A New Kind of Free Extension for Projective Planes

1962 ◽  
Vol 5 (2) ◽  
pp. 167-170 ◽  
Author(s):  
Seymour Ditor
Keyword(s):  
General Structure ◽  
Projective Planes ◽  
Line Incident ◽  
Free Extension ◽  
Extensive Class ◽  
Partial Plane ◽  
Set Of Points

Marshall Hall [l] shows how projective planes of very general structure may be constructed and at the same time exhibits an extensive class which are non-Desarguesian. Here we shall indicate how his method of free extension can be generalized to yield a class of planes which seem to be distinct from those which he obtains.A partial plane is a system consisting of two distinct sets of elements, a set of "points" P, Q,… and a set of "lines" l, m,…, and a relation between these two sets, called "incidence", such that for any two distinct points, there is at most one line incident with both (or, equivalently, for any two distinct lines, there is at most one point incident with both). A partial plane is complete if every two distinct points are joined by a line and every two distinct lines intersect in a point.

scholarly journals Analysis of Some Properties from Construction of Finite Projective Planes of Order 2 and 3

CAUCHY ◽  
2016 ◽  
Vol 4 (3) ◽  
pp. 131
Author(s):  
Vira Hari Krisnawati ◽  
Corina Karim
Keyword(s):  
Automorphism Group ◽  
Projective Plane ◽  
Symmetric Group ◽  
Block Design ◽  
Finite Projective Plane ◽  
Projective Planes ◽  
Steiner System ◽  
Incidence Relation ◽  
Finite Projective Planes ◽  
Set Of Points

<p class="abstract"><span lang="IN">In combinatorial mathematics, a Steiner system is a type of block design. Specifically, a Steiner system <em>S</em>(<em>t</em>, <em>k</em>, <em>v</em>) is a set of <em>v</em> points and <em>k</em> blocks which satisfy that every <em>t</em>-subset of <em>v</em>-set of points appear in the unique block. It is well-known that a finite projective plane is one examples of Steiner system with <em>t</em> = 2, which consists of a set of points and lines together with an incidence relation between them and order 2 is the smallest order.</span></p><p class="abstract"><span lang="IN">In this paper, we observe some properties from construction of finite projective planes of order 2 and 3. Also, we analyse the intersection between two projective planes by using some characteristics of the construction and orbit of projective planes over some representative cosets from automorphism group in the appropriate symmetric group.</span></p>

scholarly journals Large Incidence-free Sets in Geometries

10.37236/2831 ◽  
2012 ◽  
Vol 19 (4) ◽  
Author(s):  
Stefaan De Winter ◽  
Jeroen Schillewaert ◽  
Jacques Verstraete
Keyword(s):  
Projective Plane ◽  
Projective Planes ◽  
Combinatorial Proof ◽  
Partial Linear Space ◽  
Spectral Techniques ◽  
Maximal Arc ◽  
Maximal Arcs ◽  
Point Set ◽  
Partial Linear ◽  
Set Of Points

Let $\Pi = (P,L,I)$ denote a rank two geometry. In this paper, we are interested in the largest value of $|X||Y|$ where $X \subset P$ and $Y \subset L$ are sets such that $(X \times Y) \cap I = \emptyset$. Let $\alpha(\Pi)$ denote this value. We concentrate on the case where $P$ is the point set of $\mathsf{PG}(n,q)$ and $L$ is the set of $k$-spaces in $\mathsf{PG}(n,q)$. In the case that $\Pi$ is the projective plane $\mathsf{PG}(2,q)$, where $P$ is the set of points and $L$ is the set of lines of the projective plane, Haemers proved that maximal arcs in projective planes together with the set of lines not intersecting the maximal arc determine $\alpha(\mathsf{PG}(2,q))$ when $q$ is an even power of $2$. Therefore, in those cases,\[ \alpha(\Pi) = q(q - \sqrt{q} + 1)^2.\] We give both a short combinatorial proof and a linear algebraic proof of this result, and consider the analogous problem in generalized polygons. More generally, if $P$ is the point set of $\mathsf{PG}(n,q)$ and $L$ is the set of $k$-spaces in $\mathsf{PG}(n,q)$, where $1 \leq k \leq n - 1$, and $\Pi_q = (P,L,I)$, then we show as $q \rightarrow \infty$ that \[ \frac{1}{4}q^{(k + 2)(n - k)} \lesssim \alpha(\Pi) \lesssim q^{(k + 2)(n - k)}.\] The upper bounds are proved by combinatorial and spectral techniques. This leaves the open question as to the smallest possible value of $\alpha(\Pi)$ for each value of $k$. We prove that if for each $N \in \mathbb N$, $\Pi_N$ is a partial linear space with $N$ points and $N$ lines, then $\alpha(\Pi_N) \gtrsim \frac{1}{e}N^{3/2}$ as $N \rightarrow \infty$.

