scholarly journals $2$-arcs of maximal size in the affine and the projective Hjelmslev plane over $\mathbb Z$25

2011 ◽  
Vol 5 (2) ◽  
pp. 287-301 ◽  
Author(s):  
Sascha Kurz ◽  
Matthias Koch ◽  
Michael Kiermaier
Keyword(s):  
Hjelmslev Plane ◽  
Projective Hjelmslev Plane ◽  
Maximal Size

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].

Dual Numbers and Topological Hjelmslev Planes

1983 ◽  
Vol 26 (3) ◽  
pp. 297-302 ◽  
Author(s):  
J. W. Lorimer
Keyword(s):  
Local Ring ◽  
Maximal Ideal ◽  
Dual Numbers ◽  
Hjelmslev Plane ◽  
Product Topology ◽  
Topological Dimension ◽  
Locally Compact ◽  
Projective Hjelmslev Plane ◽  
Zero Divisors ◽  
Unique Maximal Ideal

AbstractIn 1929 J. Hjelmslev introduced a geometry over the dual numbers ℝ+tℝ with t2 = Q. The dual numbers form a Hjelmslev ring, that is a local ring whose (unique) maximal ideal is equal to the set of 2 sided zero divisors and whose ideals are totally ordered by inclusion. This paper first shows that if we endow the dual numbers with the product topology of ℝ2, then we obtain the only locally compact connected hausdorfT topological Hjelmslev ring of topological dimension two. From this fact we establish that Hjelmslev's original geometry, suitably topologized, is the only locally compact connected hausdorfr topological desarguesian projective Hjelmslev plane to topological dimension four.

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.

Embedding Right Chain Rings in Chain Rings

1978 ◽  
Vol 30 (5) ◽  
pp. 1079-1086 ◽  
Author(s):  
H. H. Brungs ◽  
G. Törner
Keyword(s):  
Maximal Ideal ◽  
Coordinate Ring ◽  
Hjelmslev Plane ◽  
Chain Ring ◽  
Projective Hjelmslev Plane ◽  
Algebraic Version ◽  
Zero Divisors ◽  
Starting Point ◽  
Affine Hjelmslev Plane ◽  
A Chain

The following problem was the starting point for this investigation: Can every desarguesian affine Hjelmslev plane be embedded into a desarguesian projective Hjelmslev plane [8]? An affine Hjelmslev plane is called desarguesian if it can be coordinatized by a right chain ring R with a maximal ideal J(R) consisting of two-sided zero divisors. A projective Hjemslev plane is called desarguesian if the coordinate ring is in addition a left chain ring, i.e. a chain ring. This leads to the algebraic version of the above problem, namely the embedding of right chain rings into suitable chain rings. We can prove the following result.

scholarly journals Helly families of maximal size

1979 ◽  
Vol 26 (2) ◽  
pp. 197-200 ◽  
Author(s):  
Béla Bollobás ◽  
Pierre Duchet
Keyword(s):  
Maximal Size

scholarly journals Ungeneralizable minimality in Ndebele

2001 ◽  
Vol 30 (1) ◽  
pp. 34-58
Author(s):  
Laura J. Downing
Keyword(s):  
Minimality Condition ◽  
Phonological Processes ◽  
Stress Assignment ◽  
Prosodic Morphology ◽  
Striking Finding ◽  
Maximal Size ◽  
Verb Forms ◽  
Size Constraints ◽  
Morphological Processes

A body of work in Prosodic Morphology clearly establishes the importance of prosodic constituents like the foot as templates conditioning morpheme size. A striking finding of this research is that morphological footing is independent of metrical footing in many languages, as the footing required for particular morphological processes is often not identical to that required for phonological processes like stress assignment. However, recent OT research on Prosodic Morphology has made the opposite claim. Within this theory, the Generalized Template Hypothesis (GTH) proposes that no morpheme-particular templates defining minimal and maximal size are necessary. Instead, templates are always derivable from general principles of the grammar, like independently motivated metrical footing. This paper presents evidence from Ndebele showing that the GTH is too strong. In Ndebele, several different verb forms are subject to a minimality condition. In some cases, the minimality condition can be derived through independent metrical footing, as the GTH predicts. However, in several cases it cannot, showing that morpheme-particular size constraints are still a necessary part of the grammar.

Are there mechanical limits to size in wave-swept organisms?

