A general reciprocity law for symbols on arbitrary vector spaces

2018 ◽  
Vol 17 (06) ◽  
pp. 1850101
Author(s):  
Fernando Pablos Romo
Keyword(s):  
General Theory ◽  
General Expression ◽  
Vector Spaces ◽  
Residue Theorem ◽  
Arbitrary Vector ◽  
The Past ◽  
Reciprocity Laws ◽  
Reciprocity Law ◽  
Norm Residue ◽  
Hilbert Norm

The aim of this work is to offer a general theory of reciprocity laws for symbols on arbitrary vector spaces and to show that classical explicit reciprocity laws are particular cases of this theory (sum of valuations on a complete curve, Residue Theorem, Weil Reciprocity Law and the Reciprocity Law for the Hilbert Norm Residue Symbol). Moreover, several reciprocity laws introduced over the past few years by D. V. Osipov, A. N. Parshin, I. Horozov, I. Horozov — M. Kerr and the author — together with D. Hernández Serrano — can also be deduced from this general expression.

scholarly journals Products of two idempotent transformations over arbitrary sets and vector spaces

1998 ◽  
Vol 57 (1) ◽  
pp. 59-71 ◽  
Author(s):  
Rachel Thomas
Keyword(s):  
Vector Space ◽  
Transformation Semigroup ◽  
Vector Spaces ◽  
Endomorphism Monoid ◽  
Linear Transformations ◽  
Arbitrary Vector ◽  
Full Transformation ◽  
Full Transformation Semigroup

In this paper we consider the characterisation of those elements of a transformation semigroup S which are a product of two proper idempotents. We give a characterisation where S is the endomorphism monoid of a strong independence algebra A, and apply this to the cases where A is an arbitrary set and where A is an arbitrary vector space. The results emphasise the analogy between the idempotent generated subsemigroups of the full transformation semigroup of a set and of the semigroup of linear transformations from a vector space to itself.

Situating World Englishes into a History of English Course

2017 ◽  
Author(s):  
Rakesh M. Bhatt
Keyword(s):  
General Theory ◽  
World Englishes ◽  
Post Colonial ◽  
The Past ◽  
Cultural Conditions ◽  
History Of ◽  
Colonial Encounter ◽  
World English ◽  
Local Logics

This chapter will address the teaching of “post-colonial Englishes,” focusing on the sociopolitical and cultural conditions that enabled changes in English as it was used during, and after, the colonial encounter. To capture the complexity of linguistic hybridities associated with plural identities, our disciplinary discourses of the global use and acquisition of English must (i) liberate the field of World Englishes from the orthodoxies of the past and instead connect it to a more general theory of the sociolinguistics of globalization, and, especially (ii) bring into focus local forms shaped by the local logics of practice. This chapter discusses specific examples of the practice of creativity in grammar, discourse, and sociolinguistic use of World English varieties.

The Norm Residue Theorem in Motivic Cohomology

2019 ◽  
Author(s):  
Christian Haesemeyer ◽  
Charles A. Weibel
Keyword(s):  
Residue Theorem ◽  
Motivic Cohomology ◽  
Norm Residue

Presidential Address Dictionaries and Dictionary Making: Malay and Indonesian

1978 ◽  
Vol 38 (1) ◽  
pp. 11-24 ◽  
Author(s):  
John M. Echols
Keyword(s):  
General Theory ◽  
Present State ◽  
Presidential Address ◽  
The State ◽  
The Past ◽  
Thirtieth Anniversary

Fifteen years ago, or halfway to this year's thirtieth anniversary, in his presidential address to this association, Earl Pritchard began by saying: “In accordance with tradition, it now becomes my duty to perform a time-honored rite—to inflict on you the Presidential Address. I will try to do this as painlessly and as quickly as my own inadequacies will permit.… It is … customary, according to the unwritten rules governing the rituals of the present occasion, for the president to review in some way or other the state of the profession or of the discipline to which he belongs, or to present some general theory which interests him, or to discuss the direction that studies in the profession are taking or should take.…” Like Pritchard I have no inclination to depart sharply from this pattern, and I hope here merely to review briefly the past and present state of Malay and Indonesian lexicography. I have chosen this topic because it has been of great and abiding interest to me and because I have, in a modest way, tried to contribute to its furtherance.

International Relations: The Long Road to Theory

1959 ◽  
Vol 11 (3) ◽  
pp. 346-377 ◽  
Author(s):  
Stanley H. Hoffmann
Keyword(s):  
General Theory ◽  
International Relations ◽  
Present State ◽  
Theoretical Work ◽  
The Past

It has become customary to begin a discussion of the nature and present state of the discipline of international relations with a number of complaints. This article will not abandon the custom; indeed, its purpose is, in the first place, to state the conviction that many of the problems we face in our field can be solved only by far more systematic theoretical work than has been done in the past—a conviction shared by most writers. Secondly, however, I will try to show that recent approaches to a general theory of international relations are unsatisfactory, because each one is, in its own fashion, a short cut to knowledge—sometimes even a short cut to a destination that is anything but knowledge.

