A Characterization of Some Geometries of Chains

1974 ◽  
Vol 26 (02) ◽  
pp. 257-272 ◽  
Author(s):  
Yi Chen
Keyword(s):  
Projective Plane ◽  
Minkowski Plane ◽  
Close Relation ◽  
Laguerre Plane ◽  
Geometric Structures ◽  
Möbius Plane

The geometries considered here are the Möbius plane M() (W. Benz [1]), the Laguerre plane L() (W. Benz and H. Mäurer [7]) and the Minkowski plane A() (W. Benz [5], G. Kaerlein [18]) over a field . All of them are geometries of an algebra with identity over a field. The characterization of the projective plane over a field by the proposition of Pappus first gave a close relation between algebraic and geometric structures. B. L. v. d. Waedern and L. J. Smid [28] presented a further example by characterizing the Möbius and Laguerre plane with incidence axioms and the "complete" proposition of Miquel.

A Characterization of the Hughes Planes

1965 ◽  
Vol 17 ◽  
pp. 916-922 ◽  
Author(s):  
T. G. Ostrom
Keyword(s):  
Fixed Point ◽  
Projective Plane ◽  
Related Notion ◽  
Fixed Line

Baer (1) introduced the term "(p,L)-collineation" to denote a central collineation with centre p and axis L. We shall find it convenient to use a modification of the related notion of "(p, L)-transitivity."Definition. Let π0 be a subplane of the projective plane π. Let L be a fixed line of π0, and let p be a fixed point of π0. Let r and s be any two points of π0 that are collinear with p, distinct from p, and not on L. If, for each such choice of r and s, there is a (p, L)-collineation of π that (1) carries π0 into itself and (2) carries r into s, we shall say that π is (p, L, π0)-transitive.

A CHARACTERIZATION OF THE REAL PROJECTIVE PLANE

2010 ◽  
Vol 21 (12) ◽  
pp. 1605-1617
Author(s):  
JOËL ROUYER
Keyword(s):  
Projective Plane ◽  
Riemannian Geometry ◽  
Smooth Surface ◽  
Real Projective Plane ◽  
Closed Curves ◽  
Farthest Points ◽  
The Real ◽  
Large Sets

It is proved in this article, that in the framework of Riemannian geometry, the existence of large sets of antipodes (i.e. farthest points) for diametral points of a smooth surface has very strong consequences on the topology and the metric of this surface. Roughly speaking, if the sets of antipodes of diametral points are closed curves, then the surface is nothing but the real projective plane.

scholarly journals Provable isomorphisms of types

1992 ◽  
Vol 2 (2) ◽  
pp. 231-247 ◽  
Author(s):  
Kim B. Bruce ◽  
Roberto Di Cosmo ◽  
Giuseppe Longo
Keyword(s):  
Propositional Logic ◽  
Lambda Calculus ◽  
Close Relation ◽  
Typed Lambda Calculus ◽  
Definition Of

A constructive characterization is given of the isomorphisms which must hold in all models of the typed lambda calculus with surjective pairing. Using the close relation between closed Cartesian categories and models of these calculi, we also produce a characterization of those isomorphisms which hold in all CCC's. Using the correspondence between these calculi and proofs in intuitionistic positive propositional logic, we thus provide a characterization of equivalent formulae of this logic, where the definition of equivalence of terms depends on having “invertible” proofs between the two terms. Work of Rittri (1989), on types as search keys in program libraries, provides an interesting example of use of these characterizations.

FIRST BETTI NUMBERS OF ABELIAN COVERINGS OF THE COMPLEX PROJECTIVE PLANE BRANCHED OVER LINE CONFIGURATIONS

2000 ◽  
Vol 09 (02) ◽  
pp. 271-284 ◽  
Author(s):  
IKUO TAYAMA
Keyword(s):  
Projective Plane ◽  
Real Line ◽  
General Position ◽  
Betti Numbers ◽  
Complex Projective Plane ◽  
The Real ◽  
Complex Projective

We prove the following results concerning the first Betti numbers of abelian coverings of CP2 branched over line configurations: (1) An estimate of the first Betti numbers. (2) A characterization of central and general position line configurations in terms of the first Betti numbers of abelian coverings. (3) The first Betti numbers of the abelian coverings of the real line configurations up to 7 components.

scholarly journals An Extremal Characterization of Projective Planes

10.37236/867 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Stefaan De Winter ◽  
Felix Lazebnik ◽  
Jacques Verstraëte
Keyword(s):  
Projective Plane ◽  
Projective Planes ◽  
Bipartite Graphs ◽  
Incidence Graph ◽  
Number Of Cycles

In this article, we prove that amongst all $n$ by $n$ bipartite graphs of girth at least six, where $n = q^2 + q + 1 \ge 157$, the incidence graph of a projective plane of order $q$, when it exists, has the maximum number of cycles of length eight. This characterizes projective planes as the partial planes with the maximum number of quadrilaterals.

