scholarly journals Injectivity of the Composition Operators of Étale Mappings

Algebra ◽  
2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Ronen Peretz
Keyword(s):  
Topological Space ◽  
Composition Operator ◽  
Open Problem ◽  
Fractal Structure ◽  
Composition Operators ◽  
New Method ◽  
Jacobian Conjecture ◽  
Two Dimensional ◽  
New Approach ◽  
Polynomial Mappings

Let X be a topological space. The semigroup of all the étale mappings of X (the local homeomorphisms X→X) is denoted by et(X). If G∈et(X), then the G-right (left) composition operator on et(X) is defined by RG  LG:et(X)→et(X), RGF=F∘G  (LGF=G∘F). When are the composition operators injective? The Problem originated in a new approach to study étale polynomial mappings C2→C2 and in particular the two-dimensional Jacobian conjecture. This approach constructs a fractal structure on the semigroup of the (normalized) Keller mappings and outlines a new method of a possible attack on this open problem (in preparation). The construction uses the left composition operator and the injectivity problem is essential. In this paper we will completely solve the injectivity problems of the two composition operators for (normalized) Keller mappings. We will also solve the much easier surjectivity problem of these composition operators.

A New Approach to Plasticity and Its Application to Blunt Two Dimensional Indenters

1970 ◽  
Vol 92 (2) ◽  
pp. 469-479 ◽  
Author(s):  
M. C. Shaw ◽  
G. J. DeSalvo
Keyword(s):  
Residual Stresses ◽  
Plastic Flow ◽  
Slip Line ◽  
New Method ◽  
Two Dimensional ◽  
Constraint Factor ◽  
Line Field ◽  
New Approach ◽  
Slip Line Field ◽  
First Time

The classical slip line field solution for a two-dimensional punch is found to give a constraint factor (2.57) which is too small when the specimen beneath the punch is extensive. A new approach based on elasticity provides a constraint factor of 2.75. The new method of analysis also enables residual stresses to be estimated and indicates that plastic flow occurs not only when the specimen is loaded, but also when it is unloaded. Several details concerning the performance of hardness indenters are explained by the new theory for the first time.

Performance of r-Adaptation Using Truncation Error-Based Equidistribution

2019 ◽  
Vol 4 (4) ◽  
Author(s):  
Charles W. Jackson ◽  
Christopher J. Roy
Keyword(s):  
Truncation Error ◽  
Stokes Equations ◽  
Computational Cost ◽  
Discretization Error ◽  
New Method ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Error Level ◽  
Navier Stokes Equations ◽  
New Approach

Abstract This paper investigates the computational cost of performing r-adaptation by equidistributing the truncation error. This adaptation approach is applied to several two-dimensional (2D) problems using the Euler and laminar Navier–Stokes equations. The costs of performing the adaptation are compared to uniform refinement, and it is shown that adaptation can be far cheaper than uniform refinement. This paper also presents a new method of refining the equidistributed meshes. This new approach allows the adaptation to be performed on much coarser meshes and provides a method of refining these coarse, adapted meshes to meet a discretization-error target for the problem. We show that this approach can be at least 16–24 times cheaper than uniform refinement for the problems investigated here. This approach also is at least ten times faster than performing r-adaptation on a fine enough mesh to obtain the target discretization-error level.

A New Approach for the Analysis of Mixture Toxicity Data

1992 ◽  
Vol 26 (9-11) ◽  
pp. 2345-2348 ◽  
Author(s):  
C. N. Haas
Keyword(s):  
Quantitative Analysis ◽  
Mixture Toxicity ◽  
New Method ◽  
Metal Exposure ◽  
Positive Interactions ◽  
Toxicity Data ◽  
Data Set ◽  
New Approach ◽  
Negative Interactions

A new method for the quantitative analysis of multiple toxicity data is described and illustrated using a data set on metal exposure to copepods. Positive interactions are observed for Ni-Pb and Pb-Cr, with weak negative interactions observed for Ni-Cr.

scholarly journals Compact Differences of Composition Operators on Bergman Spaces Induced by Doubling Weights

2021 ◽  
Author(s):  
Bin Liu ◽  
Jouni Rättyä ◽  
Fanglei Wu
Keyword(s):  
Bergman Space ◽  
Open Problem ◽  
Lebesgue Space ◽  
Composition Operators ◽  
Bergman Spaces ◽  
Weighted Bergman Space ◽  
Carleson Measures ◽  
Doubling Weights ◽  
The Way