Lexical government and tone group formation in Xiamen Chinese

Phonology ◽  
1994 ◽  
Vol 11 (2) ◽  
pp. 237-275 ◽  
Author(s):  
Jo-wang Lin
Keyword(s):  
General Theory ◽  
Syntactic Structure ◽  
Group Formation ◽  
Phonological Representation ◽  
Prosodic Structure ◽  
Tone Sandhi ◽  
Field Of Study ◽  
The Past ◽  
Syntactic Information

The study of the relation between syntactic structure and phonological representation has attracted the attention of many phonologists in the past few years. One important contribution to this field of study is Chen's (1987) work on Xiamen Chinese tone sandhi domains. He suggests that the syntax–phonology relation appeals to syntactic information such as category types and the edges of syntactic bracketings. This insight has been further elaborated in the general theory of the syntax—phonology relation of Selkirk (1986). In this theory, the relation between syntactic structure and prosodic structure above the foot and below the intonational phrase is defined in terms of the edges of syntactic constituents of designated types. More precisely, this theory incorporates two hypotheses. One is that there are designated category types in syntactic structure with respect to which one end (Right or Left) of the designated category is relevant in the formulation of a prosodic constituent C, which extends from one instance of the appropriate end (R/L) of the designated category to the next. This hypothesis has been called the End Parameter.

Functional Ambiguity in Musical Structures

1983 ◽  
Vol 1 (1) ◽  
pp. 3-27 ◽  
Author(s):  
William Thomson
Keyword(s):  
General Theory ◽  
Final Section ◽  
Limited Attention ◽  
Musical Structure ◽  
The Past ◽  
Extensive Analysis ◽  
Musical Structures ◽  
Definition Of

This paper first establishes a definition of ambiguity and its significance to art and to perception in general. Its understanding is framed within a hierarchical conception of musical structure most similar to that of Leonard B. Meyer (1956,1973). Following (1) an illustrative survey of occurrences of intentional ambiguity found in the standard music repertory, and (2) a discussion of the limited attention paid by music theorists to ambiguity in the past, a general theory of musical ambiguity's causes is developed. The paper's final section consists of an extensive analysis of functional ambiguity as a principal expressive vehicle in Chopin's Mazurka, Opus 17, No. 4.

scholarly journals Innovative Approach to Solving Theoretical Issues of the Ecological and Epidemiological Concept of Sapronoses

2018 ◽  
Vol 17 (1) ◽  
pp. 87-94
Author(s):  
A. B. Belov
Keyword(s):  
Veterinary Medicine ◽  
General Theory ◽  
Infectious Diseases ◽  
Biomedical Sciences ◽  
Russian Science ◽  
Research And Practice ◽  
The Past ◽  
The World ◽  
History Of ◽  
Theoretical Issues

The history of the study of infections attributed by the microbiologist and epidemiologist V.I. Tersky in 1958 as the class of human infectious diseases – «Sapronoses» is presented. Over the past 60 years in the world and especially in Russian science the knowledge that allows us to complete the development of an ecological and epidemiological theory of sapronoses infections was accumulated. This knowledge should be extended to the whole complex of biomedical sciences associated with the population pathology of biota. To solve the controversial and complex issues of the theory, terminology and classifications of population infectology, it is necessary to integrate the knowledge of specialists in various fields of research and practice in the medicine, veterinary medicine, parasitology, phytopathology and other disciplines. The ways and prospects of improving the general theory of infectology in the light of new approaches to understanding the essence of sapronoses are discussed. 

Products of idempotent linear transformations

1985 ◽  
Vol 100 (1-2) ◽  
pp. 123-138 ◽  
Author(s):  
M. A. Reynolds ◽  
R. P. Sullivan
Keyword(s):  
Hilbert Space ◽  
Separable Hilbert Space ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Bounded Operators ◽  
Linear Transformations ◽  
Arbitrary Vector ◽  
Dimensional Vector Space ◽  
Finite Dimensional Vector Space ◽  
Finite Dimensional

SynopsisIn 1966, J. M. Howie characterised the transformations of an arbitrary set that can be written as a product (under composition) of idempotent transformations of the same set. In 1967, J. A. Erdos considered the analogous problem for linear transformations of a finite-dimensional vector space and in 1983, R. J. Dawlings investigated the corresponding idea for bounded operators on a separable Hilbert space. In this paper we study the case of arbitrary vector spaces.

scholarly journals Orbifolding Frobenius Algebras

2003 ◽  
Vol 14 (06) ◽  
pp. 573-617 ◽  
Author(s):  
Ralph M. Kaufmann
Keyword(s):  
General Theory ◽  
Gauge Group ◽  
Physical Theory ◽  
Group Actions ◽  
Vector Spaces ◽  
Algebraic Structures ◽  
Jacobian Ideal ◽  
Frobenius Algebras

We study the general theory of Frobenius algebras with group actions. These structures arise when one is studying the algebraic structures associated to a geometry stemming from a physical theory with a global finite gauge group, i.e. orbifold theories. In this context, we introduce and axiomatize these algebras. Furthermore, we define geometric cobordism categories whose functors to the category of vector spaces are parameterized by these algebras. The theory is also extended to the graded and super-graded cases. As an application, we consider Frobenius algebras having some additional properties making them more tractable. These properties are present in Frobenius algebras arising as quotients of Jacobian ideal, such as those having their origin in quasi-homogeneous singularities and their symmetries.

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