Diagnostics of narrative abilities and Czech adaptation of the MAIN tool

This book develops a new theory of multi-parameter singular integrals associated with Carnot–Carathéodory balls. The book first details the classical theory of Calderón–Zygmund singular integrals and applications to linear partial differential equations. It then outlines the theory of multi-parameter Carnot–Carathéodory geometry, where the main tool is a quantitative version of the classical theorem of Frobenius. The book then gives several examples of multi-parameter singular integrals arising naturally in various problems. The final chapter of the book develops a general theory of singular integrals that generalizes and unifies these examples. This is one of the first general theories of multi-parameter singular integrals that goes beyond the product theory of singular integrals and their analogs. This book will interest graduate students and researchers working in singular integrals and related fields.

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Spaces of PL Manifolds and Categories of Simple Maps (AM-186)

10.23943/princeton/9780691157757.001.0001 ◽

2013 ◽

Cited By ~ 1

Author(s):

Friedhelm Waldhausen ◽

Bjørn Jahren ◽

John Rognes

Keyword(s):

Main Tool ◽

Homotopy Equivalence ◽

Classifying Space ◽

Deformation Retract ◽

Simplicial Sets ◽

Full Proof

Since its introduction by the author in the 1970s, the algebraic K-theory of spaces has been recognized as the main tool for studying parametrized phenomena in the theory of manifolds. However, a full proof of the equivalence relating the two areas has not appeared until now. This book presents such a proof, essentially completing the author's program from more than thirty years ago. The main result is a stable parametrized h-cobordism theorem, derived from a homotopy equivalence between a space of PL h-cobordisms on a space X and the classifying space of a category of simple maps of spaces having X as deformation retract. The smooth and topological results then follow by smoothing and triangulation theory. The proof has two main parts. The essence of the first part is a “desingularization,” improving arbitrary finite simplicial sets to polyhedra. The second part compares polyhedra with PL manifolds by a thickening procedure. Many of the techniques and results developed should be useful in other connections.

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The Novel TEM Sample Preparation Approach for Targeted via with Barrier/Cu Seed Layer Inspection

ISTFA 2009: Conference Proceedings from the 35th International Symposium for Testing and Failure Analysis ◽

10.31399/asm.cp.istfa2009p0214 ◽

2009 ◽

Author(s):

Wen-Fei Hsieh ◽

Shih-Hsiang Tseng ◽

Bo Min She

Keyword(s):

Sample Preparation ◽

Cross Section ◽

Seed Layer ◽

Target Location ◽

Process Development ◽

Process Integration ◽

Ion Beam ◽

Main Tool ◽

Dual Beam ◽

Sample Preparation Procedure

Abstract In this study, an FIB-based cross section TEM sample preparation procedure for targeted via with barrier/Cu seed layer is introduced. The dual beam FIB with electron beam for target location and Ga ion beam for sample milling is the main tool for the targeted via with barrier/Cu seed layer inspection. With the help of the FIB operation and epoxy layer protection, ta cross section TEM sample at a targeted via with barrier/Cu seed layer could be made. Subsequent TEM inspection is used to verify the quality of the structure. This approach was used in the Cu process integration performance monitor. All these TEM results are very helpful in process development and yield improvement.

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To the discussion about the modern world order

Diplomatic Service ◽

10.33920/vne-01-2003-05 ◽

2020 ◽

pp. 35-41

Author(s):

A. Mustafabeyli

Keyword(s):

Soviet Union ◽

Intergovernmental Relations ◽

World System ◽

Main Tool ◽

World Order ◽

Modern World ◽

The Soviet Union ◽

The World ◽

And Behavior ◽

Second World

In many political researches there if a conclusion that the world system which was founded after the Second world war is destroyed of chaos. But the world system couldn`t work while the two opposite systems — socialist and capitalist were in hard confrontation. After collapse of the Soviet Union and the European socialist community the nature of intergovernmental relations and behavior of the international community did not change. The power always was and still is the main tool of international communication.

