scholarly journals Positive Solutions of Transport Equations and Classical Nonuniqueness of Characteristic curves

2021 ◽  
Vol 240 (2) ◽  
pp. 1055-1090 ◽  
Author(s):  
Elia Brué ◽  
Maria Colombo ◽  
Camillo De Lellis
Keyword(s):  
Positive Solutions ◽  
Continuity Equation ◽  
Vector Fields ◽  
Superposition Principle ◽  
Negative Answer ◽  
New Class ◽  
Open Question ◽  
Invent Math ◽  
Lagrangian Flow ◽  
Selection Of

AbstractThe seminal work of DiPerna and Lions (Invent Math 98(3):511–547, 1989) guarantees the existence and uniqueness of regular Lagrangian flows for Sobolev vector fields. The latter is a suitable selection of trajectories of the related ODE satisfying additional compressibility/semigroup properties. A long-standing open question is whether the uniqueness of the regular Lagrangian flow is a corollary of the uniqueness of the trajectory of the ODE for a.e. initial datum. Using Ambrosio’s superposition principle, we relate the latter to the uniqueness of positive solutions of the continuity equation and we then provide a negative answer using tools introduced by Modena and Székelyhidi in the recent groundbreaking work (Modena and Székelyhidi in Ann PDE 4(2):38, 2018). On the opposite side, we introduce a new class of asymmetric Lusin–Lipschitz inequalities and use them to prove the uniqueness of positive solutions of the continuity equation in an integrability range which goes beyond the DiPerna–Lions theory.

Twisted Sasakian Metric on the Tangent Bundle and Harmonicity

2021 ◽  
Vol 62 ◽  
pp. 53-66
Author(s):  
Fethi Latti ◽  
◽  
Hichem Elhendi ◽  
Lakehal Belarbi
Keyword(s):  
Riemannian Manifold ◽  
Vector Field ◽  
Tangent Bundle ◽  
Vector Fields ◽  
Sufficient Conditions ◽  
Harmonic Vector ◽  
New Class ◽  
Necessary And Sufficient ◽  
Sasakian Metric ◽  
Harmonic Vector Fields

In the present paper, we introduce a new class of natural metrics on the tangent bundle $TM$ of the Riemannian manifold $(M,g)$ denoted by $G^{f,h}$ which is named a twisted Sasakian metric. A necessary and sufficient conditions under which a vector field is harmonic with respect to the twisted Sasakian metric are established. Some examples of harmonic vector fields are presented as well.

Stable Index Pairs for Discrete Dynamical Systems

1997 ◽  
Vol 40 (4) ◽  
pp. 448-455 ◽  
Author(s):  
Tomasz Kaczynski ◽  
Marian Mrozek
Keyword(s):  
Dynamical Systems ◽  
Vector Fields ◽  
Discrete Dynamical Systems ◽  
Discrete Case ◽  
Smooth Vector ◽  
Small Perturbations ◽  
Index Pairs ◽  
Open Question ◽  
Stable Index

AbstractA new shorter proof of the existence of index pairs for discrete dynamical systems is given. Moreover, the index pairs defined in that proof are stable with respect to small perturbations of the generating map. The existence of stable index pairs was previously known in the case of diffeomorphisms and flows generated by smooth vector fields but it was an open question in the general discrete case.

scholarly journals Positive solutions for nonlinear elastic beam models

2001 ◽  
Vol 27 (6) ◽  
pp. 365-375 ◽  
Author(s):  
Bendong Lou
Keyword(s):  
Positive Solutions ◽  
Elastic Beam ◽  
Negative Answer ◽  
Existence Of Positive Solutions ◽  
Nonlinear Elastic ◽  
Positive Results

We give a negative answer to a conjecture of Korman on nonlinear elastic beam models. Moreover, by modifying the main conditions in the conjecture (generalizing the original ones at some points), we get positive results, that is, we obtain the existence of positive solutions for the models.

scholarly journals IDEAL PROJECTIONS AND FORCING PROJECTIONS

2014 ◽  
Vol 79 (4) ◽  
pp. 1247-1285 ◽  
Author(s):  
SEAN COX ◽  
MARTIN ZEMAN
Keyword(s):  
Set Theory ◽  
Negative Answer ◽  
Large Cardinals ◽  
Normal Ideal ◽  
List Type ◽  
Type Number ◽  
Inner Model ◽  
Image Position ◽  
Open Question ◽  
Woodin Cardinal

AbstractIt is well known that saturation of ideals is closely related to the “antichain-catching” phenomenon from Foreman–Magidor–Shelah [10]. We consider several antichain-catching properties that are weaker than saturation, and prove:(1)If${\cal I}$is a normal ideal on$\omega _2 $which satisfiesstationary antichain catching, then there is an inner model with a Woodin cardinal;(2)For any$n \in \omega $, it is consistent relative to large cardinals that there is a normal ideal${\cal I}$on$\omega _n $which satisfiesprojective antichain catching, yet${\cal I}$is not saturated (or even strong). This provides a negative answer to Open Question number 13 from Foreman’s chapter in the Handbook of Set Theory ([7]).

