Conditions under which every arc of a continuous curve is a subset of a maximal arc of the curve

1929 ◽  
Vol 101 (1) ◽  
pp. 194-209 ◽  
Author(s):  
W. L. Ayres
Keyword(s):  
Continuous Curve ◽  
Maximal Arc

scholarly journals Continuous curve textures

2020 ◽  
Vol 39 (6) ◽  
pp. 1-16
Author(s):  
Peihan Tu ◽  
Li-Yi Wei ◽  
Koji Yatani ◽  
Takeo Igarashi ◽  
Matthias Zwicker
Keyword(s):  
Continuous Curve

scholarly journals Maximal Arcs, Codes, and New Links Between Projective Planes of Order 16

10.37236/9008 ◽  
2020 ◽  
Vol 27 (1) ◽  
Author(s):  
Mustafa Gezek ◽  
Rudi Mathon ◽  
Vladimir D. Tonchev
Keyword(s):  
Minimum Distance ◽  
Linear Codes ◽  
Projective Planes ◽  
Upper And Lower Bounds ◽  
Dual Codes ◽  
Binary Linear Codes ◽  
Incidence Matrices ◽  
Maximal Arc ◽  
Maximal Arcs ◽  
Even Order

In this paper we consider binary linear codes spanned by incidence matrices of Steiner 2-designs associated with maximal arcs in projective planes of even order, and their dual codes. Upper and lower bounds on the 2-rank of the incidence matrices are derived. A lower bound on the minimum distance of the dual codes is proved, and it is shown that the bound is achieved if and only if the related maximal arc contains a hyperoval of the plane. The  binary linear codes of length 52 spanned by the incidence matrices of 2-$(52,4,1)$ designs associated with previously known and some newly found maximal arcs of degree 4 in projective planes of order 16 are analyzed and classified up to equivalence. The classification shows that some designs associated with maximal arcs in nonisomorphic planes generate equivalent codes. This phenomenon establishes new links between several of the known planes. A conjecture concerning the codes of maximal arcs in $PG(2,2^m)$ is formulated.

scholarly journals Expression of a hypomorphic Pomc allele alters leptin dynamics during late pregnancy

2020 ◽  
Vol 245 (1) ◽  
pp. 115-127 ◽  
Author(s):  
Hui Yu ◽  
Zoe Thompson ◽  
Sylee Kiran ◽  
Graham L Jones ◽  
Lakshmi Mundada ◽  
...  
Keyword(s):  
Fat Mass ◽  
Energy Homeostasis ◽  
Leptin Receptor ◽  
Late Pregnancy ◽  
Placental Development ◽  
Hypomorphic Mutation ◽  
Protein Levels ◽  
Maximal Arc ◽  
Hypothalamic Arcuate Nucleus ◽  
Pregnancy And Lactation

Proopiomelanocortin (POMC) neurons in the hypothalamic arcuate nucleus (ARC) are essential for normal energy homeostasis. Maximal ARC Pomc transcription is dependent on neuronal Pomc enhancer 1 (nPE1), located 12 kb upstream from the promoter. Selective deletion of nPE1 in mice decreases ARC Pomc expression by 70%, sufficient to induce mild obesity. Because nPE1 is located exclusively in the genomes of placental mammals, we questioned whether its hypomorphic mutation would also alter placental Pomc expression and the metabolic adaptations associated with pregnancy and lactation. We assessed placental development, pup growth, circulating leptin and expression of Pomc, Agrp and alternatively spliced leptin receptor (LepR) isoforms in the ARC and placenta of Pomc∆1/∆1 and Pomc+/+ dams. Despite indistinguishable body weights, lean mass, food intake, placental histology and Pomc expression and overall pregnancy outcomes between the genotypes, Pomc ∆1/∆1 females had increased pre-pregnancy fat mass that paradoxically decreased to control levels by parturition. However, Pomc∆1/∆1 dams had exaggerated increases in circulating leptin, up to twice of that of the typically elevated levels in Pomc+/+ mice at the end of pregnancy, despite their equivalent fat mass. Pomc∆1/∆1dams also had increased placental expression of soluble leptin receptor (LepRe), although the protein levels of LEPRE in circulation were the same as Pomc+/+ controls. Together, these data suggest that the hypomorphic Pomc∆1/∆1 allele is responsible for the perinatal super hyperleptinemia of Pomc∆1/∆1 dams, possibly due to upregulated leptin secretion from individual adipocytes.

scholarly journals Some Results and Problems Concerning Chordal Principal Cluster Sets

1967 ◽  
Vol 29 ◽  
pp. 7-18 ◽  
Author(s):  
F. Bagemihl
Keyword(s):  
Meromorphic Function ◽  
Unit Circle ◽  
Unit Disk ◽  
Riemann Sphere ◽  
Open Unit ◽  
Open Unit Disk ◽  
Continuous Curve ◽  
Cluster Set ◽  
Asymptotic Values ◽  
Principal Cluster

Let Γ be the unit circle and D be the open unit disk in the complex plane, and denote the Riemann sphere by Ω. By an arc at a point ζ∈Γ we mean a continuous curve such that |z(t)| < 1 for 0 ≦ t < 1 and . A terminal subarc of an arc Λ at ζ is a subarc of the form z = z (t) (t0 ≦ t < 1), where 0 ≦ t0<1. Suppose that f(z) is a meromorphic function in D. Then A(f) denotes the set of asymptotic values of f; and if ζ∈Γ, then C(f, ζ) means the cluster set of f at ζ and is the outer angular cluster set of f at ζ (see [13]).

Secondary Development of Automatic Drawing Software of Spindle of Numerical Control Lathe

2011 ◽  
Vol 109 ◽  
pp. 571-574
Author(s):  
Shu Lan Zhang ◽  
Nan Qiao Zhang
Keyword(s):  
Computer Technology ◽  
Structural Design ◽  
Search Algorithm ◽  
Numerical Control ◽  
Secondary Development ◽  
Automatic Design ◽  
Continuous Curve ◽  
Related Data ◽  
Automatic Drawing ◽  
Common Components

Looking up data mainly depends on the designer. Automation of looking up related data of charts, curve resource is a key to automatic design of common components, and is neccessory to be solved for strength and structural design automation of common components. A continuous curve on the logarithmic coordinates taken automatically search algorithm and discrete forms of data management and automated check to take the basic data structure to solve all the data graphs and charts automatically check the computer taken. With computer technology, in mechanical product design, various standards curves and tables can be processed.

scholarly journals On the Asymptotic Behavior of Functions Harmonic in a Disc

1966 ◽  
Vol 28 ◽  
pp. 187-191
Author(s):  
J. E. Mcmillan
Keyword(s):  
Asymptotic Behavior ◽  
Unit Circle ◽  
Complex Plane ◽  
Unit Disc ◽  
Open Unit ◽  
Continuous Curve ◽  
Open Unit Disc ◽  
Boundary Path

Let D be the open unit disc, and let C be the unit circle in the complex plane. Let f be a (real-valued) function that is harmonic in D. A simple continuous curve β: z(t) (0≦t<1) contained in D such that |z(t)|→1 as t→1 is a boundary path with end (the bar denotes closure).

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