scholarly journals The escaping set of transcendental self-maps of the punctured plane

2016 ◽  
Vol 38 (2) ◽  
pp. 739-760 ◽  
Author(s):  
DAVID MARTÍ-PETE
Keyword(s):  
Different Types ◽  
Disjoint Sets ◽  
Escaping Orbits ◽  
Class Of Functions

We study the different rates of escape of points under iteration by holomorphic self-maps of $\mathbb{C}^{\ast }=\mathbb{C}\setminus \{0\}$ for which both zero and infinity are essential singularities. Using annular covering lemmas we construct different types of orbits, including fast escaping and arbitrarily slowly escaping orbits to either zero, infinity or both. We also prove several properties about the set of fast escaping points for this class of functions. In particular, we show that there is an uncountable collection of disjoint sets of fast escaping points, each of which has $J(f)$ as its boundary.

scholarly journals Some new Simpson-type inequalities for generalized p-convex function on fractal sets with applications

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Thabet Abdeljawad ◽  
Saima Rashid ◽  
Zakia Hammouch ◽  
İmdat İşcan ◽  
Yu-Ming Chu
Keyword(s):  
Convex Functions ◽  
Fractional Derivatives ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Auxiliary Result ◽  
Fractal Sets ◽  
Different Types ◽  
Novel Applications ◽  
Class Of Functions ◽  
Harmonically Convex Functions

Abstract The present article addresses the concept of p-convex functions on fractal sets. We are able to prove a novel auxiliary result. In the application aspect, the fidelity of the local fractional is used to establish the generalization of Simpson-type inequalities for the class of functions whose local fractional derivatives in absolute values at certain powers are p-convex. The method we present is an alternative in showing the classical variants associated with generalized p-convex functions. Some parts of our results cover the classical convex functions and classical harmonically convex functions. Some novel applications in random variables, cumulative distribution functions and generalized bivariate means are obtained to ensure the correctness of the present results. The present approach is efficient, reliable, and it can be used as an alternative to establishing new solutions for different types of fractals in computer graphics.

scholarly journals D-optimal designs of experiments for trigonometric regression on interval with heteroscedastic observations

2020 ◽  
pp. 80-85
Author(s):  
Valery P. Kirlitsa
Keyword(s):  
Optimal Designs ◽  
Different Types ◽  
Designs Of Experiments ◽  
Trigonometric Regression ◽  
Class Of Functions

In article the problem of construction continuous (number of observations is not fixed) D-optimal designs of experiments for trigonometric regression in a case when variance of errors of observations depend on a point in which is made is investigated. Class of functions which describe change variance of heteroscedastic observations is defined for which it is possible construct continuous D-optimal designs of experiments. For trigonometric regression with three factors it is constructed continuous D-optimal designs of experiments with different types heteroscedastic observations. For each of these types the own class of functions describing change variance of observations is defined.

scholarly journals Construction D-optimal designs of experiments for linear multiple regression with heteroscedastic observations

2019 ◽  
pp. 27-33
Author(s):  
Valery P. Kirlitsa
Keyword(s):  
Multiple Regression ◽  
Optimal Designs ◽  
Linear Multiple Regression ◽  
Different Types ◽  
Designs Of Experiments ◽  
Class Of Functions

In article the problem of construction exact D-optimal designs of experiments for linear multiple regression in a case when variance of errors of observations depend on a point in which is made is investigated. Class of functions which describe change variance of heteroscedastic observations is defined for which it is possible construct D-optimal continues designs of experiments. For linear multiple regression with three factors it is constructed five different types of D-optimal continues designs of experiments with heteroscedastic observations. For each of these types the own class of functions describing change variance of observations is defined.

scholarly journals On common fixed points, periodic points, and recurrent points of continuous functions

2003 ◽  
Vol 2003 (39) ◽  
pp. 2465-2473 ◽  
Author(s):  
Aliasghar Alikhani-Koopaei
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Dense Subset ◽  
Periodic Points ◽  
Continuous Functions ◽  
Common Fixed Points ◽  
Closed Intervals ◽  
Disjoint Sets ◽  
The Common ◽  
Class Of Functions

It is known that two commuting continuous functions on an interval need not have a common fixed point. However, it is not known if such two functions have a common periodic point. we had conjectured that two commuting continuous functions on an interval will typically have disjoint sets of periodic points. In this paper, we first prove thatSis a nowhere dense subset of[0,1]if and only if{f∈C([0,1]):Fm(f)∩S¯≠∅}is a nowhere dense subset ofC([0,1]). We also give some results about the common fixed, periodic, and recurrent points of functions. We consider the class of functionsfwith continuousωfstudied by Bruckner and Ceder and show that the set of recurrent points of such functions are closed intervals.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Differentiating between different forms of moral obligations

2020 ◽  
Vol 43 ◽  
Author(s):  
Rajen A. Anderson ◽  
Benjamin C. Ruisch ◽  
David A. Pizarro
Keyword(s):  
Moral Character ◽  
Moral Obligations ◽  
Different Types

Abstract We argue that Tomasello's account overlooks important psychological distinctions between how humans judge different types of moral obligations, such as prescriptive obligations (i.e., what one should do) and proscriptive obligations (i.e., what one should not do). Specifically, evaluating these different types of obligations rests on different psychological inputs and has distinct downstream consequences for judgments of moral character.