Effects of competitor spacing in a new class of individual-tree indices of competition: semi-distance-independent indices computed for Bitterlich versus fixed-area plots

2008 ◽  
Vol 38 (4) ◽  
pp. 890-898 ◽  
Author(s):  
Albert R. Stage ◽  
Thomas Ledermann
Keyword(s):  
Basal Area ◽  
Area Ratio ◽  
Individual Tree ◽  
Competitive Effects ◽  
New Class ◽  
Distance Effects ◽  
Fixed Area ◽  
Tree Increment ◽  
Competition Indices ◽  
Selection Of

We illustrate effects of competitor spacing for a new class of individual-tree indices of competition that we call semi-distance-independent. This new class is similar to the class of distance-independent indices except that the index is computed independently at each subsampling plot surrounding a subject tree for which growth is to be modelled. We derive the effects of distance for this class as the expected value over independent samples containing a particular subject tree. In a previous paper, we illustrated distance effects implicit in eight indices of the distance-dependent class. Here, we present distance effects of four semi-distance-independent indices: density, sum of diameters, basal area, and tree-area ratio; each determined for small fixed-area plots of 0.04 ha and for Bitterlich samples of 6 m2·ha–1. We show that several members of this new class have distance effects very similar to the distance-dependent class and should, therefore, be equally effective in accounting for competitive effects in individual-tree increment models. The comparisons should inform selection of competition indices and sampling designs for growth modelling.

scholarly journals Seleção de tecnologias digitais para a gerência de projetos em disciplinas de projeto integrado

2018 ◽  
Vol 7 (1) ◽  
Author(s):  
Danilo Almeida Felipe ◽  
Tânia Saraiva de Melo Pinheiro
Keyword(s):  
Project Management ◽  
Digital Technologies ◽  
Digital Tools ◽  
Agile Methods ◽  
Pedagogical Practice ◽  
New Class ◽  
Class Time ◽  
De Se ◽  
Integrated Project ◽  
Selection Of

Resumo: A disciplina de Projeto Integrado estudada é um componente curricular de caráter interdisciplinar que visa relacionar as unidades do currículo entre si em e com a realidade profissional. Além da interlocução com outras disciplinas – seus conteúdos e docentes – tem-se equipes de alunos resolvendo problemas sociais reais, desenvolvendo projetos enquanto aprendem os conteúdos necessários para desenvolvê-los. Dificuldades em sua complexa condução levaram à constatação da importância de se utilizar métodos de gerenciamento de projetos, e posteriormente de se dispor de tecnologias digitais que as apoiassem. Este estudo teve o objetivo geral de selecionar tecnologias digitais online para apoiar a gerência dos projetos integrados. A metodologia adotada consistiu, inicialmente, da observação da prática pedagógica para identificar os requisitos necessários a serem atendidos pelas tecnologias, seguida da análise comparativa de ferramentas digitais gratuitas disponíveis, finalizando com sua configuração para uma nova turma de Projeto Integrado. A partir de princípios pedagógicos estabelecidos foram selecionadas duas ferramentas, sendo uma para gerência de projetos e, de forma complementar, outra para organização dos arquivos digitais manuseados. A análise dos resultados ainda é preliminar, porque o semestre letivo ainda está em andamento, mas já apontam para uma maior capacidade de acompanhamento do trabalho, por alunos e docentes envolvidos. Entretanto, já se observa a necessidade de se alocar mais tempo de aula para orientações tanto em gerência de projetos quando na ferramenta selecionada para este fim.Palavras-chave: Projeto Integrado. Gerência de Projetos. Métodos Ágeis.  SELECTION OF DIGITAL TECHNOLOGIES FOR PROJECT MANAGEMENT IN DISCIPLINES OF INTEGRATED PROJECT Abstract: The Integrated Project discipline is an interdisciplinary curricular component that aims to relate curriculum units, themselves and with professional reality. In addition to the connection with other disciplines - their contents and professors - it has teams of students solving real social problems, developing projects while they learn the necessary contents. Such complexity led to the importance of using project management methods, and to have digital technologies to support them. This study aimed to select online digital technologies to support the management of Integrated Projects. The methodology consisted initially of observing the pedagogical practice to identify the technologies requirements to be met, followed by the comparative analysis of available free digital tools, and finalizing with its configuration for a new class of Integrated Project. Based on established pedagogical principles, two tools were selected, one for project management and another for the organization of digital files handled. The analysis of the results is still preliminary because the semester is still in progress, but they point out to a better condition to monitor the work, by students and teachers involved. However, we have already observed the need to allocate more class time to orientations both in project management and in the tool selected for this purpose.Keywords: Integrated Project. Project Management. Agile Methods.

scholarly journals Non-renormalized solutions to the continuity equation

2019 ◽  
Vol 58 (6) ◽  
Author(s):  
Stefano Modena ◽  
László Székelyhidi
Keyword(s):  
Continuity Equation ◽  
Vector Fields ◽  
Renormalized Solutions ◽  
Uniqueness Of Solutions

Abstract We show that there are continuous, $$W^{1,p}$$W1,p ($$p<d-1$$p<d-1), incompressible vector fields for which uniqueness of solutions to the continuity equation fails.

