Independent Axioms for Vector Spaces

1973 ◽  
Vol 57 (399) ◽  
pp. 56-62 ◽  
Author(s):  
J. F. Rigby ◽  
James Wiegold
Keyword(s):  
Vector Space ◽  
Present Article ◽  
The Other ◽  
Vector Spaces ◽  
To Receive

In a recent paper [1], Victor Bryant shows how the number of axioms required to define a vector space can be reduced to seven (in addition to closure requirements). The main result of his article is that commutativity of addition can be deduced from the other axioms. In the present article we show how to reduce this number to six. For certain underlying fields one or more of these axioms can be deduced from the others. However, the six axioms are in general independent; we invite interested readers to show this by constructing their own counter-examples, which the editor of the Gazette will be pleased to receive.

scholarly journals Archaeology in Greece, 1900–1901

1901 ◽  
Vol 21 ◽  
pp. 334-352 ◽  
Author(s):  
R. C. Bosanquet
Keyword(s):  
Present Article ◽  
The Other ◽  
Asia Minor ◽  
French School ◽  
To Receive

There is so much to record from Greece proper and the islands, that it will be necessary to omit Asia Minor from the scope of the present article. It has been a year of surprises, from the episode of the sponge-diver knocking at the door of the Minister of Education to report a shipload of statues lying under the sea, to the rediscovery of Aphaea, the unknown goddess who emerged the other day from the pages of Pausanias and Antoninus Liberalis to receive the honours due to her in the famous temple on Aegina.In describing the results of excavations it is convenient to begin as I did last year with the prehistoric period and with Crete, where a number of workers, two Italians, two Americans, seven Englishmen, have been exploring early sites. The French School has not excavated there this year, but has organized a geographical expedition under the leadership of M. Ardaillon which is to make a much-needed survey of the island.

GLOBAL ZETA FUNCTIONS OF FREUDENTHAL QUARTICS

2002 ◽  
Vol 13 (08) ◽  
pp. 797-820
Author(s):  
HIROSHI SAITO
Keyword(s):  
Vector Space ◽  
Zeta Function ◽  
Explicit Formula ◽  
Explicit Form ◽  
Zeta Functions ◽  
The Other ◽  
Vector Spaces ◽  
Prehomogeneous Vector Space ◽  
Prehomogeneous Vector Spaces

We give two applications of an explicit formula for global zeta functions of prehomogeneous vector spaces in Math. Ann.315 (1999), 587–615. One is concerned with an explicit form of global zeta functions associated with Freudenthal quartics, and the other the comparison of the zeta function of a unsaturated prehomogeneous vector space with that of the saturated one obtained from it.

scholarly journals Arithmetic of Orthogonal Groups (II)

1955 ◽  
Vol 9 ◽  
pp. 129-146 ◽  
Author(s):  
Takashi Ono
Keyword(s):  
Vector Space ◽  
Orthogonal Group ◽  
The Other ◽  
Vector Spaces ◽  
Structure Theory ◽  
Orthogonal Groups

In [0], the writer proved some theorems of Hasse type for two orthogonal groups which operate on the same vector space. In this paper, we shall further generalize those results in two directions. One is to consider the propositions of that type for two orthogonal groups which operate respectively on two vector spaces whose dimensions are different from each other, and the other is to deal with some conspicuous subgroups of an orthogonal group simultaneously which play important roles in the structure theory for orthogonal groups. For this reason, the present paper consists of three steps §1, §2 and §3 which give the generalizations in the above sense of the results in the corresponding sections of [0].

ODD–EVEN DECOMPOSITION OF FUNCTIONS

2020 ◽  
Vol 102 (1) ◽  
pp. 104-108 ◽  
Author(s):  
IOSIF PINELIS
Keyword(s):  
Vector Space ◽  
The Other ◽  
Vector Spaces ◽  
Orthogonal Functions ◽  
Decomposition Of Functions

The main result of this note implies that any function from the product of several vector spaces to a vector space can be uniquely decomposed into the sum of mutually orthogonal functions that are odd in some of the arguments and even in the other arguments. Probabilistic notions and facts are employed to simplify statements and proofs.

