scholarly journals Review of the Dynamical Aspects of Triple Systems

1977 ◽  
Vol 33 ◽  
pp. 145-150
Author(s):  
V. Szebehely
Keyword(s):  
Fundamental Problem ◽  
Stellar Dynamics ◽  
Close Approach ◽  
Type Systems ◽  
Computational Results ◽  
Transient Phenomena ◽  
Triple Systems ◽  
Families Of Periodic Orbits ◽  
Negative Total Energy

AbstractA classification of possible motions of triple systems is presented emphasizing the transient phenomena occurring in addition to the final (asymptotic) outcome and clarifying the discrepancies between the astronomical and mathematical formulations. A conjectured possible instability is described and it is shown that systems with negative total energy and low angular momentum may lead to instability and to the formation of binaries. The ejected or escaping star may have high velocity if the triple close approach preceding the escape is sufficiently close. The computational results of several systematic series of such escapes are applied to various stellar configurations.The present status of the fundamental problem of partitioning the phase-space into stable and unstable regions is reviewed and a recently developed technique, applicable to stellar dynamics is described. Recently discovered families of periodic orbits and previously established classical configurations are shown to weaken the general instability conjecture.The possible existence of triple systems in states of dissolution offer intriguing observational challenges regarding the discovery of these projected temporary trapezium type systems.

scholarly journals On a solvable class of product-type systems of difference equations

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6113-6129 ◽  
Author(s):  
Stevo Stevic ◽  
Bratislav Iricanin ◽  
Zdenk Smarda
Keyword(s):  
Closed Form ◽  
Difference Equations ◽  
Type Systems ◽  
Product Type ◽  
Dependent Variables ◽  
Solvable Class ◽  
Solvable Product

It is shown that the following class of systems of difference equations zn+1 = ?zanwbn, wn+1 = ?wcnzdn-2, n ? N0, where a,b,c,d ? Z, ?, ?, z-2, z-1, z0,w0 ? C \ {0}, is solvable, continuing our investigation of classification of solvable product-type systems with two dependent variables. We present closed form formulas for solutions to the systems in all the cases. In the main case, when bd ? 0, a detailed investigation of the form of the solutions is presented in terms of the zeros of an associated polynomial whose coefficients depend on some of the parameters of the system.

scholarly journals Classification of Variable Foundation Properties Based on Vehicle–Pavement–Foundation Interaction Dynamics

Sensors ◽  
2020 ◽  
Vol 20 (21) ◽  
pp. 6263
Author(s):  
Robin Eunju Kim
Keyword(s):  
Fundamental Problem ◽  
Interaction Model ◽  
Nonlinear Behavior ◽  
Complex Problem ◽  
Noise Model ◽  
Space Representation ◽  
Linear Discriminant ◽  
The Road ◽  
Pavement Foundation

The dynamic interaction between vehicle, roughness, and foundation is a fundamental problem in road management and also a complex problem, with their coupled and nonlinear behavior. Thus, in this study, the vehicle–pavement–foundation interaction model was formulated to incorporate the mass inertia of the vehicle, stochastic roughness, and non-uniform and deformable foundation. Herein, a quarter-car model was considered, a filtered white noise model was formulated to represent the road roughness, and a two-layered foundation was employed to simulate the road structure. To represent the non-uniform foundation, stiffness and damping coefficients were assumed to vary either in a linear or in a quadratic manner. Subsequently, an augmented state-space representation was formulated for the entire system. The time-varying equation governing the covariance of the response was solved to examine the vehicle response, subject to various foundation properties. Finally, a linear discriminant analysis method was employed for classifying the foundation types. The performance of the classifier was validated by test sets, which contained 100 cases for each foundation type. The results showed an accuracy of over 90%, indicating that the machine learning-based classification of the foundation had the potential of using vehicle responses in road managements.

scholarly journals The Classification of M 1-78

1995 ◽  
Vol 12 (1) ◽  
pp. 31-36 ◽  
Author(s):  
G. T. Gussie
Keyword(s):  
Planetary Nebula ◽  
Main Sequence ◽  
Central Star ◽  
Expansion Velocity ◽  
Sequence Evolution ◽  
High Luminosity ◽  
Hii Region ◽  
Transient Phenomena ◽  
Ultracompact Hii

AbstractThe published properties of M1-78 are discussed with the purpose of resolving the object’s classification as either a planetary nebula or an ultracompact HII region. A classification as a planetary nebula is rejected primarily because of the high luminosity of the object, but because of the chemical composition and expansion velocity of the nebula, a novel classification is proposed instead: that of an ultracompact HII region with a post-main sequence central star (possibly a WN star). It must therefore follow that observable ultracompact HII regions persist beyond the main sequence lifetimes of at least some massive stars, and so cannot be transient phenomena that are seen only during pre-main sequence or early main sequence evolution.

scholarly journals Transient phenomena in ecology

Science ◽  
2018 ◽  
Vol 361 (6406) ◽  
pp. eaat6412 ◽  
Author(s):  
Alan Hastings ◽  
Karen C. Abbott ◽  
Kim Cuddington ◽  
Tessa Francis ◽  
Gabriel Gellner ◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Systems Theory ◽  
Ecological Systems ◽  
Dynamical Systems Theory ◽  
Model Systems ◽  
Transient Dynamics ◽  
Transient Phenomena ◽  
Ecological Theories

The importance of transient dynamics in ecological systems and in the models that describe them has become increasingly recognized. However, previous work has typically treated each instance of these dynamics separately. We review both empirical examples and model systems, and outline a classification of transient dynamics based on ideas and concepts from dynamical systems theory. This classification provides ways to understand the likelihood of transients for particular systems, and to guide investigations to determine the timing of sudden switches in dynamics and other characteristics of transients. Implications for both management and underlying ecological theories emerge.

