13) ◽  
pp. 2133-2158 ◽  
Author(s):  
Michael Berg
Keyword(s):  
Open Problem ◽  
Derived Categories ◽  
Derived Category ◽  
Analytic Approach ◽  
Topological Spaces ◽  
Analytic Proof ◽  
Reciprocity Laws

We reformulate Hecke's open problem of 1923, regarding the Fourier-analytic proof of higher reciprocity laws, as a theorem about morphisms involving stratified topological spaces. We achieve this by placing Kubota's formulations ofn-Hilbert reciprocity in a new topological context, suited to the introduction of derived categories of sheaf complexes. Subsequently, we begin to investigate conditions on associated sheaves and a derived category of sheaf complexes specifically designed for an attack on Hecke's eighty-year-old challenge.

MANUSCRIPT EVIDENCE FOR ALPHABET-SWITCHING IN THE WORKS OF CICERO: COMMON NOUNS AND ADJECTIVES

2018 ◽  
Vol 68 (2) ◽  
pp. 498-516
Author(s):  
Neil O'Sullivan
Keyword(s):  
Recent Work ◽  
Code Switching ◽  
Consistent Pattern ◽  
Current Interest ◽  
Reliable Transmission ◽  
Accurate Record ◽  
The Way

Of the hundreds of Greek common nouns and adjectives preserved in our MSS of Cicero, about three dozen are found written in the Latin alphabet as well as in the Greek. So we find, alongside συμπάθεια, also sympathia, and ἱστορικός as well as historicus. This sort of variation has been termed alphabet-switching; it has received little attention in connection with Cicero, even though it is relevant to subjects of current interest such as his bilingualism and the role of code-switching and loanwords in his works. Rather than addressing these issues directly, this discussion sets out information about the way in which the words are written in our surviving MSS of Cicero and takes further some recent work on the presentation of Greek words in Latin texts. It argues that, for the most part, coherent patterns and explanations can be found in the alphabetic choices exhibited by them, or at least by the earliest of them when there is conflict in the paradosis, and that this coherence is evidence for a generally reliable transmission of Cicero's original choices. While a lack of coherence might indicate unreliable transmission, or even an indifference on Cicero's part, a consistent pattern can only really be explained as an accurate record of coherent alphabet choice made by Cicero when writing Greek words.

Church Discipline in the Later Middle Ages: the Priors of Durham as Archdeacons

2004 ◽  
Vol 40 ◽  
pp. 95-105
Author(s):  
Margaret Harvey
Keyword(s):  
Recent Work ◽  
Middle Ages ◽  
Fourteenth Century ◽  
Local Level ◽  
Church Discipline ◽  
Full Account ◽  
Church Courts ◽  
Medieval Church ◽  
The Church ◽  
The Way

It is often forgotten that the medieval Church imposed public penance and reconciliation by law. The discipline was administered by the church courts, among which one of the most important, because it acted at local level, was that of the archdeacon. In the later Middle Ages and certainly by 1435, the priors of Durham were archdeacons in all the churches appropriated to the monastery. The priors had established their rights in Durham County by the early fourteenth century and in Northumberland slightly later. Although the origins of this peculiar jurisdiction were long ago unravelled by Barlow, there is no full account of how it worked in practice. Yet it is not difficult from the Durham archives to elicit a coherent account, with examples, of the way penance and ecclesiastical justice were administered from day to day in the Durham area in this period. The picture that emerges from these documents, though not in itself unusual, is nevertheless valuable and affords an extraordinary degree of detail which is missing from other places, where the evidence no longer exists. This study should complement the recent work by Larry Poos for Lincoln and Wisbech, drawing attention to an institution which would reward further research. It is only possible here to outline what the court did and how and why it was used.

The Toccatas of Bach

1912 ◽  
Vol 39 ◽  
pp. 45-53
Author(s):  
J. A. Fuller-Maitland
Keyword(s):  
Recent Work ◽  
Good Reason ◽  
General Character ◽  
Valuable Book ◽  
The Way

