scholarly journals Basic properties of differential fields of an arbitrary characteristic and the Picard-Vessiot theory

1962 ◽  
Vol 2 (3) ◽  
pp. 295-322 ◽  
Author(s):  
Kôtaro Okugawa
Keyword(s):  
Arbitrary Characteristic ◽  
Basic Properties ◽  
Differential Fields

scholarly journals Algebraic Barth-Lefschetz theorems

1996 ◽  
Vol 142 ◽  
pp. 17-38 ◽  
Author(s):  
Lucian Bădescu
Keyword(s):  
Positive Integer ◽  
Projective Space ◽  
Algebraic Variety ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Arbitrary Characteristic ◽  
Basic Properties ◽  
Positive Integers ◽  
Lefschetz Theorems ◽  
Algebraic Scheme

We shall work over a fixed algebraically closed field k of arbitrary characteristic. By an algebraic variety over k we shall mean a reduced algebraic scheme over k. Fix a positive integer n and e = (e0, el,…, en) a system of n + 1 weights (i.e. n + 1 positive integers e0, el,…, en). If k[T0, Tl,…, Tn] is the polynomial k-algebra in n + 1 variables, graded by the conditions deg(Ti) = ei i = 0, 1,…, n, denote by Pn(e) = Proj(k[T0, T1,…, Tn]) the n-dimensional weighted projective space over k of weights e. We refer the reader to [3] for the basic properties of weighted projective spaces.

Asymptotic Fields and Asymptotic Couples

2017 ◽  
Author(s):  
Matthias Aschenbrenner ◽  
Lou van den Dries ◽  
Joris van der Hoeven
Keyword(s):  
Differential Polynomials ◽  
Asymptotic Field ◽  
Valued Fields ◽  
Basic Properties ◽  
Differential Fields ◽  
Asymptotic Fields

This chapter deals with asymptotic differential fields and their asymptotic couples. Asymptotic fields include Rosenlicht's differential-valued fields and share many of their basic properties. A key feature of an asymptotic field is its asymptotic couple. The chapter first defines asymptotic fields and their asymptotic couples before discussing H-asymptotic couples. It then considers asymptotic couples independent of their connection to asymptotic fields, along with the behavior of differential polynomials as functions on asymptotic fields. It also describes asymptotic fields with small derivation and the operations of coarsening and specialization, algebraic and immediate extensions of asymptotic fields, and differential polynomials of order one. Finally, it proves some useful extension results about asymptotic couples and establishes a property of closed H-asymptotic couples.

On the Essence and Tipology of International Public Goods

2005 ◽  
pp. 131-141
Author(s):  
V. Mortikov
Keyword(s):  
Economic Policy ◽  
Social Construction ◽  
Public Goods ◽  
Public Good ◽  
Global Public Goods ◽  
Club Goods ◽  
Basic Properties ◽  
International Public Goods ◽  
Regional Public Goods ◽  
Joint Products

The basic properties of international public goods are analyzed in the paper. Special attention is paid to the typology of international public goods: pure and impure, excludable and nonexcludable, club goods, regional public goods, joint products. The author argues that social construction of international public good depends on many factors, for example, government economic policy. Aggregation technologies in the supply of global public goods are examined.

The advancement of silicon-on-insulator (SOI) devices and their basic properties

2020 ◽  
Vol 23 (3) ◽  
pp. 227-252
Author(s):  
T.E. Rudenko ◽  
◽  
A.N. Nazarov ◽  
V.S. Lysenko ◽  
◽  
...  
Keyword(s):  
Silicon On Insulator ◽  
Basic Properties ◽  
Soi Devices

Basic Properties of an Ultrasonic Probe with a Through Hole for Puncture and Detection Principle of a Puncture Needle

2012 ◽  
Vol 132 (11) ◽  
pp. 420-424 ◽  
Author(s):  
Yuusuke Tanaka ◽  
Katsuhiko Tanaka ◽  
Susumu Sugiyama ◽  
Hisanori Shiomi ◽  
Yoshimasa Kurumi ◽  
...  
Keyword(s):  
Ultrasonic Probe ◽  
Basic Properties ◽  
Puncture Needle ◽  
Through Hole ◽  
Detection Principle

ON A NEW CLASS OF SEMI GENERALIZED CLOSED SETS IN STRONG GENERALIZED TOPOLOGICAL SPACES

2020 ◽  
Vol 9 (11) ◽  
pp. 9353-9360
Author(s):  
G. Selvi ◽  
I. Rajasekaran
Keyword(s):  
Topological Spaces ◽  
Closed Set ◽  
Basic Properties ◽  
Closed Sets ◽  
New Class ◽  
Open Set ◽  
Continuous Maps

This paper deals with the concepts of semi generalized closed sets in strong generalized topological spaces such as $sg^{\star \star}_\mu$-closed set, $sg^{\star \star}_\mu$-open set, $g^{\star \star}_\mu$-closed set, $g^{\star \star}_\mu$-open set and studied some of its basic properties included with $sg^{\star \star}_\mu$-continuous maps, $sg^{\star \star}_\mu$-irresolute maps and $T_\frac{1}{2}$-space in strong generalized topological spaces.

New family of Whitney numbers

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 309-320 ◽  
Author(s):  
B.S. El-Desouky ◽  
Nenad Cakic ◽  
F.A. Shiha
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Stirling Numbers ◽  
Explicit Formulas ◽  
Basic Properties ◽  
New Family ◽  
Whitney Numbers ◽  
Special Cases

In this paper we give a new family of numbers, called ??-Whitney numbers, which gives generalization of many types of Whitney numbers and Stirling numbers. Some basic properties of these numbers such as recurrence relations, explicit formulas and generating functions are given. Finally many interesting special cases are derived.

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