Pascal Ovals in Projective Planes

1969 ◽  
Vol 21 ◽  
pp. 1462-1476 ◽  
Author(s):  
J. F. Rigby
Keyword(s):  
Projective Plane ◽  
Projective Planes ◽  
Unique Point ◽  
Unique Line ◽  
Set Of Points

A projective plane consists of a set of points and a set of lines, together with a relation of incidence between points and lines, such that(i) any two distinct points P, Q are incident with a unique line PQ,(ii) any two distinct lines p, q are incident with a unique point p ∩ q,(iii) there exist four points, no three of which are incident with the same line.We shall use the usual geometrical terminology.An oval in a projective plane π is a set of points of π such that:(i) no three points of are collinear; this means that a line of π is either a secant of , containing two points of , or a tangent of , containing just one point of , or a non-secant of , containing no point of ;

On Subplanes of Free Planes

1964 ◽  
Vol 16 ◽  
pp. 379-385 ◽  
Author(s):  
Reuben Sandler
Keyword(s):  
Projective Plane ◽  
Free Groups ◽  
Projective Planes ◽  
Incidence Relation ◽  
Free Generators ◽  
Set Of Points

In 1945, L. I. Kopejkina (4), at the suggestion of A. G. Kurosh, began a programme of studying the properties of free projective planes and the analogies between free planes and free groups. In this paper, this study will be extended by proving a tool theorem and several of its consequences. The theorem deals with the existence of "minimal free generators" for subplanes of free planes.A set of points and lines and an incidence relation are said to form a projective plane if the following three axioms are satisfied.

Video Graphics and High-Voltage Electron Microscopy For Analysis of Microtubule Distributions In Fixed Cells

1990 ◽  
Vol 48 (1) ◽  
pp. 524-525
Author(s):  
Richard Mcintosh ◽  
David Mastronarde ◽  
Kent McDonald ◽  
Rubai Ding
Keyword(s):  
Electron Microscopy ◽  
Cross Sections ◽  
Cell Shape ◽  
Video Camera ◽  
Computer Memory ◽  
High Voltage Electron Microscopy ◽  
Thin Sections ◽  
Voltage Electron ◽  
Morphogenetic Event ◽  
Set Of Points

Microtubules (MTs) are cytoplasmic polymers whose dynamics have an influence on cell shape and motility. MTs influence cell behavior both through their growth and disassembly and through the binding of enzymes to their surfaces. In either case, the positions of the MTs change over time as cells grow and develop. We are working on methods to determine where MTs are at different times during either the cell cycle or a morphogenetic event, using thin and thick sections for electron microscopy and computer graphics to model MT distributions.One approach is to track MTs through serial thin sections cut transverse to the MT axis. This work uses a video camera to digitize electron micrographs of cross sections through a MT system and create image files in computer memory. These are aligned and corrected for relative distortions by using the positions of 8 - 10 MTs on adjacent sections to define a general linear transformation that will align and warp adjacent images to an optimum fit. Two hundred MT images are then used to calculate an “average MT”, and this is cross-correlated with each micrograph in the serial set to locate points likely to correspond to MT centers. This set of points is refined through a discriminate analysis that explores each cross correlogram in the neighborhood of every point with a high correlation score.

Cloning of the Rat Tissue Factor cDNA and Promoter: Identification of a Serum-response Region

1996 ◽  
Vol 76 (05) ◽  
pp. 697-702 ◽  
Author(s):  
Olivier Taby ◽  
Claire-Lise Rosenfield ◽  
Vladimir Bogdanov ◽  
Yale Nemerson ◽  
Mark B Taubman
Keyword(s):  
Tissue Factor ◽  
General Structure ◽  
Amino Acid Sequences ◽  
Proximal Promoter ◽  
Striking Similarity ◽  
Upstream Sequence ◽  
Tf Gene ◽  
Rat Tissue ◽  
High Degree ◽  
Transcriptional Elements

SummaryTissue factor (TF) initiates coagulation and its expression in vascular smooth muscle cells (VSMC) likely plays a role in the propagation of arterial thrombosis. We report cloning the cDNA and proximal promoter region of the rat TF gene. While maintaining the general structure and organization of the TF molecule, there is a surprising divergence (≈ 18%) between the derived amino acid sequences of the rat and mouse TF. In contrast, there is striking similarity (90%) in the 5’ untranslated regions. High levels of basal promoter activity were seen in rat VSMC with constructs containing 106 bp of sequence downstream from the putative transcription start site and 426 to 103 bp of upstream sequence. Deletion of the sequence from −103 to −79, containing a single SP1 site, removed virtually all of the basal and serum-induced activity. Removal of the NFkB site or two additional upstream SP1 sites had little effect on serum responsiveness. Removal of the 5’ untranslated region abolished most of the basal activity of the TF promoter, suggesting that its high degree of conservation may be due to the presence of transcriptional elements critical for TF expression in rodent VSMC.

