A-normality, strong normality and ℱ-dual pronormal subgroups

2000 ◽  
Vol 3 (2) ◽  
Author(s):  
M. D. PéREZ-RAMOS
Keyword(s):  
Strong Normality

scholarly journals On normal and strongly normal lattices

1993 ◽  
Vol 16 (2) ◽  
pp. 337-344
Author(s):  
El-Bachir Yallaoui
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Strong Normality ◽  
Necessary And Sufficient

In this paper we will investigate the properties of normality and strong normality of lattices and their relationships to zero-one measures. We will eventually establish necessary and sufficient conditions for lattices to be strongly normal. These properties are then investigated in the case of separated lattices.

scholarly journals General solutions depending algebraically on arbitrary constants

1989 ◽  
Vol 113 ◽  
pp. 1-6 ◽  
Author(s):  
Keiji Nishioka
Keyword(s):  
Differential Equations ◽  
Higher Order ◽  
General Solutions ◽  
Algebraic Differential Equations ◽  
First Order ◽  
Order Case ◽  
Rational Dependence ◽  
Strong Normality ◽  
Solutions Of Equations ◽  
The Given

In his famous lectures [7] Painlevé investigates general solutions of algebraic differential equations which depend algebraically on some of arbitrary constants. Although his discussions are beyond our understanding, the rigorous and accurate interpretation to make his intuition true would be possible. Successful accomplishments have been done by some authors, for example, Kimura [1], Umemura [8, 9]. From differential algebraic viewpoint in [5] the author introduces the notion of rational dependence on arbitrary constants of general solutions of algebraic differential equations, and in [6] clarifies the relation between it and the notion of strong normality. Here we aim at generalizing to higher order case the result in [4] that in the first order case solutions of equations depend algebraically on those of equations free from moving singularities which are determined uniquely as the closest ones to the given. Part of our result can be seen in [7].

Strong normality and normality for difference fields

1979 ◽  
Vol 19 (1) ◽  
pp. 121-122 ◽  
Author(s):  
Ronald P. Infante
Keyword(s):  
Difference Fields ◽  
Strong Normality

scholarly journals Some Variants of Strong Normality in Closure Spaces Generated via Relations

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Ria Gupta ◽  
Ananga Kumar Das
Keyword(s):  
Binary Relation ◽  
Normal Closure ◽  
Separation Axioms ◽  
Closure Spaces ◽  
Strong Normality

In this paper, some variants of strongly normal closure spaces obtained by using binary relation are introduced, and examples in support of existence of the variants are provided by using graphs. The relationships that exist between variants of strongly normal closure spaces and covering axioms in absence/presence of lower separation axioms are investigated. Further, closure subspaces and preservation of the properties studied under mapping are also discussed.

On Strongly Normal Functions

1996 ◽  
Vol 39 (4) ◽  
pp. 408-419 ◽  
Author(s):  
Huaihui Chen ◽  
Paul M. Gauthier
Keyword(s):  
Complex Plane ◽  
Riemann Sphere ◽  
Integral Conditions ◽  
Normal Functions ◽  
Strong Normality ◽  
Class Of Functions

AbstractLoosely speaking, a function (meromorphic or harmonic) from the hyperbolic disk of the complex plane to the Riemann sphere is normal if its dilatation is bounded. We call a function strongly normal if its dilatation vanishes at the boundary. A sequential property of this class of functions is proved. Certain integral conditions, known to be sufficient for normality, are shown to be in fact sufficient for strong normality.

Normal Completions of Small Categories

1969 ◽  
Vol 21 ◽  
pp. 196-201 ◽  
Author(s):  
J. F. Kennison
Keyword(s):  
Full Subcategory ◽  
Normality Condition ◽  
Strong Normality ◽  
Complete Category

In (3), Isbell proposed a stronger definition for the term “complete category” and obtained many nice theorems for the resulting notion of a completion. In particular, he showed (3, Theorem 3.20) that completions of small categories satisfy a strong normality condition.In this paper we shall always use the term “complete” in the weaker sense of Freyd (1). (In (3), Isbell used the term “small-complete” for this weaker notion.) We shall prove that the completions, in the sense of Freyd, of small categories also enjoy the same normality condition, provided they admit at least one bicategory structure. (The complete categories in the sense of Isbell always admit bicategory structures; see the remark following Proposition 2.4.)In what follows, we let mean that is a full subcategory of . Moreover, if , then means that each object of is equivalent to an object in .

Strong normality and normality for difference fields

1980 ◽  
Vol 20 (1) ◽  
pp. 159-165 ◽  
Author(s):  
Ronald P. Infante
Keyword(s):  
Difference Fields ◽  
Strong Normality
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