scholarly journals Semiarcs with Long Secants

10.37236/3771 ◽  
2014 ◽  
Vol 21 (1) ◽  
Author(s):  
Bence Csajbók
Keyword(s):  
Lower Bound ◽  
Projective Plane ◽  
Complete Characterization ◽  
Symmetric Difference ◽  
Blocking Set ◽  
Point Set

In a projective plane $\Pi_q$ of order $q$, a non-empty point set $\mathcal{S}_t$ is a $t$-semiarc if the number of tangent lines to $\mathcal{S}_t$ at each of its points is $t$. If $\mathcal{S}_t$ is a $t$-semiarc in $\Pi_q$, $t<q$, then each line intersects $\mathcal{S}_t$ in at most $q+1-t$ points. Dover proved that semiovals (semiarcs with $t=1$) containing $q$ collinear points exist in $\Pi_q$ only if $q\leq 3$. We show that if $t>1$, then $t$-semiarcs with $q+1-t$ collinear points exist only if $t\geq \sqrt{q-1}$. In $\mathrm{PG}(2,q)$ we prove the lower bound $t\geq(q-1)/2$, with equality only if $\mathcal{S}_t$ is a blocking set of Rédei type of size $3(q+1)/2$.We call the symmetric difference of two lines, with $t$ further points removed from each line, a $V_t$-configuration. We give conditions ensuring a $t$-semiarc to contain a $V_t$-configuration and give the complete characterization of such $t$-semiarcs in $\mathrm{PG}(2,q)$.

scholarly journals Morphological, ecological and molecular characterization of Pyropia vietnamensis (Bangiales, Rhodophyta) from the Konkan region, India

Phytotaxa ◽  
2015 ◽  
Vol 224 (1) ◽  
pp. 45 ◽  
Author(s):  
Monica Gajanan Kavale ◽  
Mudassar Anisoddin Kazi ◽  
Nived Sreenadhan ◽  
Veerendra Veer Singh
Keyword(s):  
Plant Morphology ◽  
Close Relation ◽  
Morphological Characters ◽  
Molecular Characteristics ◽  
Ecological Parameter ◽  
Indian Waters ◽  
Taxonomic Implications ◽  
Ecological Parameters ◽  
Cox 1

Pyropia vietnamensis is one of the most luxuriously growing seaweed in Konkan coast, India. In the present study we attempted to explore the morphology, ecology and molecular characteristics exhibited by P. vietnamensis and its taxonomic implications. We described the effects of ecological parameters on the variability of morphological characters. The water motion was found to be one of the most important ecological parameter that governs the plant morphology. The plant was found to grow on entire intertidal region and this may be one of the possible reasons for high morphological variation among the taxa in this region. The molecular analysis utilizing cox 1 gene sequences clearly revealed the close relation of Indian and Brazilian specimens with only 0-1 bp intraspecific variation. The present study provides a beginning to a clearly required detailed study of the morphology, ecology and genetic diversity showed by Pyropia species from Indian waters.

scholarly journals Isolation and characterization of bacteria associated with silkworm gut under antibiotic-treated larval feeding

2024 ◽  
Vol 84 ◽  
Author(s):  
A. Javaid ◽  
M. Hussain ◽  
K. Aftab ◽  
M. F. Malik ◽  
M. Umar ◽  
...  
Keyword(s):  
16S Rrna ◽  
16S Rrna Gene ◽  
Close Relation ◽  
Rrna Gene ◽  
Bacterial Strains ◽  
Larval Weight ◽  
Silkworm Larvae ◽  
Cocoon Production ◽  
Isolation And Characterization

Abstract The impact of antibiotics on growth, cocoon production was assessed in addition to isolation and characterization of bacteria associated with silkworm gut of infected larvae. Larval rearing was maintained at recommended conditions of temperature and humidity. Silkworm larvae showing abnormal symptoms were collected from the control group and dissected for gut collection. Bacteria were isolated from the gut content by spreading on agar plates and incubated at 37 °C for 48 hrs. Bacterial identification and phylogenetic analysis were carried out by 16S rRNA gene sequencing. The isolated bacteria were subjected to antimicrobial susceptibility test (disc diffusion methods) by using Penicillin (10 µg/mL), Tetracycline (30 µg/mL), Amoxicillin (25 µg/mL), Ampicillin (10 µg/mL), and Erythromycin (15 µg/mL). All isolated strains showed positive results for the catalase test. We isolated and identified bacterial strains (n = 06) from the gut of healthy and diseased silkworm larvae. Based on the 16S rRNA gene sequence, isolated bacteria showed close relation with Serratia, Bacillus, and Pseudomonas spp. Notably, 83.3% of strains were resistant to Penicillin, Tetracycline, Amoxicillin, Ampicillin, and Erythromycin but 16.6% showed antibiotic susceptibility to the above-mentioned commonly used antibiotics. Silkworm larvae fed on penicillin-treated leaves showed significant improvement in larval weight, larval length, and cocoon production. Significantly higher larval weight (6.88g), larval length (5.84cm), and cocoon weight (1.33g) were recorded for larvae fed on leaves treated with penicillin as compared to other antibiotics. Isolated bacterial strains showed close relation with Serratia spp., Bacillus spp. and Pseudomonas spp.

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