Active Prominences

1979 ◽  
Vol 44 ◽  
pp. 214-225 ◽  
Author(s):  
J. McKim Malville

Those prominences which are identified as active lie near the middle of a large group of objects found in the low corona bordered on the high energy side by flares and on the low energy side by quiescent prominences. Known by descriptive terms such as eruptive, surge, spray, tornado, and loop, active prominences typically have shorter lifetimes, broader line widths, larger internal motions, and stronger internal magnetic fields than quiescent prominences (Tandberg-Hanssen, 1974). When dealing with specific examples, however, it is often difficult to establish a necessary and sufficient condition for classification of such an object as an active prominence. The ambiguity at the low energy end involves “hybrid” objects which possess features of both quiescent and active prominences. For example, the active region filament may have a lifetime of several days, have large internal motions and relatively strong magnetic fields. The stable hedgerow quiescent prominence may contain small regions with large widths and large velocities. On the average, a quiescent will typically erupt every five to eight days, (Serio, et al., 1978; Bryson and Malville, 1978) and at those times a prominence is transformed from the quiescent to the active state. For these objects something other than morphology, velocity fields, or even magnetic fields is necessary to specify their condition; something less symptomatic and more fundamental is required. That necessary parameter may be, I shall suggest, the total current, J, flowing in the structure.

2019 ◽  
Vol 7 (1) ◽  
pp. 257-262
Author(s):  
Kenji Toyonaga

Abstract Given a combinatorially symmetric matrix A whose graph is a tree T and its eigenvalues, edges in T can be classified in four categories, based upon the change in geometric multiplicity of a particular eigenvalue, when the edge is removed. We investigate a necessary and sufficient condition for each classification of edges. We have similar results as the case for real symmetric matrices whose graph is a tree. We show that a g-2-Parter edge, a g-Parter edge and a g-downer edge are located separately from each other in a tree, and there is a g-neutral edge between them. Furthermore, we show that the distance between a g-downer edge and a g-2-Parter edge or a g-Parter edge is at least 2 in a tree. Lastly we give a combinatorially symmetric matrix whose graph contains all types of edges.


1996 ◽  
Vol 16 (1) ◽  
pp. 45-50 ◽  
Author(s):  
Fabio Fagnani

AbstractIn this paper we study expansive automorphisms of compact 0-dimensional abelian groups. Our main result is the complete algebraic and topological classification of the transitive expansive automorpisms for which the maximal order of the elements isp2for a primep. This yields a classification of the transitive expansive automorphisms with topological entropy logp2. Finally, we prove a necessary and sufficient condition for an expansive automorphism to be conjugated, topologically and algebraically, to a shift over a finite group.


1996 ◽  
Vol 143 ◽  
pp. 59-92
Author(s):  
Takayoshi Yamazaki ◽  
Atsuko Yamada Yoshikawa

We studied plane curves in Lie sphere geometry in [YY]. Especially we constructed Lie frames of curves in S2 and classified them by the Lie equivalence. In this paper we are concerned with surfaces in S3. We construct Lie frames and classify them. We moreover obtain the necessary and sufficient condition that two surfaces are Lie equivalent.


Robotica ◽  
2007 ◽  
Vol 25 (6) ◽  
pp. 677-689 ◽  
Author(s):  
Philippe Wenger

SUMMARYThis article synthezises the most important results on the kinematics of cuspidal manipulators i.e. nonredundant manipulators that can change posture without meeting a singularity. The characteristic surfaces, the uniqueness domains and the regions of feasible paths in the workspace are defined. Then, several sufficient geometric conditions for a manipulator to be noncuspidal are enumerated and a general necessary and sufficient condition for a manipulator to be cuspidal is provided. An explicit DH-parameter-based condition for an orthogonal manipulator to be cuspidal is derived. The full classification of 3R orthogonal manipulators is provided and all types of cuspidal and noncuspidal orthogonal manipulators are enumerated. Finally, some facts about cuspidal and noncuspidal 6R manipulators are reported.


