Resolvents and trace form

1975 ◽  
Vol 78 (2) ◽  
pp. 185-210 ◽  
Author(s):  
A. Fröhlich
Keyword(s):  
General Theory ◽  
Number Fields ◽  
The Other ◽  
General Context ◽  
Module Structure ◽  
Galois Module ◽  
Trace Form ◽  
Root Numbers ◽  
Arithmetic Theory ◽  
The One

This paper is a continuation of (F3). In its first part we shall expand and extend the general theory of the earlier paper, while in the second part we specialize to number fields. The theory of resolvents and of the trace form, presented here, complements the more arithmetic theory of module conductors and module resolvents as described elsewhere (cf. (F4)). Both these papers will be applied in work on the connexion, for tame extensions, between Galois module structure of algebraic integers on the one hand, and Artin conductors and root numbers on the other hand (cf. (F5)). The results of the present paper are however not restricted to the tame case and, it is hoped, will subsequently be applied in a more general context.

scholarly journals FACTOR EQUIVALENCE OF GALOIS MODULES AND REGULATOR CONSTANTS

2014 ◽  
Vol 10 (01) ◽  
pp. 1-12
Author(s):  
ALEX BARTEL
Keyword(s):  
Number Fields ◽  
The Other ◽  
Module Structure ◽  
Integral Group ◽  
Galois Module ◽  
Group Representations ◽  
Galois Modules ◽  
Rings Of Integers ◽  
The One ◽  
Module Structures

We compare two approaches to the study of Galois module structures: on the one hand, factor equivalence, a technique that has been used by Fröhlich and others to investigate the Galois module structure of rings of integers of number fields and of their unit groups, and on the other hand, regulator constants, a set of invariants attached to integral group representations by Dokchitser and Dokchitser, and used by the author, among others, to study Galois module structures. We show that the two approaches are in fact closely related, and interpret results arising from these two approaches in terms of each other. We then use this comparison to derive a factorizability result on higher K-groups of rings of integers, which is a direct analogue of a theorem of de Smit on S-units.

On p-adic height pairings and locally free classgroups of Hopf orders

1998 ◽  
Vol 123 (3) ◽  
pp. 447-459
Author(s):  
A. AGBOOLA
Keyword(s):  
Elliptic Curve ◽  
Quadratic Field ◽  
Homogeneous Spaces ◽  
Complex Multiplication ◽  
Imaginary Quadratic Field ◽  
The Other ◽  
Module Structure ◽  
Galois Module ◽  
Ring Of Integers ◽  
The One

Let E be an elliptic curve with complex multiplication by the ring of integers [Ofr ] of an imaginary quadratic field K. The purpose of this paper is to describe certain connections between the arithmetic of E on the one hand and the Galois module structure of certain arithmetic principal homogeneous spaces arising from E on the other. The present paper should be regarded as a complement to [AT]; we assume that the reader is equipped with a copy of the latter paper and that he is not averse to referring to it from time to time.

scholarly journals Eternal Contemporaneity in Advertisements of „Naujoji Romuva“ (1931–1940)

2014 ◽  
Vol 26 (31) ◽  
pp. 177-189
Author(s):  
Gabija Bankauskaitė-Sereikienė ◽  
Eglė Keturakienė
Keyword(s):  
Modern Society ◽  
The Other ◽  
General Context ◽  
Other Hand ◽  
The One ◽  
A Performance

Advertising appealing to senses is satiated with the dream of immortality. The society striving for an eternal state of mythical youth lives in the reality of theatre and manipulations. On the one hand, advertising offers certain society life models through myth, archetypical symbols. On the other hand, culture of global observation, watching changes life into an illusion and life simulation. The more a person succumbs to abstractedness of life in advertisements, the greater demand for mythical time, eternal moment and harmony arises. Advertising which has categorically prohibited for a society to get older, gives an individual an illusion of eternal contemporaneity through archetypes. Modern man sees himself as a creator of history, hence, he feels great temptation to take part in an imaginary act of creation. The article provides the analysis of archetypac imagery in interwar advertisements on the basis of insights of R. Barthes, G. Debord and M. McLuhan on mythological structures of thinking, advertisements and modern society of a performance as well as thoughts of M. Eliade on repetition of time. For the analysis publication Naujoji Romuva (1931-1940) has been chosen. The expression of archetypes has been discussed after they have been categorized into three groups under character and general context of archetypal structures: archetypes of world creation, prototypes of man and woman, and mythical, folklore. Prototypes of man as a hero and woman as having a mystic role to continue the cycle of life, as well as mythical, folklore symbols (mirror, horseshoe, spruce, flower) also play the said role. Archetypal imagery is often found in advertisements of cosmetics, chemicals and sealants.

scholarly journals Galois module structure of units in real biquadratic number fields

2004 ◽  
Vol 111 (2) ◽  
pp. 105-124 ◽  
Author(s):  
Marcin Mazur ◽  
Stephen V. Ullom
Keyword(s):  
Number Fields ◽  
Module Structure ◽  
Galois Module ◽  
Galois Module Structure

scholarly journals Deformation of finite morphisms and smoothing of ropes

2008 ◽  
Vol 144 (3) ◽  
pp. 673-688 ◽  
Author(s):  
Francisco Javier Gallego ◽  
Miguel González ◽  
Bangere P. Purnaprajna
Keyword(s):  
General Theory ◽  
Projective Space ◽  
General Result ◽  
The Other ◽  
Independent Interest ◽  
Higher Dimension ◽  
Smooth Curves ◽  
Other Hand ◽  
Finite Covers ◽  
The One

AbstractIn this paper we prove that most ropes of arbitrary multiplicity supported on smooth curves can be smoothed. By a rope being smoothable we mean that the rope is the flat limit of a family of smooth, irreducible curves. To construct a smoothing, we connect, on the one hand, deformations of a finite morphism to projective space and, on the other hand, morphisms from a rope to projective space. We also prove a general result of independent interest, namely that finite covers onto smooth irreducible curves embedded in projective space can be deformed to a family of 1:1 maps. We apply our general theory to prove the smoothing of ropes of multiplicity 3 on P1. Even though this paper focuses on ropes of dimension 1, our method yields a general approach to deal with the smoothing of ropes of higher dimension.

