scholarly journals On maximal Kn domains for certain families of rational functions

2008 ◽  
Vol 48 ◽  
Author(s):  
Jevgenij Kiriyatzkii ◽  
Eduard Kiriyatzkii
Keyword(s):  
Boundary Point ◽  
Rational Functions ◽  
Maximal Domain ◽  
The Family ◽  
Angular Domains ◽  
Special Classes

Let Kn(D) be a class of analytic in domain D functions such that [F(z); z0,...,zn] for any z0,...,zn ∈ D. The domain D is called by maximal Kn-domain of the family T of functions which are analytic in D, if for any neighborhood ε(ψ) of any boundary point ψ of D there exists a function from T which does not belong to Kn(D \smile ε(ψ)). The maximal domain of univalence, i.e., maximal K1 domain was investigated by Bulgarian mathematician L. Chakalov. In this paper as maximal Kn-domains the angular domains are examined. Kn-domains for two special classes of rational functions are established.  

scholarly journals Operations on partially ordered sets and rational identities of type A

2013 ◽  
Vol Vol. 15 no. 2 (Combinatorics) ◽  
Author(s):  
Adrien Boussicault
Keyword(s):  
Partially Ordered Sets ◽  
Rational Functions ◽  
Hasse Diagram ◽  
Linear Extensions ◽  
Ordered Sets ◽  
Closed Expression ◽  
Schubert Polynomials ◽  
Special Cases ◽  
The Family ◽  
International Audience

Combinatorics International audience We consider the family of rational functions ψw= ∏( xwi - xwi+1 )-1 indexed by words with no repetition. We study the combinatorics of the sums ΨP of the functions ψw when w describes the linear extensions of a given poset P. In particular, we point out the connexions between some transformations on posets and elementary operations on the fraction ΨP. We prove that the denominator of ΨP has a closed expression in terms of the Hasse diagram of P, and we compute its numerator in some special cases. We show that the computation of ΨP can be reduced to the case of bipartite posets. Finally, we compute the numerators associated to some special bipartite graphs as Schubert polynomials.

scholarly journals Steiner's Hat: a Constant-Area Deltoid Associated with the Ellipse

KoG ◽  
2020 ◽  
pp. 12-28
Author(s):  
Ronaldo Garcia ◽  
Dan Reznik ◽  
Hellmuth Stachel ◽  
Mark Helman
Keyword(s):  
Boundary Point ◽  
Closed Curve ◽  
Constant Area ◽  
The Family ◽  
Affine Image ◽  
Pedal Curve

The Negative Pedal Curve (NPC) of the Ellipse with respect to a boundary point M is a 3-cusp closed-curve which is the affine image of the Steiner Deltoid. Over all M the family has invariant area and displays an array of interesting properties.

Reader Reflections: March 2003

2003 ◽  
Vol 96 (3) ◽  
pp. 164-209
Keyword(s):  
Mathematics Teacher ◽  
Special Class ◽  
Rational Functions ◽  
Special Classes

In “Reader Reflections: Pseudoinverse functions” on page 723 of the December 2001 issue of the Mathematics Teacher, Larry Hoehn presents a special class of rational functions for which f(g(x)) = g(f(x)) ≠ x and asks whether other special classes of functions of this type exist

On the iteration of rational functions

1978 ◽  
Vol 84 (3) ◽  
pp. 497-505 ◽  
Author(s):  
V. Garber
Keyword(s):  
Rational Function ◽  
Entire Functions ◽  
Rational Functions ◽  
Transcendental Entire Function ◽  
The Family ◽  
Transcendental Entire Functions ◽  
Definition Of ◽  
Iteration Of Rational Functions ◽  
Image Position ◽  
Set Of Points

In the theory of the iteration of a rational function or transcendental entire function R(z) of the complex variable z we study the sequence of natural iterates, {Rn(z):n = 0, 1,…}, of R, whereThe domain of definition of the iterates is , the extended complex plane (if R is rational), and (if R is entire transcendental) with the topology of the chordal metric and euclidean metric respectively. Fatou(5) and Julia(9) developed a global theory of the iteration of a rational function. In (6) Fatou extended the theory of (5) to transcendental entire functions. A central role is played in the theory by the F-set, F(R), of R, R rational or entire, which is defined to be the set of points at which the family of iterates do not form a normal family in the sense of Montel.