2005 ◽  
Vol Vol. 7 ◽  
Author(s):  
Shigeki Akiyama ◽  
Nertila Gjini

International audience Let T=T(A,D) be a self-affine tile in \reals^n defined by an integral expanding matrix A and a digit set D. In connection with canonical number systems, we study connectedness of T when D corresponds to the set of consecutive integers \0,1,..., |det(A)|-1\. It is shown that in \reals^3 and \reals^4, for any integral expanding matrix A, T(A,D) is connected. We also study the connectedness of Pisot dual tilings which play an important role in the study of β -expansion, substitution and symbolic dynamical system. It is shown that each tile generated by a Pisot unit of degree 3 is arcwise connected. This is naturally expected since the digit set consists of consecutive integers as above. However surprisingly, we found families of disconnected Pisot dual tiles of degree 4. Also we give a simple necessary and sufficient condition for the connectedness of the Pisot dual tiles of degree 4. As a byproduct, a complete classification of the β -expansion of 1 for quartic Pisot units is given.


1987 ◽  
Vol 62 (3) ◽  
pp. 213-217 ◽  
Author(s):  
E. A. Belogorlov ◽  
G. I. Britvich ◽  
G. I. Krupnyi ◽  
V. N. Lebedev ◽  
V. S. Lukanin ◽  
...  

2002 ◽  
Vol 31 (5) ◽  
pp. 271-282
Author(s):  
N. E. Livingston

The concept of a tracially AF (TAF)C*-algebra was introduced recently to aid in the classification of nuclearC*-algebrasHere, we construct and study a broad class of inductive-limitC*-algebras. We give a numerical condition which, when satisfied, ensures that the corresponding algebra in our construction has the TAF property. We further give a necessary and sufficient condition under which certain of theseC*-algebras are TAF.


2021 ◽  
Vol 19 (1) ◽  
pp. 63-68
Author(s):  
Pengfei Guo ◽  
Zhangjia Han

Abstract In this paper, we call a finite group G G an N L M NLM -group ( N C M NCM -group, respectively) if every non-normal cyclic subgroup of prime order or order 4 (prime power order, respectively) in G G is contained in a non-normal maximal subgroup of G G . Using the property of N L M NLM -groups and N C M NCM -groups, we give a new necessary and sufficient condition for G G to be a solvable T T -group (normality is a transitive relation), some sufficient conditions for G G to be supersolvable, and the classification of those groups whose all proper subgroups are N L M NLM -groups.


2021 ◽  
Vol 157 (9) ◽  
pp. 2026-2045
Author(s):  
Haowu Wang

We prove a necessary and sufficient condition for the graded algebra of automorphic forms on a symmetric domain of type IV being free. From the necessary condition, we derive a classification result. Let $M$ be an even lattice of signature $(2,n)$ splitting two hyperbolic planes. Suppose $\Gamma$ is a subgroup of the integral orthogonal group of $M$ containing the discriminant kernel. It is proved that there are exactly 26 groups $\Gamma$ such that the space of modular forms for $\Gamma$ is a free algebra. Using the sufficient condition, we recover some well-known results.


1988 ◽  
Vol 31 (4) ◽  
pp. 439-447
Author(s):  
Ian F. Putnam

AbstractThe C*-algebras associated with irrational rotations of the circle were classified up to strong Morita equivalence by M. A. Rieffel. As a corollary, he gave a complete classification of the C*-algebras arising from irrational or Kronecker flows on the 2-torus up to *-isomorphism. Here, we extend the result to the socalled Denjoy homeomorphisms. Specifically, we give a necessary and sufficient condition for the strong Morita equivalence of two C*-algebras arising from homeomorphisms of the circle without periodic points. As a corollary, we show that two C*-algebras arising from flows on the 2-torus obtained from such homeomorphisms by the “flow under constant function” construction are *-isomorphic if and only if the flows themselves are topologically conjugate.


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