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On mappings with finite length distortion on Riemann surfaces

Proceedings of the Institute of Applied Mathematics and Mechanics NAS of Ukraine ◽

10.37069/1683-4720-2019-33-4 ◽

2019 ◽

Vol 33 ◽

Cited By ~ 1

Author(s):

Serhii Volkov ◽

Vladimir Ryazanov

Keyword(s):

Finite Length ◽

Riemann Surfaces ◽

Boundary Behavior ◽

Main Tool ◽

Natural Generalization ◽

Finite Distortion ◽

Lipschitz Mappings ◽

Geometric Function ◽

Mappings With Finite Distortion ◽

Length Distortion

The present paper is a natural continuation of our previous paper (2017) on the boundary behavior of mappings in the Sobolev classes on Riemann surfaces, where the reader will be able to find the corresponding historic comments and a discussion of many definitions and relevant results. The given paper was devoted to the theory of the boundary behavior of mappings with finite distortion by Iwaniec on Riemannian surfaces first introduced for the plane in the paper of Iwaniec T. and Sverak V. (1993) On mappings with integrable dilatation and then extended to the spatial case in the monograph of Iwaniec T. and Martin G. (2001) devoted to Geometric function theory and non-linear analysis. At the present paper, it is developed the theory of the boundary behavior of the so--called mappings with finite length distortion first introduced in the paper of Martio O., Ryazanov V., Srebro U. and Yakubov~E. (2004) in the spatial case, see also Chapter 8 in their monograph (2009) on Moduli in modern mapping theory. As it was shown in the paper of Kovtonyuk D., Petkov I. and Ryazanov V. (2017) On the boundary behavior of mappings with finite distortion in the plane, such mappings, generally speaking, are not mappings with finite distortion by Iwaniec because their first partial derivatives can be not locally integrable. At the same time, this class is a generalization of the known class of mappings with bounded distortion by Martio--Vaisala from their paper (1988). Moreover, this class contains as a subclass the so-called finitely bi-Lipschitz mappings introduced for the spatial case in the paper of Kovtonyuk D. and Ryazanov V. (2011) On the boundary behavior of generalized quasi-isometries, that in turn are a natural generalization of the well-known classes of bi-Lipschitz mappings as well as isometries and quasi-isometries. In the research of the local and boundary behavior of mappings with finite length distortion in the spatial case, the key fact was that they satisfy some modulus inequalities which was a motivation for the consideration more wide classes of mappings, in particular, the Q-homeomorphisms (2005) and the mappings with finite area distortion (2008). Hence it is natural that under the research of mappings with finite length distortion on Riemann surfaces we start from establishing the corresponding modulus inequalities that are the main tool for us. On this basis, we prove here a series of criteria in terms of dilatations for the continuous and homeomorphic extension to the boundary of the mappings with finite length distortion between domains on arbitrary Riemann surfaces.

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Positive Solutions for a Class of Nonlinear Singular Fractional Differential Systems with Riemann–Stieltjes Coupled Integral Boundary Value Conditions

Symmetry ◽

10.3390/sym13010107 ◽

2021 ◽

Vol 13 (1) ◽

pp. 107

Author(s):

Daliang Zhao ◽

Juan Mao

Keyword(s):

Positive Solutions ◽

Boundary Value ◽

Sufficient Conditions ◽

Main Tool ◽

Integral Boundary ◽

Differential Systems ◽

Fractional Differential Systems ◽

Existence And Multiplicity ◽

Fractional Differential ◽

Multiplicity Of Positive Solutions

In this paper, sufficient conditions ensuring existence and multiplicity of positive solutions for a class of nonlinear singular fractional differential systems are derived with Riemann–Stieltjes coupled integral boundary value conditions in Banach Spaces. Nonlinear functions f(t,u,v) and g(t,u,v) in the considered systems are allowed to be singular at every variable. The boundary conditions here are coupled forms with Riemann–Stieltjes integrals. In order to overcome the difficulties arising from the singularity, a suitable cone is constructed through the properties of Green’s functions associated with the systems. The main tool used in the present paper is the fixed point theorem on cone. Lastly, an example is offered to show the effectiveness of our obtained new results.