There are no fewer than twelve complete works of Sebastian Bach to which the name Toccata is applied, and in nearly all cases the title seems to have come from the composer himself. It is always worth while to trace, if we can, the reasons which led a great man to choose one name rather than another for his creations; and in the case of Bach, I think we are justified in supposing that the names he gave were not purely arbitrary, but were chosen for some good reason. Certain modern composers, notably Brahms, have shown a strange indifference to the effect wrought by a well-chosen name for their music. His later works for pianoforte, often grouped under the heading of “Fantasias,” are divided into “Intermezzi” and “‘Capricci” according to whether they are slow movements or fast. But Bach, with his methodical habits, never showed that kind of almost perverse nonchalance in regard to the names his works were to bear. Remember the “Partitas,” and how each of the six introductory movements had a different designation from all the rest. As a matter of fact, there is not much indication of any inner variety of structure among the six, for all are preludial in general character, and it is evidently only a whim of the composer to give the six different titles. One of these, the sixth by the way, is styled “Toccata,” but has none of the distinguishing marks which, I hope to persuade you, Bach had in his mind when he used the title for independent compositions. Mr. Albert Schweitzer in his exceedingly valuable book on Bach (I am speaking of the recent work in two volumes, translated from the French by Mr. Ernest Newman) says that these Toccatas might just as well have been called Sonatas, or by any other name. Here I cannot agree with him, and the main object of my remarks on the present occasion.is to examine into the structure and style of the pieces, and see if we cannot discern some characteristic common to them all, and not shared by any other compositions of Bach.

Divine Attributes as a Topic in Analytic Theology

2020 ◽  
pp. 83-97
Author(s):  
Michael C. Rea
Keyword(s):  
Philosophy Of Religion ◽  
Analytic Philosophy ◽  
Analytic Approach ◽  
Divine Attributes ◽  
Distinctive Character ◽  
Philosophical Literature ◽  
Distinctive Features ◽  
Distinguishing Features ◽  
The Way

Analytic theology differs from other forms of theology primarily in its methodology: its ambitions, its style, its conversation partners, and so on. This is where the most interesting differences between analytic philosophical discussions of the divine attributes and contemporary theological discussions of that topic are to be found. The main positive thesis of this chapter is that the most distinctive features of the approach to divine attributes that one finds in the analytic philosophical literature are simply instances of more general distinctives of analytic theology. The chapter focuses on some of the distinguishing features of the way in which the topic of divine attributes is approached in analytic philosophy of religion as contrasted with the way(s) in which many contemporary theologians are inclined to approach it. The end result is a clearer picture both of the nature of analytic theology in general and of the distinctive character of an analytic approach to the topic of divine attributes.

scholarly journals Derived Categories and the Analytic Approach to General Reciprocity Laws—Part II

2007 ◽  
Vol 2007 ◽  
pp. 1-27 ◽  
Author(s):  
Michael C. Berg
Keyword(s):  
Number Field ◽  
Open Problem ◽  
Special Linear Group ◽  
Derived Categories ◽  
Topological Spaces ◽  
Base Field ◽  
Analytic Proof ◽  
Reciprocity Laws ◽  
Fold Cover ◽  
Topological Form

Building on the topological foundations constructed in Part I, we now go on to address the homological algebra preparatory to the projected final arithmetical phase of our attack on the analytic proof of general reciprocity for a number field. In the present work, we develop two algebraic frameworks corresponding to two interpretations of Kubota'sn-Hilbert reciprocity formalism, presented in a quasi-dualized topological form in Part I, delineating two sheaf-theoretic routes toward resolving the aforementioned (open) problem. The first approach centers on factoring sheaf morphisms eventually to yield a splitting homomorphism for Kubota'sn-fold cover of the adelized special linear group over the base field. The second approach employs linked exact triples of derived sheaf categories and the yoga of gluingt-structures to evolve a means of establishing the vacuity of certain vertices in diagrams of underlying topological spaces from Part I. Upon assigning properly designedt-structures to three of seven specially chosen derived categories, the collapse just mentioned is enough to yieldn-Hilbert reciprocity.

Co-constructing referential space in multimodal narratives

2014 ◽  
Vol 7 (1) ◽  
pp. 31-59 ◽  
Author(s):  
Kashmiri Stec ◽  
Mike Huiskes
Keyword(s):  
Recent Work ◽  
Meaning Making ◽  
Spatial Location ◽  
Multimodal Communication ◽  
Dynamic Processes ◽  
Multimodal Process ◽  
Spatial Locations ◽  
The Way

Abstract Meaning-making is a situated, multimodal process. Although most research has focused on conceptualization in individuals, recent work points to the way dynamic processes can affect both conceptualization and expression in multiple individuals (e.g. Özyürek 2002; Fusaroli and Tylén 2012; Narayan 2012). In light of this, we investigate the co-construction of referential space in dyadic multimodal communication. Referential space is the association of a referent with a particular spatial location (McNeill and Pedelty 1995). We focus on the multimodal means by which dyads collaboratively co-construct or co-use referential space, and use it to answer questions related to its use and stability in communication. Whereas previous work has focused on an individual's use of referential space (So et al. 2009), our data suggest that spatial locations are salient to both speakers and addressees: referents assigned to particular spatial locations can be mutually accessible to both participants, as well as stable across longer stretches of discourse.