Global Economic Crisis of 2008-2009: Sources and Roots

2009 ◽  
pp. 18-31
Author(s):  
G. Rapoport ◽  
A. Guerts
Keyword(s):  
Oil And Gas ◽  
Trade Deficit ◽  
Developed Countries ◽  
The Other ◽  
Energy Resources ◽  
Market Mechanisms ◽  
Production Output ◽  
The One ◽  
To Receive ◽  
Partial Destruction

In the article the global crisis of 2008-2009 is considered as superposition of a few regional crises that occurred simultaneously but for different reasons. However, they have something in common: developed countries tend to maintain a strong level of social security without increasing the real production output. On the one hand, this policy has resulted in trade deficit and partial destruction of market mechanisms. On the other hand, it has clashed with the desire of several oil and gas exporting countries to receive an exclusive price for their energy resources.

La transposition profane de l’Exode dans Moïse fiction de Gilles Rozier

2013 ◽  
pp. 174-183
Author(s):  
Piotr Sadkowski
Keyword(s):  
Present Article ◽  
Old Testament ◽  
The Other ◽  
Jewish Tradition ◽  
Human Being ◽  
The Novel ◽  
Jewish Origin ◽  
French Writer ◽  
The World ◽  
Jewish Writers

Throughout the centuries French and Francophone writers were relatively rarely inspired by the figure of Moses and the story of Exodus. However, since the second half of 20th c. the interest of the writers in this Old Testament story has been on the rise: by rewriting it they examine the question of identity dilemmas of contemporary men. One of the examples of this trend is Moïse Fiction, the 2001 novel by the French writer of Jewish origin, Gilles Rozier, analysed in the present article. The hypertextual techniques, which result in the proximisation of the figure of Moses to the reality of the contemporary reader, constitute literary profanation, but at the same time help place Rozier’s text in the Jewish tradition, in the spirit of talmudism understood as an exchange of views, commentaries, versions and additions related to the Torah. It is how the novel, a new “midrash”, avoids the simple antinomy of the concepts of the sacred and the profane. Rozier’s Moses, conscious of his complex identity, is simultaneously a Jew and an Egyptian, and faces, like many contemporary Jewish writers, language dilemmas, which constitute one of the major motifs analysed in the present article. Another key question is the ethics of the prophetism of the novelistic Moses, who seems to speak for contemporary people, doomed to in the world perceived as chaos unsupervised by an absolute being. Rozier’s agnostic Moses is a prophet not of God (who does not appear in the novel), but of humanism understood as the confrontation of a human being with the absurdity of his or her own finiteness, which produces compassion for the other, with whom the fate of a mortal is shared.

Termin kandaulos/kandylos (κανδαυλοσ/ κανδυλοσ) na podstawie λεχεων συναγωγη Focjusza oraz "Commentari ad Homeri Iliadem" Eustacjusza z Tessaloniki

Vox Patrum ◽  
2010 ◽  
Vol 55 ◽  
pp. 361-373
Author(s):  
Maciej Kokoszko ◽  
Katarzyna Gibel-Buszewska
Keyword(s):  
Social Status ◽  
Present Article ◽  
The Other ◽  
Other Hand ◽  
The Social ◽  
Cooked Meat

The present article focuses on one of the Greek delicacies mentioned by Photius and Eustathius, i.e. a Lydian import called kandaulos/kandylos. The dish was developed before the mid. VI th c. BC and named after a Lydian king, Kandaules, who ruled in the VII th c. BC. The delicacy was (via the Ionians) borrowed by the Helens and established itself in Greece sometime in the V th c. It became popular in Hellenistic times. The information we possess allow us to reconstruct two varieties of kandaulos/ kandylos. The first was savoury and consisted of cooked meat, stock, Phrygian cheese, breadcrumbs and dill (or fennel). The other included milk, lard, cheese and honey. The dish is reported to have been costly, prestigious and indicating the social status of those who would eat it. Though there is much evidence suggesting its popularity in antiquity, we lack solid evidence proving that kaunaudlos/kandylos was eaten in Byzantine times. On the other hand, Byzantine authors preserved the most detailed literary data on the delicacy. If it had not been for the Byzantine interest, our competence in the field of Greek cuisine would be even faultier.