AbstractBounded and compact differences of two composition operators acting from the weighted Bergman space $$A^p_\omega $$ A ω p to the Lebesgue space $$L^q_\nu $$ L ν q , where $$0<q<p<\infty $$ 0 < q < p < ∞ and $$\omega $$ ω belongs to the class "Equation missing" of radial weights satisfying two-sided doubling conditions, are characterized. On the way to the proofs a new description of q-Carleson measures for $$A^p_\omega $$ A ω p , with $$p>q$$ p > q and "Equation missing", involving pseudohyperbolic discs is established. This last-mentioned result generalizes the well-known characterization of q-Carleson measures for the classical weighted Bergman space $$A^p_\alpha $$ A α p with $$-1<\alpha <\infty $$ - 1 < α < ∞ to the setting of doubling weights. The case "Equation missing" is also briefly discussed and an open problem concerning this case is posed.

scholarly journals New Method for Generating New Families of Distributions

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 726
Author(s):  
Lamya A. Baharith ◽  
Wedad H. Aljuhani
Keyword(s):  
Exponential Distribution ◽  
Real Data ◽  
Rate Function ◽  
New Method ◽  
Likelihood Method ◽  
Alpha Power ◽  
Unknown Parameters ◽  
Failure Rate Function ◽  
New Approach ◽  
Numerical Studies

This article presents a new method for generating distributions. This method combines two techniques—the transformed—transformer and alpha power transformation approaches—allowing for tremendous flexibility in the resulting distributions. The new approach is applied to introduce the alpha power Weibull—exponential distribution. The density of this distribution can take asymmetric and near-symmetric shapes. Various asymmetric shapes, such as decreasing, increasing, L-shaped, near-symmetrical, and right-skewed shapes, are observed for the related failure rate function, making it more tractable for many modeling applications. Some significant mathematical features of the suggested distribution are determined. Estimates of the unknown parameters of the proposed distribution are obtained using the maximum likelihood method. Furthermore, some numerical studies were carried out, in order to evaluate the estimation performance. Three practical datasets are considered to analyze the usefulness and flexibility of the introduced distribution. The proposed alpha power Weibull–exponential distribution can outperform other well-known distributions, showing its great adaptability in the context of real data analysis.

scholarly journals Two-color two-dimensional terahertz spectroscopy: A new approach for exploring even-order nonlinearities in the nonperturbative regime

2021 ◽  
Vol 154 (15) ◽  
pp. 154203
Author(s):  
Michael Woerner ◽  
Ahmed Ghalgaoui ◽  
Klaus Reimann ◽  
Thomas Elsaesser
Keyword(s):  
Terahertz Spectroscopy ◽  
Two Dimensional ◽  
New Approach ◽  
Even Order

Two-dimensional asynchronous spectrum with auxiliary cross peaks in probing intermolecular interactions

RSC Advances ◽  
2015 ◽  
Vol 5 (107) ◽  
pp. 87739-87749 ◽  
Author(s):  
Xiaopei Li ◽  
Anqi He ◽  
Kun Huang ◽  
Huizhou Liu ◽  
Ying Zhao ◽  
...  
Keyword(s):  
Intermolecular Interaction ◽  
Intermolecular Interactions ◽  
Two Dimensional ◽  
New Approach

A new approach called “asynchronous spectrum with auxiliary peaks (ASAP)” is proposed for generating a 2D asynchronous spectrum to investigate the intermolecular interaction between two solutes (P and Q) dissolved in the same solution.

Comparison of New Telescopic Video Microlaryngoscopic and Standard Microlaryngoscopic Techniques

1992 ◽  
Vol 101 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Eiji Yanagisawa ◽  
Ken Yanagisawa ◽  
Jay B. Horowitz ◽  
Lawrence J. Mambrino
Keyword(s):  
Video Camera ◽  
New Method ◽  
Depth Of Field ◽  
Microscopic Technique ◽  
New Approach ◽  
Advantages And Disadvantages ◽  
Laryngeal Surgery ◽  
Valuable Method ◽  
Microlaryngeal Surgery ◽  
Television Image

A new approach to microlaryngeal surgery using a specially designed video microlaryngoscope with a rigid endoscopic telescope and an attached video camera was introduced by Kantor et al in 1990. The ability to video document and perform surgery of the larynx by viewing a high-resolution television image was demonstrated. This method was recommended over the standard microscopic technique for increased visibility with greater depth of field, unimpeded instrument access, instant documentation, and superior teaching value. The authors tried this new method and the standard microscopic technique at the same sitting on a series of patients. This paper will compare these two different techniques and discuss their advantages and disadvantages. Although the new method has many advantages, the standard microscopic technique remains as a valuable method in laryngeal surgery.

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