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Blowing-up solutions of the time-fractional dispersive equations

Advances in Nonlinear Analysis ◽

10.1515/anona-2020-0153 ◽

2021 ◽

Vol 10 (1) ◽

pp. 952-971

Author(s):

Ahmed Alsaedi ◽

Bashir Ahmad ◽

Mokhtar Kirane ◽

Berikbol T. Torebek

Keyword(s):

Boundary Value Problems ◽

Boundary Value ◽

Sufficient Conditions ◽

Main Tool ◽

Initial Boundary ◽

Initial Boundary Value Problems ◽

Nonlinear Capacity ◽

Blowing Up ◽

De Vries ◽

Initial Boundary Value

Abstract This paper is devoted to the study of initial-boundary value problems for time-fractional analogues of Korteweg-de Vries, Benjamin-Bona-Mahony, Burgers, Rosenau, Camassa-Holm, Degasperis-Procesi, Ostrovsky and time-fractional modified Korteweg-de Vries-Burgers equations on a bounded domain. Sufficient conditions for the blowing-up of solutions in finite time of aforementioned equations are presented. We also discuss the maximum principle and influence of gradient non-linearity on the global solvability of initial-boundary value problems for the time-fractional Burgers equation. The main tool of our study is the Pohozhaev nonlinear capacity method. We also provide some illustrative examples.

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Inverse problems for stochastic parabolic equations with additive noise

Journal of Inverse and Ill-Posed Problems ◽

10.1515/jiip-2017-0003 ◽

2020 ◽

Vol 29 (1) ◽

pp. 93-108

Author(s):

Ganghua Yuan

Keyword(s):

Inverse Problems ◽

Parabolic Equations ◽

Additive Noise ◽

Stability Result ◽

Main Tool ◽

Conditional Stability ◽

Final Time ◽

History Of ◽

Global Carleman Estimate ◽

Stochastic Parabolic Equation

Abstract In this paper, we study two inverse problems for stochastic parabolic equations with additive noise. One is to determinate the history of a stochastic heat process and the random heat source simultaneously by the observation at the final time 𝑇. For this inverse problem, we obtain a conditional stability result. The other one is an inverse source problem to determine two kinds of sources simultaneously by the observation at the final time and on the lateral boundary. The main tool for solving the inverse problems is a new global Carleman estimate for the stochastic parabolic equation.

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Ranking Environmental Aspects of Sustainable Tourism: Case of Selected European Countries

Sustainability ◽

10.3390/su13105701 ◽

2021 ◽

Vol 13 (10) ◽

pp. 5701

Author(s):

Tihana Škrinjarić

Keyword(s):

Decision Making ◽

Sustainable Tourism ◽

Multiple Criteria Decision Making ◽

Main Tool ◽

Tourism Industry ◽

European Countries ◽

Environmental Aspects ◽

Grey Systems Theory ◽

Insightful Analysis ◽

Critical Overview

The tourism industry is one of the fastest-growing industries today, and it is important to obtain insights into its good and bad practices. This will provide policymakers with as much information as possible to tailor specific policies to facilitate tourism and economic growth. The main purpose of this paper is a critical overview of the related research on the topic of evaluating sustainable tourism in European countries and extensive empirical research on achieving sustainable tourism. This research includes Grey Systems Theory (GST) as the main tool in evaluating the efficiency of sustainable tourism. Robustness checking is done via the multiple criteria decision making (MCDM) approach. Although the literature on tourism efficiency is vast, there is a smaller amount of research related to the approach taken in this paper. Thus, a comprehensive and insightful analysis will be done so that relevant and timely information can be obtained for the future decision-making process. Furthermore, a dynamic analysis will be provided so that changes in time can be observed and a detailed analysis can be made.

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