Ultrastructural Investigations of the Contractile Filaments of Amoebae

1974 ◽  
Vol 32 ◽  
pp. 188-189
Author(s):  
P.L. Moore
Keyword(s):  
Cytoplasmic Streaming ◽  
Three Dimensional ◽  
Freeze Fracture ◽  
Amoeboid Movement ◽  
Different Types ◽  
Chemical Conditions ◽  
Complete Interpretation

Previous freeze fracture results on the intact giant, amoeba Chaos carolinensis indicated the presence of a fibrillar arrangement of filaments within the cytoplasm. A complete interpretation of the three dimensional ultrastructure of these structures, and their possible role in amoeboid movement was not possible, since comparable results could not be obtained with conventional fixation of intact amoebae. Progress in interpreting the freeze fracture images of amoebae required a more thorough understanding of the different types of filaments present in amoebae, and of the ways in which they could be organized while remaining functional.The recent development of a calcium sensitive, demembranated, amoeboid model of Chaos carolinensis has made it possible to achieve a better understanding of such functional arrangements of amoeboid filaments. In these models the motility of demembranated cytoplasm can be controlled in vitro, and the chemical conditions necessary for contractility, and cytoplasmic streaming can be investigated. It is clear from these studies that “fibrils” exist in amoeboid models, and that they are capable of contracting along their length under conditions similar to those which cause contraction in vertebrate muscles.

Study of the Molecular Architecture of Keratin Filaments by Electron Microscopy

1982 ◽  
Vol 40 ◽  
pp. 118-119
Author(s):  
U. Aebi ◽  
P. Rew ◽  
T.-T. Sun
Keyword(s):  
Electron Microscopy ◽  
Structural Organization ◽  
Cell Types ◽  
Structural Features ◽  
Molecular Architecture ◽  
The Past ◽  
Keratin Filaments ◽  
Different Types ◽  
10 Nm Filaments ◽  
Different Cell Types

Various types of intermediate-sized (10-nm) filaments have been found and described in many different cell types during the past few years. Despite the differences in the chemical composition among the different types of filaments, they all yield common structural features: they are usually up to several microns long and have a diameter of 7 to 10 nm; there is evidence that they are made of several 2 to 3.5 nm wide protofilaments which are helically wound around each other; the secondary structure of the polypeptides constituting the filaments is rich in ∞-helix. However a detailed description of their structural organization is lacking to date.

A New Defect in Polyethylene Single Crystals

1973 ◽  
Vol 31 ◽  
pp. 70-71
Author(s):  
E. L. Thomas ◽  
S. L. Sass
Keyword(s):  
Single Crystals ◽  
Screw Dislocation ◽  
Small Distance ◽  
Dipole Model ◽  
Dislocation Dipole ◽  
Chain Folding ◽  
Black And White ◽  
Polymer Crystal ◽  
Different Types

In polyethylene single crystals pairs of black and white lines spaced 700-3,000Å apart, parallel to the [100] and [010] directions, have been identified as microsector boundaries. A microsector is formed when the plane of chain folding changes over a small distance within a polymer crystal. In order for the different types of folds to accommodate at the boundary between the 2 fold domains, a staggering along the chain direction and a rotation of the chains in the plane of the boundary occurs. The black-white contrast from a microsector boundary can be explained in terms of these chain rotations. We demonstrate that microsectors can terminate within the crystal and interpret the observed terminal strain contrast in terms of a screw dislocation dipole model.

Methionine-Specific Staining of Collagen

1982 ◽  
Vol 40 ◽  
pp. 294-295
Author(s):  
E.M. Kuhn ◽  
K.D. Marenus ◽  
M. Beer
Keyword(s):  
Amino Acids ◽  
Collagen Fibers ◽  
Type Iii Collagen ◽  
Type I ◽  
Electron Microscopic ◽  
Good Correspondence ◽  
Specific Staining ◽  
Type Iii ◽  
Different Types ◽  
Sulfur Containing

Fibers composed of different types of collagen cannot be differentiated by conventional electron microscopic stains. We are developing staining procedures aimed at identifying collagen fibers of different types.Pt(Gly-L-Met)Cl binds specifically to sulfur-containing amino acids. Different collagens have methionine (met) residues at somewhat different positions. A good correspondence has been reported between known met positions and Pt(GLM) bands in rat Type I SLS (collagen aggregates in which molecules lie adjacent to each other in exact register). We have confirmed this relationship in Type III collagen SLS (Fig. 1).

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