scholarly journals Cálculo variacional e aplicações

2020 ◽  
Vol 42 ◽  
pp. 50
Author(s):  
Jardel Carpes Meurer ◽  
Lucas Tavares Cardoso ◽  
Glauber Rodrigues de Quadros
Keyword(s):  
Sufficient Conditions ◽  
Variational Calculus ◽  
Necessary And Sufficient Conditions ◽  
Stationary Points ◽  
Second Variation ◽  
Rigorous Treatment ◽  
Necessary And Sufficient ◽  
First And Second Variation ◽  
Lagrange Mechanics

This paper consists of a brief review and introduction to the main concepts of Classic Variational Calculus. Starting from thedefinitions of the concepts of first and second variation of a functional, we present a mathematically rigorous treatment for theVariational Calculus, establishing necessary and sufficient conditions for obtaining extrema. In this context, the notion of conjugatepoints is introduced, which is fundamental for the classification of weak extrema. Some simple and enlightening examples are dealtwith throughout the paper. Strong extrema are characterized and sufficient conditions for their occurrence are given. The paperconcludes with a brief application to Lagrange mechanics, showing the existence of actions whose stationary points are saddlepoints instead of minima.

The λ-classification of continuous-time birth-and-death processes

2003 ◽  
Vol 35 (04) ◽  
pp. 1111-1130 ◽  
Author(s):  
Andrew G. Hart ◽  
Servet Martínez ◽  
Jaime San Martín
Keyword(s):  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Birth And Death Processes ◽  
Positive Recurrent ◽  
Necessary And Sufficient

We study the λ-classification of absorbing birth-and-death processes, giving necessary and sufficient conditions for such processes to be λ-transient, λ-null recurrent and λ-positive recurrent.

Asymptotic stability of heteroclinic cycles in systems with symmetry. II

2004 ◽  
Vol 134 (6) ◽  
pp. 1177-1197 ◽  
Author(s):  
Martin Krupa ◽  
Ian Melbourne
Keyword(s):  
Asymptotic Stability ◽  
Transition Matrix ◽  
Sufficient Conditions ◽  
Systematic Investigation ◽  
Necessary And Sufficient Conditions ◽  
Sufficient Condition ◽  
Heteroclinic Cycles ◽  
Higher Dimensional ◽  
Necessary And Sufficient

Systems possessing symmetries often admit robust heteroclinic cycles that persist under perturbations that respect the symmetry. In previous work, we began a systematic investigation into the asymptotic stability of such cycles. In particular, we found a sufficient condition for asymptotic stability, and we gave algebraic criteria for deciding when this condition is also necessary. These criteria are satisfied for cycles in R3.Field and Swift, and Hofbauer, considered examples in R4 for which our sufficient condition for stability is not optimal. They obtained necessary and sufficient conditions for asymptotic stability using a transition-matrix technique.In this paper, we combine our previous methods with the transition-matrix technique and obtain necessary and sufficient conditions for asymptotic stability for a larger class of heteroclinic cycles. In particular, we obtain a complete theory for ‘simple’ heteroclinic cycles in R4 (thereby proving and extending results for homoclinic cycles that were stated without proof by Chossat, Krupa, Melbourne and Scheel). A partial classification of simple heteroclinic cycles in R4 is also given. Finally, our stability results generalize naturally to higher dimensions and many of the higher-dimensional examples in the literature are covered by this theory.

scholarly journals The Q0-matrix completion problem

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Kalyan Sinha
Keyword(s):  
Matrix Completion ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Completion Problem ◽  
Matrix Completion Problem ◽  
Necessary And Sufficient ◽  
The Relationship

A matrix is a Q0-matrix if for every k∈{1,2,…,n}, the sum of all k×k principal minors is nonnegative. In this paper, we study some necessary and sufficient conditions for a digraph to have Q0-completion. Later on we discuss the relationship between Q and Q0-matrix completion problem. Finally, a classification of the digraphs of order up to four is done based on Q0-completion.

scholarly journals Asynchronous Computability Theorem in Arbitrary Solo Models

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 757
Author(s):  
Yunguang Yue ◽  
Fengchun Lei ◽  
Xingwu Liu ◽  
Jie Wu
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Computational Power ◽  
Nest Structure ◽  
Combinatorial Topology ◽  
Necessary And Sufficient ◽  
As If

In this paper, we establish the asynchronous computability theorem in d-solo system by borrowing concepts from combinatorial topology, in which we state a necessary and sufficient conditions for a task to be wait-free computable in that system. Intuitively, a d-solo system allows as many d processes to access it as if each were running solo, namely, without detecting communication from any peer. As an application, we completely characterize the solvability of the input-less tasks in such systems. This characterization also leads to a hardness classification of these tasks according to whether their output complexes hold a d-nest structure. As a byproduct, we find an alternative way to distinguish the computational power of d-solo objects for different d.

A classification of vertex-transitive Cayley digraphs of strong semilattices of completely simple semigroups

2012 ◽  
Vol 62 (5) ◽  
Author(s):  
Shou-feng Wang ◽  
Di Zhang
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Completely Simple Semigroups ◽  
Vertex Transitive ◽  
Necessary And Sufficient ◽  
Completely Simple

AbstractWith the help of a property of completely simple semigroups proved in this paper we give necessary and sufficient conditions for vertex-transitivity of Cayley digraphs of strong semilattices of completely simple semigroups.