"GENERAL STRUCTURE AND REQUIREMENTS FOR THE GEOKHOD CONTROL SYSTEM "

2017 ◽  
Vol 17 (6) ◽  
pp. 41-46
Author(s):  
V.V. Aksenov ◽  
◽  
I.V. Chicherin ◽  
Keyword(s):  
Control System ◽  
General Structure

THE CORRELATION POVERTY – DEVIANT BEHAVIOR – SOCIAL EXCLUSION (SAMPLE MODEL OF A SEMINAR)

2020 ◽  
Vol 11 (1) ◽  
pp. 78-82
Author(s):  
Toni Manasieva ◽  
Keyword(s):  
Social Exclusion ◽  
Deviant Behavior ◽  
General Structure ◽  
Causal Connection ◽  
Social Activities

The article presents an example model of a seminar on the topic of the connection between three phenomena: poverty, deviant behavior, social exclusion. Taking into account the general parameters valid for the whole community, the attention is focused on the specific dimensions in children. The general structure follows the logic: from the identification of the problem in its essence, through its causal connection, to the approaches to dealing with it. The possibilities and limitations in principle and in individual cases that affect the analysis and methodological decisions are taken into account – e.g. some popular stereotypes and prejudices. The model can be used both in the form of the above – in the training of students – future specialists in pedagogy and social activities, as well as for work with current specialists in practice.

Pharmacoepidemiological Analysis of Pharmacotherapy for Burn Injuries in Real Clinical Practice

2020 ◽  
pp. 70-79
Author(s):  
Olga Vyacheslavovna Zhukova ◽  
Ekaterina Sergeevna Nekaeva ◽  
Elena Sergeevna Khoroshavina ◽  
Ekaterina Alexeevna Kozlova ◽  
Yulia Alexandrovna Dudukina ◽  
...  
Keyword(s):  
Clinical Practice ◽  
Average Cost ◽  
Burn Injury ◽  
General Structure ◽  
Burn Injuries ◽  
Antimicrobial Drugs ◽  
Positive Tendency ◽  
Defined Daily Doses ◽  
Duration Of Hospitalization ◽  
Real Clinical Practice

Objective: to conduct pharmacoepidemiological analysis and analysis of the costs of pharmacotherapy, taking into account the actual consumption of drugs in the real inpatient clinical practice at the federal center in Russia. Materials and methods. Data from the medical records of 14 patients with burn injury, who were hospitalized in 2018, was analyzed. Patients’ age was from 23 to 67 years (44,93 ± 14,66). Duration of hospitalization was from 17 to 62 days (35,93 ± 14,17). We calculated rate of prescription foe each drug and its share in general structure of all utilized drug courses (n = 460). We performed frequency analysis of prescription structure, DDD (defined daily doses) analysis, DU90% (Drug Utilization 90%) analysis, ABC-analysis and analysis of average cost of pharmacotherapy. Results. Most frequently used drugs, prescribed in 75-100% of all hospital cases, included 15 names, e.g. 2 antimicrobial drugs (vancomycin and amikacin), 19 were used commonly, including 4 antimicrobial drugs (co-trimoxazole, cefoperazone/sulbactam, tigecyclin and cefepime). Other drugs were used in less than 25% of cases. 33 drugs made 90% of all consumed NDDD, including 5 antimicrobial drugs (vancomycin, amikacin, co-trimoxazole, cefoperazone/sulbactam and tigecyclin). These drugs comprised 70,24% in the prescription structure. The cost of one DDD in DU90% segments (512,33 rubles) is 1,4 higher than in DU10% segment (649,34 rubles). Average cost of drugs included in DU90% group was 4735,89 rubles vs 4966,80 rubles for drugs from DU10% group. This finding shows positive tendency of burn injuries pharmacological treatment. Conclusion. We obtained the data, which can be used for comparison of real clinical practice costs with a current payment rates for medical care.

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