1999 ◽  
Vol 202 (23) ◽  
pp. 3463-3467 ◽  
Author(s):  
M. Denny
Keyword(s):  
Ocean Waves ◽  
Hydrodynamic Forces ◽  
General Question ◽  
Inertial Forces ◽  
Maximal Size

Hydrodynamic forces imposed by ocean waves are thought to limit the size of nearshore plants and animals, but it has proved difficult to determine the mechanism. Explanations based on the scaling mismatch between hydrodynamic accelerational forces and the strength of organisms do not work. Mechanisms that incorporate the allometry of drag and strength accurately predict the maximal size of intertidal algae but not of animals, and internally imposed inertial forces may explain the limits to size in large kelps. The general question of size in wave-swept organisms remains open and intriguing.

An Account of Larval Budding in the Compound Ascidian, Hypsistozoa fasmeriana

1959 ◽  
Vol s3-100 (52) ◽  
pp. 575-589
Author(s):  
BERYL I. BREWIN
Keyword(s):  
Neural Tube ◽  
Ventral Side ◽  
The Other ◽  
Free Swimming ◽  
Close Link ◽  
Bud Formation ◽  
Maximal Size ◽  
The Right ◽  
Sexually Mature ◽  
Posterior Position

Larval budding in Hypsistozoa fasmeriana is in many ways unique in the sub-family Holozoinae. The stolon, which projects from the left side of the oozooid, is large (235 µ in diameter, 1.8 mm in length) and reaches maximal size before severance of buds occurs. The buds arise one at a time and 9 to 14 are formed. Test forms rapidly between a newly severed bud and the remainder of the stolon. Thus the buds are moved along an arc of a spiral which runs from the left side of the oozooid somewhat anteriorly across the ventral side and posteriorly up the right side. By the end of bud formation the first-formed bud occupies the most posterior position, lying high up on the right side of the oozooid. Each larval bud develops directly into a blastozooid and by the time the tadpole becomes free-swimming there is a considerable degree of organogenesis. The blastozooids together with the oozooid form a ring of zooids tilted slightly away from the vertical. After metamorphosis of the tadpole this ring becomes horizontal, but the tilt is still maintained with the oozooid occupying the most elevated position. Thus in the young colonies the plane of the head is slightly off the horizontal--an arrangement which persists throughout the life of the colony. The development of larval buds in this ascidian is not delayed until after dedifferentiation of the oozooid, as is the case in the other Holozoinae. The blastozooids function simultaneously with the oozooid. They do not, however, become sexually mature, being presumably of sub-maximal size for the species. The newly severed bud differs from that of other Holozoinae in having an extensive epicardial tube and a thick mesenchymal layer of densely granulated cells. The epicardium of the blastozooid is formed from the posterior end of the original epicardial tube. It remains single. The neural tube arises from the left peribranchial sac. H. fasmeriana forms a close link between the sub-family Holozoinae and the sub-family Polyclininae. It resembles the Holozoinae in form of gut, position and mode of origin of the brood pouch, and position of the cardio-pericardium. It shares with the Polyclininae the post-abdominal position of the gonads as well as the structure and organogenesis of the buds.

Seasonal variations in length of copepods in South Pacific New Zealand waters

1966 ◽  
Vol 17 (2) ◽  
pp. 155 ◽  
Author(s):  
GB Deevey
Keyword(s):  
New Zealand ◽  
Seasonal Variations ◽  
Spring Bloom ◽  
Narrow Temperature Range ◽  
Temperature Range ◽  
Maximal Size ◽  
Cephalothorax Length ◽  
Autumn And Winter ◽  
Cycle Temperature ◽  
Paracalanus Parvus

Measurements of cephalothorax length were made on females and males of Centropages aucklandicus, Acartia clausi, Paracalanus parvus, and Clausocalanus arcuicornis, and on female Calanus australis for the period from April 1964 to May 1965. Centropages aucklandicus and A. clausi increased gradually in length during autumn and winter to maximal size in the spring and were smaller again in summer. Paracalanus parvus was larger in spring and smaller the rest of the year. Calanus australis and C. arcuicornis were large in spring, but during summer they were also large on occasion, possibly because offshore populations had been brought into the area. Length-temperature-phytoplankton correlations showed that in temperate New Zealand waters with a relatively narrow temperature range the seasonal variations in length of all the copepods studied were significantly related to the annual phytoplankton cycle; temperature was an important factor for only two of the species. Some of the species measured are primarily herbivorous whereas others, such as Centropages and Acartia, are probably omnivores. Data are lacking for carnivorous copepods. However, since the spring bloom acts as a stimulus to zooplankton reproduction, it is suggested that all copepods that feed on living food might attain maximal size at around the time of the spring bloom in temperate waters with a relatively narrow temperature range.

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