A Comprehensive Comparison Between Different Multiaxial Cycle Counting Procedure

2021 ◽  
Author(s):  
Andrea Rovinelli ◽  
Mark C. Messner ◽  
T.-L. Sham
Keyword(s):  
High Temperature ◽  
Strain Range ◽  
Loading Conditions ◽  
Loading History ◽  
Counting Procedure ◽  
Dwell Fatigue ◽  
Comprehensive Comparison ◽  
High Temperature Components ◽  
Open Question ◽  
Selection Of

Abstract High-temperature nuclear design codes, such as Section III, Division 5 of the American ASME Boiler and Pressure Vessel Code and the French RCC-MRx, require evaluating fatigue damage for qualifying high-temperature components. Both codes provide clear guidance for counting cycles under uniaxial loading conditions, but neither provides a cycle counting procedure for multiaxial loading conditions. The ASTM E1049 also does not address multiaxial cycle counting. However, several widely utilized multiaxial cycle counting procedures are available in the open literature, but there is no agreement on the most appropriate method for high-temperature applications. Applying the different cycle counting methods to the same loading history generally produces different results. Comparisons between cycle counting procedures are available for low-temperature high-cycle fatigue but not for high-temperature low-cycle dwell-fatigue applications. This work presents an extensive comparison between different multiaxial cycle counting procedures potentially suitable for high-temperature low-cycle dwell-fatigue applications. Furthermore, how to conservatively assemble design transients to construct a loading history is also an open question. This work also investigates the uncertainty related to the loading sequence. The results guide the selection of the most appropriate cycle counting procedure, strain range metric, and cycle distribution for ASME Section III, Division 5 applications.

Evaluation of Commercial and Next Generation Alumina-Forming Austenitic Foil for Advanced Recuperators

2013 ◽  
Author(s):  
Bruce A. Pint ◽  
Sebastien Dryepondt ◽  
Michael P. Brady ◽  
Yukinori Yamamoto
Keyword(s):  
Creep Resistance ◽  
Annealing Temperature ◽  
Austenitic Steels ◽  
Initial Material ◽  
Next Generation ◽  
Final Annealing ◽  
New Class ◽  
Higher Temperature ◽  
Commercial Applications ◽  
Selection Of

Alumina-forming austenitic (AFA) steels represent a new class of corrosion- and creep-resistance austenitic steels to enable higher temperature recuperators. Several commercial batches of the first AFA composition have been produced with different thicknesses and widths over 39cm. This commercial AFA foil was successfully folded by two manufacturers. Creep and laboratory oxidation results at 650°-800°C are presented to compare to conventional recuperator alloy performance. While this initial effort was successful, concerns with cost and ease of production suggested that a leaner AFA composition with a lower final annealing temperature would be more attractive for commercial applications. Therefore, several new AFA compositions are being evaluated in laboratory trials and compared to the initial material for down selection of a better AFA composition for commercialization.

scholarly journals Fuzzy Triangular Aggregation Operators

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Ulrich Florian Simo ◽  
Henri Gwét
Keyword(s):  
Fuzzy Numbers ◽  
Aggregation Operators ◽  
Triangular Norms ◽  
New Class ◽  
Weighted Arithmetic ◽  
Wide Range ◽  
Fuzzy Aggregation ◽  
Available Information ◽  
Selection Of ◽  
Do So

We present a new class of fuzzy aggregation operators that we call fuzzy triangular aggregation operators. To do so, we focus on the situation where the available information cannot be assessed with exact numbers and it is necessary to use another approach to assess uncertain or imprecise information such as fuzzy numbers. We also use the concept of triangular norms (t-norms and t-conorms) as pseudo-arithmetic operations. As a result, we get notably the fuzzy triangular weighted arithmetic (FTWA), the fuzzy triangular ordered weighted arithmetic (FTOWA), the fuzzy generalized triangular weighted arithmetic (FGTWA), the fuzzy generalized triangular ordered weighted arithmetic (FGTOWA), the fuzzy triangular weighted quasi-arithmetic (Quasi-FTWA), and the fuzzy triangular ordered weighted quasi-arithmetic (Quasi-FTOWA) operators. Main properties of these operators are discussed as well as their comparison with other existing ones. The fuzzy triangular aggregation operators not only cover a wide range of useful existing fuzzy aggregation operators but also provide new interesting cases. Finally, an illustrative example is also developed regarding the selection of strategies.

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