The Aš‘arite Ontology: I Primary Entities

1999 ◽  
Vol 9 (2) ◽  
pp. 163-231 ◽  
Author(s):  
Richard M. Frank
Keyword(s):  
The Other ◽  
Careful Examination ◽  
General Context ◽  
The One

The present study seeks to lay out the most basic elements of the ontology of classical Aš‘arite theology. In several cases this requires a careful examination of the traditional and the formal lexicography of certain key expressions. The topics primarily treated are: (1) how they understood “Being/ existence” and “being/existent” and essential natures; the systematic exploitation of the equivocities of certain expressions (e.g., ḫaqīqa, ḫadd, ma‘na) within a general context in which other than words there are no universals proves to be elegant as well as insightful; (2) the basic categories of primary entities: independant beings and nonindependant beings, (a) created and (b) uncreated, the equivocity of “being/existent” as predicated of contingent entities on the one hand and of God and His attributes on the other, and certain problems that arise because of the rigid application of the system's underlying analytic principles.

Reflections on the Epistemology of Psychiatry

1988 ◽  
Vol 33 (8) ◽  
pp. 686-690 ◽  
Author(s):  
Keith A. Yonge
Keyword(s):  
General Theory ◽  
Theoretical Basis ◽  
Training Programs ◽  
The Other ◽  
Psychiatric Training ◽  
Modus Operandi ◽  
Course Content ◽  
Holistic Concept ◽  
The One ◽  
True Knowledge

A re-examination of the theoretical basis of our practice of psychiatry (that is, its epistemology) reveals the insufficiency of the empirical, inductive approach which we have come to regard, too myopically, as the sine qua non of our science. Traditionally in psychiatry, the discipline of philosophy, of which epistemology is one of its major fields of endeavour, has generally come to be regarded as irrelevant or unreliable as a source of true knowledge. But an objective look at our variegated practice of psychiatry — roughly divided into two groups — the biological on the one side and the psychosocial on the other — reveals a glaring lack of integration, cohesion, or synthesis in basic theory. While analysis is the prime modus operandi of science, synthesis is the main objective of philosophy. While we subscribe to various operational theories to explain how our various procedures work, we lack an overarching, unified, general theory to subsume them. Hence we lack a truly holistic concept of the person who is our patient. In this we are much in need of the discipline of philosophy, which promotes clarity of thought, breadth of comprehension, and systematic (logical) reasoning. Psychiatrists acquire more of this philosophic expertise through collaboration with professional philosophers (epistemologists in particular) and through the introduction into our graduate psychiatric training programs of some specific course content from the literature of philosophy. As a preliminary suggestion for this, an “Annotated Reading List” is appended.

A Module-on-module Manufacturing Process and the Study of its Warpage and Signal Integrity

2015 ◽  
Vol 2015 (DPC) ◽  
pp. 001429-001444
Author(s):  
Thomas Wang ◽  
James Lin ◽  
Tony Cheng ◽  
Ping-Chi Hong ◽  
Albert Lin ◽  
...  
Keyword(s):  
Manufacturing Process ◽  
Signal Integrity ◽  
Product Line ◽  
The Other ◽  
Module Structure ◽  
Assembly Process ◽  
Package Design ◽  
Manufacturing Assembly ◽  
The One ◽  
Electrical Connections

This paper describes a package design and associated manufacturing assembly process that stack a module on top of another module using a frame board. The module on the top could be in molded or open frame form. In addition, this manufacturing process is compatible with the conformal shielding process important in RF applications. The complete module-on-module can be coated seamlessly and connected to the ground planes of the two substrates. The module may be a part of product line that requires more functionality over the same foot print. There is the need to houses more components than its predecessor. Such example includes the standard memory package-on-package. However, if the module on top is not of commodity type, or when the volume is not big enough to develop a standard package, this module-on-module architecture and process could be a good solution. Alternatively, one could fix the design of bottom module , and design multiple choices of the top module. When stacked together, the two modules form various different configurations in order to serve different functionalities. The structure of the module on module is shown in figure 1 below: Figure 1 Structure of the Module on Module On the frame board, there are vertical via where vertical electrical and power connection can be made. The frame board is mounted on the main board-II by surface mount process with underfill option. In the figure, a molded module on the top is shown, and an overall coating is applied to the whole module-on-module. Figure 2 Manufacturing Process of the Module-on-module The assembly process of the module-on-module is shown in Figure 2. First, the bottom module is manufactured by a one side SMT process and sawed, with the frame board soldered and underfilled. Then, the top module is SMT and molded in a panel form on the one side, and the bottom module is SMT and underfilled on the other side. Last, the complete module is sawed and conformal shielded by the sputtering process. The design of the ground plans of the substrates, together with that of the frame board, makes it such that the coating is connected to the ground planes of the boards. It is important to study the warpage of such a module-on-module to make sure that it meets the JDEC standards. It is important to assure that the signal integrity of the electrical connections, including RF connections, inside of the frame board meets the requirement. Both simulation and measurement are made to test vehicles of the module-on-module. It is found that the simulation matches the measurement nicely. This module structure can be used for a variety of applications.

Sign in / Sign up

Export Citation Format

Share Document