Geometric constrained variational calculus. II: The second variation (Part I)

2016 ◽  
Vol 13 (01) ◽  
pp. 1550132 ◽  
Author(s):  
Enrico Massa ◽  
Danilo Bruno ◽  
Gianvittorio Luria ◽  
Enrico Pagani
Keyword(s):  
Gauge Transformation ◽  
Sufficient Conditions ◽  
Variational Calculus ◽  
Second Variation ◽  
Action Functional ◽  
Covariant Representation ◽  
Jacobi Fields ◽  
Necessary And Sufficient ◽  
The Second Variation ◽  
Variation Part

Within the geometrical framework developed in [Geometric constrained variational calculus. I: Piecewise smooth extremals, Int. J. Geom. Methods Mod. Phys. 12 (2015) 1550061], the problem of minimality for constrained calculus of variations is analyzed among the class of differentiable curves. A fully covariant representation of the second variation of the action functional, based on a suitable gauge transformation of the Lagrangian, is explicitly worked out. Both necessary and sufficient conditions for minimality are proved, and reinterpreted in terms of Jacobi fields.

scholarly journals On the Classification of Bol-Moufang Type of Some Varieties of Quasi Neutrosophic Triplet Loop (Fenyves BCI-Algebras)

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 427 ◽  
Author(s):  
Tèmítọ́pẹ́ Jaíyéọlá ◽  
Emmanuel Ilojide ◽  
Memudu Olatinwo ◽  
Florentin Smarandache
Keyword(s):  
Research Finding ◽  
Research Work ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Algebraic Structures ◽  
Associative Algebras ◽  
Necessary And Sufficient

In this paper, Bol-Moufang types of a particular quasi neutrosophic triplet loop (BCI-algebra), chritened Fenyves BCI-algebras are introduced and studied. 60 Fenyves BCI-algebras are introduced and classified. Amongst these 60 classes of algebras, 46 are found to be associative and 14 are found to be non-associative. The 46 associative algebras are shown to be Boolean groups. Moreover, necessary and sufficient conditions for 13 non-associative algebras to be associative are also obtained: p-semisimplicity is found to be necessary and sufficient for a F 3 , F 5 , F 42 and F 55 algebras to be associative while quasi-associativity is found to be necessary and sufficient for F 19 , F 52 , F 56 and F 59 algebras to be associative. Two pairs of the 14 non-associative algebras are found to be equivalent to associativity ( F 52 and F 55 , and F 55 and F 59 ). Every BCI-algebra is naturally an F 54 BCI-algebra. The work is concluded with recommendations based on comparison between the behaviour of identities of Bol-Moufang (Fenyves’ identities) in quasigroups and loops and their behaviour in BCI-algebra. It is concluded that results of this work are an initiation into the study of the classification of finite Fenyves’ quasi neutrosophic triplet loops (FQNTLs) just like various types of finite loops have been classified. This research work has opened a new area of research finding in BCI-algebras, vis-a-vis the emergence of 540 varieties of Bol-Moufang type quasi neutrosophic triplet loops. A ‘Cycle of Algebraic Structures’ which portrays this fact is provided.

scholarly journals Common stationary points of multivalued mappings on bounded metric spaces

2000 ◽  
Vol 24 (11) ◽  
pp. 773-779 ◽  
Author(s):  
Zeqing Liu ◽  
Shin Min Kang
Keyword(s):  
Stationary Point ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Stationary Points ◽  
Multivalued Mappings ◽  
Necessary And Sufficient

Necessary and sufficient conditions for the existence of common stationary points of two multivalued mappings and common stationary point theorems for multivalued mappings on bounded metric spaces are given. Our results extend the theorems due to Fisher in 1979, 1980, and 1983 and Ohta and Nikaido in 1994.

Complete Moment Balancing of Contra Planar 5R Linkages

2012 ◽  
Author(s):  
Brian Moore ◽  
Clément Gosselin
Keyword(s):  
Special Class ◽  
Sufficient Conditions ◽  
Complete Classification ◽  
Necessary And Sufficient Conditions ◽  
Design Parameters ◽  
Balancing Conditions ◽  
Necessary And Sufficient

In this paper, the complete shaking force and moment balancing conditions for a special class of planar 5R linkages, the contra 5R linkage, is considered. Contra 5R linkages are planar 5R linkages in which the two input links are mechanically coupled and rotate at the same speed in opposite directions. A method to derive necessary and sufficient conditions on the design parameters to achieve moment balancing without introducing additional components is presented. Using this method, a complete classification of all shaking force and moment balanced contra 5R linkages is given.

scholarly journals A classification of explosions in dimension one

2009 ◽  
Vol 29 (2) ◽  
pp. 715-731 ◽  
Author(s):  
E. SANDER ◽  
J. A. YORKE
Keyword(s):  
Sufficient Conditions ◽  
Global Bifurcation ◽  
Necessary And Sufficient Conditions ◽  
Homoclinic Tangency ◽  
Discontinuous Change ◽  
One Dimensional ◽  
One Dimensional Maps ◽  
Dimension One ◽  
Necessary And Sufficient

AbstractA discontinuous change in the size of an attractor is the most easily observed type of global bifurcation. More generally, anexplosionis a discontinuous change in the set of recurrent points. An explosion often results from heteroclinic and homoclinic tangency bifurcations. We prove that, for one-dimensional maps, explosions are generically the result of either tangency or saddle-node bifurcations. Furthermore, we give necessary and sufficient conditions for generic tangency bifurcations to lead to explosions.

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