Review of Malahara Kalpana of Rasa Tarangani

2019 ◽  
Vol 4 (02) ◽  
Author(s):  
Dubey Somil
Keyword(s):  
Present Article ◽  
20Th Century ◽  
The Other ◽  
Mineral Contents ◽  
Basic Constituent

The word Malahara or Malhama is derived from unani system of medicine. Yogaratnakara mentioned this first by the name of Malahara Kalpana. It derives its name as it removes Mala (residue etc.) from Vrana (wounds), Vidradhi (abscess) etc. This is similar to ointments in modern pharmaceutics. Malahara Kalpana is the ointment preparation which has Siktha Taila (bees wax and oil mixture) or Ghrita, as the basic constituent. The other ingredients may include herbal, metal, or mineral contents depending upon the usage. Malahara has a property like Snehana (oelation), cleansing, Ropana (healing), Lekhana (scaraping), and Varnya (beautifying), depending on the drugs used in the preparation. Rasa Tarangani a Rasa Shastra treatise of 20th century by Acharya Sadananda Sharma has enumerated various types of Malahara Kalpana taking mainly Siktha Taila as a base. Though this Kalpana holds firm roots in treating diseases the mention and explanation of this particular topic is scattered in this treatise. Hence the present article is an attempt to elucidate and unfold the Malahara Kalpana of Rasatarangani.

scholarly journals M-Hazy Vector Spaces over M-Hazy Field

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1118
Author(s):  
Faisal Mehmood ◽  
Fu-Gui Shi
Keyword(s):  
Vector Space ◽  
Linear Transformation ◽  
Binary Operation ◽  
Vector Spaces ◽  
Fundamental Properties ◽  
Classical Algebra ◽  
Important Development ◽  
Fuzzy Algebra ◽  
Convex Spaces

The generalization of binary operation in the classical algebra to fuzzy binary operation is an important development in the field of fuzzy algebra. The paper proposes a new generalization of vector spaces over field, which is called M-hazy vector spaces over M-hazy field. Some fundamental properties of M-hazy field, M-hazy vector spaces, and M-hazy subspaces are studied, and some important results are also proved. Furthermore, the linear transformation of M-hazy vector spaces is studied and their important results are also proved. Finally, it is shown that M-fuzzifying convex spaces are induced by an M-hazy subspace of M-hazy vector space.

The genus of graphs associated with vector spaces

2019 ◽  
Vol 19 (05) ◽  
pp. 2050086 ◽  
Author(s):  
T. Tamizh Chelvam ◽  
K. Prabha Ananthi
Keyword(s):  
Finite Field ◽  
Vector Space ◽  
Undirected Graph ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Vertex Connectivity ◽  
Dimensional Vector Space ◽  
Nonzero Component ◽  
Vertex Set ◽  
Component Graph

Let [Formula: see text] be a k-dimensional vector space over a finite field [Formula: see text] with a basis [Formula: see text]. The nonzero component graph of [Formula: see text], denoted by [Formula: see text], is a simple undirected graph with vertex set as nonzero vectors of [Formula: see text] such that there is an edge between two distinct vertices [Formula: see text] if and only if there exists at least one [Formula: see text] along which both [Formula: see text] and [Formula: see text] have nonzero scalars. In this paper, we find the vertex connectivity and girth of [Formula: see text]. We also characterize all vector spaces [Formula: see text] for which [Formula: see text] has genus either 0 or 1 or 2.

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