scholarly journals On projective Hjelmslev planes of level n

1989 ◽  
Vol 31 (3) ◽  
pp. 257-261 ◽  
Author(s):  
G. Hanssens ◽  
H. van Maldeghem
Keyword(s):  
Existence Theorem ◽  
Inverse Limits ◽  
Hjelmslev Plane ◽  
Projective Hjelmslev Plane ◽  
Equivalent Definition ◽  
Triangle Building ◽  
Infinite Case ◽  
Definition Of

In this paper, we establish a new (but equivalent) definition of projective Hjelmslev planes of level n. This shows that the nth floor of a triangle building is a projective Hjelmslev plane of level n (a result already announced in [9], but left unproved). This will allow us to characterize Artmann-sequences by means of their inverse limits and to construct new ones. We also deduce a new existence theorem for level n projective Hjelmslev planes. All results hold in the finite as well as in the infinite case.

Remarks on some generalization of the notion of microscopic sets

2020 ◽  
Vol 70 (6) ◽  
pp. 1349-1356
Author(s):  
Aleksandra Karasińska
Keyword(s):  
General Sense ◽  
Equivalent Definition ◽  
Definition Of ◽  
Null Set

AbstractWe consider properties of defined earlier families of sets which are microscopic (small) in some sense. An equivalent definition of considered families is given, which is helpful in simplifying a proof of the fact that each Lebesgue null set belongs to one of these families. It is shown that families of sets microscopic in more general sense have properties analogous to the properties of the σ-ideal of classic microscopic sets.

Locally Compact Hjelmslev Planes and Rings

1981 ◽  
Vol 33 (4) ◽  
pp. 988-1021 ◽  
Author(s):  
J. W. Lorimer
Keyword(s):  
Projective Planes ◽  
Equivalence Relations ◽  
Topological Spaces ◽  
Hjelmslev Plane ◽  
Projective Hjelmslev Plane ◽  
Quotient Spaces ◽  
Continuous Maps ◽  
Topological Plane ◽  
Line Point ◽  
Canonical Image

Affine and projective Hjelmslev planes are generalizations of ordinary affine and projective planes where two points (lines) may be joined by (may intersect in) more than one line (point). The elements involved in multiple joinings or intersections are neighbours, and the neighbour relations on points respectively lines are equivalence relations whose quotient spaces define an ordinary affine or projective plane called the canonical image of the Hjelmslev plane. An affine or projective Hjelmslev plane is a topological plane (briefly a TH-plane and specifically a TAH-plane respectively a TPH-plane) if its point and line sets are topological spaces so that the joining of non-neighbouring points, the intersection of non-neighbouring lines and (in the affine case) parallelism are continuous maps, and the neighbour relations are closed.In this paper we continue our investigation of such planes initiated by the author in [38] and [39].

Characterizations for the n-strong Drazin invertibility in a ring

2020 ◽  
pp. 2150141
Author(s):  
Honglin Zou ◽  
Jianlong Chen ◽  
Huihui Zhu ◽  
Yujie Wei
Keyword(s):  
Positive Integer ◽  
Generalized Inverse ◽  
Product Formula ◽  
Drazin Inverse ◽  
Equivalent Definition ◽  
New Type ◽  
Definition Of ◽  
Existence Criteria

Recently, a new type of generalized inverse called the [Formula: see text]-strong Drazin inverse was introduced by Mosić in the setting of rings. Namely, let [Formula: see text] be a ring and [Formula: see text] be a positive integer, an element [Formula: see text] is called the [Formula: see text]-strong Drazin inverse of [Formula: see text] if it satisfies [Formula: see text], [Formula: see text] and [Formula: see text]. The main aim of this paper is to consider some equivalent characterizations for the [Formula: see text]-strong Drazin invertibility in a ring. Firstly, we give an equivalent definition of the [Formula: see text]-strong Drazin inverse, that is, [Formula: see text] is the [Formula: see text]-strong Drazin inverse of [Formula: see text] if and only if [Formula: see text], [Formula: see text] and [Formula: see text]. Also, we obtain some existence criteria for this inverse by means of idempotents. In particular, the [Formula: see text]-strong Drazin invertibility of the product [Formula: see text] are investigated, where [Formula: see text] is regular and [Formula: see text] are arbitrary elements in a ring.

The linear canonical wavelet transform on some function spaces

2018 ◽  
Vol 16 (01) ◽  
pp. 1850010 ◽  
Author(s):  
Yong Guo ◽  
Bing-Zhao Li
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Continuous Operator ◽  
Function Spaces ◽  
Linear Continuous Operator ◽  
Convolution Theorem ◽  
Linear Canonical Transform ◽  
Equivalent Definition ◽  
New Space ◽  
Definition Of

It is well known that the domain of Fourier transform (FT) can be extended to the Schwartz space [Formula: see text] for convenience. As a generation of FT, it is necessary to detect the linear canonical transform (LCT) on a new space for obtaining the similar properties like FT on [Formula: see text]. Therefore, a space [Formula: see text] generalized from [Formula: see text] is introduced firstly, and further we prove that LCT is a homeomorphism from [Formula: see text] onto itself. The linear canonical wavelet transform (LCWT) is a newly proposed transform based on the convolution theorem in LCT domain. Moreover, we propose an equivalent definition of LCWT associated with LCT and further study some properties of LCWT on [Formula: see text]. Based on these properties, we finally prove that LCWT is a linear continuous operator on the spaces of [Formula: see text] and [Formula: see text].

scholarly journals FRACTAL ANALYSIS OF HOPF BIFURCATION AT INFINITY

2012 ◽  
Vol 22 (12) ◽  
pp. 1230043 ◽  
Author(s):  
GORAN RADUNOVIĆ ◽  
DARKO ŽUBRINIĆ ◽  
VESNA ŽUPANOVIĆ
Keyword(s):  
Hopf Bifurcation ◽  
Fractal Analysis ◽  
Stereographic Projection ◽  
Riemann Sphere ◽  
Box Dimension ◽  
Euclidean Spaces ◽  
Equivalent Definition ◽  
Basic Properties ◽  
Definition Of

Using geometric inversion with respect to the origin, we extend the definition of box dimension to the case of unbounded subsets of Euclidean spaces. Alternative but equivalent definition is provided using stereographic projection on the Riemann sphere. We study its basic properties, and apply it to the study of the Hopf–Takens bifurcation at infinity.

Sign in / Sign up

Export Citation Format

Share Document