Ménière, a Man of Many Interests

2016 ◽  
Author(s):  
Robert W. Baloh
Keyword(s):  
19Th Century ◽  
Analytic Approach ◽  
Medical Studies ◽  
Preparatory School ◽  
School Of Medicine ◽  
The University ◽  
19Th Century France ◽  
The Way

Prosper Ménière was born in1799 in Angers, France. Ménière completed 3 years at the Preparatory School of Medicine at the University of Angers before moving to Paris in 1819 to complete his medical studies. He received his doctorate of medicine in 1828 and was appointed as an aide in the clinic of the famous surgeon Baron Dupuytren in the Hôtel-Dieu. The way that Ménière went about educating himself on the anatomy, physiology, and pathology of the ear after his appointment to head the Deaf-Mute Institute in 1838 provides insight to his analytic approach. In the years that he served as Director of the Deaf-Mute Institute, Ménière socialized with some of the most prominent members of mid-19th-century France. He was probably as well known a figure in society as he was as a physician. Ménière was a complex man with many different interests and many talents.

The Byzantine Church: a bibliographical note on recent work

1950 ◽  
Vol 1 (1) ◽  
pp. 102-113
Author(s):  
Norman H. Baynes
Keyword(s):  
United States ◽  
Recent Work ◽  
The United States ◽  
British Isles ◽  
Bibliographical Note ◽  
Byzantine Church ◽  
The Way ◽  
Byzantine History

In these days the compilation of a bibliography of the publications of recent years is an exasperating occupation: if a book or journal has not been destroyed by bombing, it will probably be out of print, and it is not easy to understand why so many obstacles are set in the way of a free commerce in books. The result has been that students have tended to limit themselves to recording the works published in their own country. Take, for example, the field of Byzantine studies: A. Grabar has reported on ‘La Byzantinologie française pendant la Guerre 1940–45”, Byzantion, 17 (1944–5), 431–8; Wilhelm Ensslin has written a valuable critical report on German work on Byzantine history for the years 1939–47, Byzantion, 17 (1946–8), 261–302, cf. Klio 33 (1940), 349–68, 35 (1942), 164–77; in Byzantinoslavica there has appeared a series of bibliographical reports: Grabar for France in 9 (1947), 126–32, Ostrogorsky and Radolchich for Yugoslavia, ibid., 133–42; Lebedev for Russia (1936 to 1946), ibid., 97–112; M. Paulova for Czechoslovakia, ibid., 144–7; Runciman for Turkey, ibid., 143–4; A. Elian for Roumania, ibid., 393–405; Anguélov and Dimitrov for Bulgaria, ibid., 355–78; Moravcsik for Hungary, ibid., 379–92; Charanis for the United States, ibid., 342–54; for the British Isles Hussey and Baynes, ibid., 113ñ26, while Soloviev has written on Byzantine work published in Yugoslavia (1937 to 1947) in Byzantion 17 (1946–8), 303–10 and Delvoye has reported on Travaux récents sur les Monuments byzantins de la Grèce (1938ñ47), ibid., 229–60 and has studied L'Ecole Française d'Athènes et les Etudes Byzantines, R.E.B., 6 (1948), 86–93.

Initiation of archaeal DNA replication

2003 ◽  
Vol 31 (3) ◽  
pp. 669-673 ◽  
Author(s):  
E.R. Jenkinson ◽  
J.P.J. Chong
Keyword(s):  
Dna Replication ◽  
Recent Work ◽  
Genetic Information ◽  
Genetic Material ◽  
50Th Anniversary ◽  
Enormous Amount ◽  
Biological Concepts ◽  
Archaeal Dna Replication ◽  
The Way

The identification of DNA as the genetic material and the elucidation of its structure by Watson and Crick [Watson and Crick, (1953) Nature (London) 171, 737–738], which has its 50th anniversary this year, first suggested the simple elegance with which the problem of passing on precise genetic information from one generation to the next could be solved. Semi-conservative replication is perhaps one of the simplest biological concepts to explain and understand. However, despite an enormous amount of effort in the intervening years, details of the way in which this process is regulated and performed are still unclear in many organisms. Recent work suggests that, due to their simplicity, the Archaea may make a good model for understanding some of the aspects of eukaryotic replication that still elude us.

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