On constructions of Lie (super) algebras and (𝜀,δ)-Freudenthal–Kantor triple systems defined by bilinear forms

2019 ◽  
Vol 19 (11) ◽  
pp. 2050223
Author(s):  
Noriaki Kamiya ◽  
Daniel Mondoc
Keyword(s):  
Lie Algebras ◽  
Complex Structure ◽  
Bilinear Forms ◽  
Simple Lie Algebras ◽  
Triple Systems ◽  
Dynkin Diagrams

In this work, we discuss a classification of [Formula: see text]-Freudenthal–Kantor triple systems defined by bilinear forms and give all examples of such triple systems. From these results, we may see a construction of some simple Lie algebras or superalgebras associated with their Freudenthal–Kantor triple systems. We also show that we can associate a complex structure into these ([Formula: see text]-Freudenthal–Kantor triple systems. Further, we introduce the concept of Dynkin diagrams associated to such [Formula: see text]-Freudenthal–Kantor triple systems and the corresponding Lie (super) algebra construction.

scholarly journals The Problem of Three Stars: Stability Limit

2007 ◽  
Vol 3 (S246) ◽  
pp. 209-217 ◽  
Author(s):  
M. Valtonen ◽  
A. Mylläri ◽  
V. Orlov ◽  
A. Rubinov
Keyword(s):  
Analytical Formula ◽  
Analytical Calculation ◽  
Stability Limit ◽  
Stellar Dynamics ◽  
Energy Change ◽  
Orbital Energy ◽  
Single Star ◽  
Triple Systems ◽  
Numerical Orbit ◽  
Three Body

AbstractThe problem of three stars arises in many connections in stellar dynamics: three-body scattering drives the evolution of star clusters, and bound triple systems form long-lasting intermediate structures in them. Here we address the question of stability of triple stars. For a given system the stability is easy to determine by numerical orbit calculation. However, we often have only statistical knowledge of some of the parameters of the system. Then one needs a more general analytical formula. Here we start with the analytical calculation of the single encounter between a binary and a single star by Heggie (1975). Using some of the later developments we get a useful expression for the energy change per encounter as a function of the pericenter distance, masses, and relative inclination of the orbit. Then we assume that the orbital energy evolves by random walk in energy space until the accumulated energy change leads to instability. In this way we arrive at a stability limit in pericenter distance of the outer orbit for different mass combinations, outer orbit eccentricities and inclinations. The result is compared with numerical orbit calculations.

scholarly journals VII. The monotreme skull: A contribution to mammalian morphogenesis

1916 ◽  
Vol 207 (335-347) ◽  
pp. 311-374 ◽  
Keyword(s):  
Close Approach ◽  
Text Book ◽  
Independent Investigation ◽  
Philosophical Methods ◽  
General Work

From the time, now nearly a century ago, when de Blainville, applying the philosophical methods he had developed for the classification of mammals to the knowledge of the structure of Echidna and Ornithorhynchus which had been obtained by Lamarck, Geoffroy St. Hilaire, and G. Cuvier, suggested that these two animals should perhaps form a group of the same order as the Marsupials and “Monodelphes,” many authors have studied their structure and discussed their affinities. Nearly all the great anatomists of the last century have at one time or another described the skull of a monotreme, either formally or in some text-book or other general work. Owing to the extreme difficulty of obtaining skulls which show sutures, their accounts vary to a very great extent. Finally, in 1901, Prof, van Bemmelen published a lengthy and magnificently illustrated account of the skulls of both monotremes which had every appearance of being a definitive description. Some years ago, when describing the skull of the “Cynodont” Diademodon, I endeavoured to institute a comparison between that animal, which in all ways makes an extremely close approach to mammalian structure, and the monotremes, admittedly the most reptilian of all mammals. To my very great surprise I found it impossible to compare the skull of Ornithorhynchus as interpreted by van Bemmelen with Diademodon. As at that time I had not sufficient material satisfactorily to undertake an independent investigation of the monotreme skull, I compared Diademodon with Dasyurus, a comparison which involves no difficulty.

scholarly journals A classification of intersection type systems

2002 ◽  
Vol 67 (1) ◽  
pp. 353-368
Author(s):  
M. W. Bunder
Keyword(s):  
Type Systems ◽  
Equivalence Classes ◽  
Type Assignment ◽  
Emptiness Problem ◽  
Intersection Types

AbstractThe first system of intersection types. Coppo and Dezani [3], extended simple types to include intersections and added intersection introduction and elimination rules ((ΛI ) and (ΛE) ) to the type assignment system. The major advantage of these new types was that they were invariant under β-equality, later work by Barendregt, Coppo and Dezani [1], extended this to include an (η) rule which gave types invariant under βη-reduction.Urzyczyn proved in [6] that for both these systems it is undecidable whether a given intersection type is empty. Kurata and Takahashi however have shown in [5] that this emptiness problem is decidable for the sytem including (η). but without (ΛI).The aim of this paper is to classify intersection type systems lacking some of (ΛI), (ΛE) and (η), into equivalence classes according to their strength in typing λ-terms and also according to their strength in possessing inhabitants.This classification is used in a later paper to extend the above (un)decidability results to two of the five inhabitation-equivalence classes. This later paper also shows that the systems in two more of these classes have decidable inhabitation problems and develops algorithms to find such inhabitants.

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