Regulation of Emotional Security by Children after Entry to Special and Regular Kindergarten Classes

2003 ◽  
Vol 93 (3_suppl) ◽  
pp. 1319-1334 ◽  
Author(s):  
Helma M. Y. Koomen ◽  
Jan B. Hoeksma
Keyword(s):  
Behavioral Inhibition ◽  
Emotional Security ◽  
After School ◽  
Normal Children ◽  
The Family ◽  
Entry Behavior ◽  
Externalizing Problem ◽  
Internalizing Problem ◽  
Regular Classes ◽  
Special Classes

In this paper early adaptation after children's entry to kindergarten is conceptualized as a process of achieving emotional security. It was hypothesized that children adapt to school by means of security seeking from the teacher and behavioral inhibition. 30 normal children from regular classes and 36 children with a variety of problems, e.g., behavioral, emotional, and family problems, from special classes were rated by their teachers on the Inhibition Scale and Security Seeking Scale on 5 occasions during the first 3 mo. at school. By the end of this period teachers judged the intensity of behavior problems on the Internalizing Problem Scale and the Externalizing Problem Scale. Analysis showed that initial high scores on the Security Seeking Scale and Inhibition Scale decreased sharply during the first weeks, and that children from special classes scored consistently higher on the Security Seeking Scale and more variable on the Inhibition Scale than children from regular classes. Girls had higher scores than boys on both scales. Recent stress in the family as rated by the teacher was positively related to both scores on the Inhibition and Security Seeking Scales after entry. Finally, scores on the Security Seeking and Inhibition Scales over the first three months predicted scores on the Internalizing Problem Scale by the end of this period, especially for children in special classes. We conclude that understanding adaptation after school entry as a process of obtaining emotional security is productive, providing a means to link entry behavior to precursors and consequences.

Triassic sponges (Sphinctozoa) from Hells Canyon, Oregon

1988 ◽  
Vol 62 (03) ◽  
pp. 419-423 ◽  
Author(s):  
Baba Senowbari-Daryan ◽  
George D. Stanley
Keyword(s):  
Endemic Species ◽  
Upper Triassic ◽  
Island Arc ◽  
Tropical Island ◽  
The Family ◽  
Wallowa Terrane ◽  
Unique Condition ◽  
Hells Canyon

Two Upper Triassic sphinctozoan sponges of the family Sebargasiidae were recovered from silicified residues collected in Hells Canyon, Oregon. These sponges areAmblysiphonellacf.A. steinmanni(Haas), known from the Tethys region, andColospongia whalenin. sp., an endemic species. The latter sponge was placed in the superfamily Porata by Seilacher (1962). The presence of well-preserved cribrate plates in this sponge, in addition to pores of the chamber walls, is a unique condition never before reported in any porate sphinctozoans. Aporate counterparts known primarily from the Triassic Alps have similar cribrate plates but lack the pores in the chamber walls. The sponges from Hells Canyon are associated with abundant bivalves and corals of marked Tethyan affinities and come from a displaced terrane known as the Wallowa Terrane. It was a tropical island arc, suspected to have paleogeographic relationships with Wrangellia; however, these sponges have not yet been found in any other Cordilleran terrane.

Electron Microscopy of Mycoplasma Pneumoniae

1971 ◽  
Vol 29 ◽  
pp. 258-259 ◽  
Author(s):  
E. S. Boatman ◽  
G. E. Kenny
Keyword(s):  
Electron Microscopy ◽  
Light Microscopy ◽  
Growth Phase ◽  
Hela Cells ◽  
Sulfonic Acid ◽  
Gamma Globulin ◽  
Horse Serum ◽  
Morphological Aspects ◽  
The Family

Information concerning the morphology and replication of organism of the family Mycoplasmataceae remains, despite over 70 years of study, highly controversial. Due to their small size observations by light microscopy have not been rewarding. Furthermore, not only are these organisms extremely pleomorphic but their morphology also changes according to growth phase. This study deals with the morphological aspects of M. pneumoniae strain 3546 in relation to growth, interaction with HeLa cells and possible mechanisms of replication.The organisms were grown aerobically at 37°C in a soy peptone yeast dialysate medium supplemented with 12% gamma-globulin free horse serum. The medium was buffered at pH 7.3 with TES [N-tris (hyroxymethyl) methyl-2-aminoethane sulfonic acid] at 10mM concentration. The inoculum, an actively growing culture, was filtered through a 0.5 μm polycarbonate “nuclepore” filter to prevent transfer of all but the smallest aggregates. Growth was assessed at specific periods by colony counts and 800 ml samples of organisms were fixed in situ with 2.5% glutaraldehyde for 3 hrs. at 4°C. Washed cells for sectioning were post-fixed in 0.8% OSO4 in veronal-acetate buffer pH 6.1 for 1 hr. at 21°C. HeLa cells were infected with a filtered inoculum of M. pneumoniae and incubated for 9 days in Leighton tubes with coverslips. The cells were then removed and processed for electron microscopy.

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