Coordinates of the representation space in the semisimple Lie group of rank one

In this paper we show that the space of irreducible representations from a finitely presented group into the group of isometries of a rank one symmetric space of non-compact type, embeds into ℝn for some n, where the coordinates are the translation lengths of isometries in the representation. The ingredients of the proof consist of the two facts that the representation is determined by its marked length spectrum and that the nested sequence of algebraic subvarieties is stabilised at a finite step by the Noetherian property of the polynomial ring. As a minor application, we use this fact to simplify McMullen's proof about the exponential algebraic convergence of Thurston's double limit to the geometrically infinite manifold in the space of discrete faithful representations of π1(S) in Iso+.

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Ergodic theory and rigidity on the symmetric space of non-compact type

Ergodic Theory and Dynamical Systems ◽

10.1017/s0143385701001080 ◽

2001 ◽

Vol 21 (1) ◽

pp. 93-114 ◽

Cited By ~ 6

Author(s):

INKANG KIM

Keyword(s):

Ergodic Theory ◽

Symmetric Spaces ◽

Isometry Group ◽

Length Spectrum ◽

Compact Type ◽

Negatively Curved ◽

Rank One ◽

Convex Cocompact ◽

Marked Length Spectrum ◽

Locally Symmetric Manifolds

In this paper we investigate the rigidity of symmetric spaces of non-compact type using ergodic theory such as Patterson–Sullivan measure and the marked length spectrum along with the cross ratio on the limit set. In particular, we prove that the marked length spectrum determines the Zariski dense subgroup up to conjugacy in the isometry group of the product of rank-one symmetric spaces. As an application, we show that two convex cocompact, negatively curved, locally symmetric manifolds are isometric if the Thurston distance is zero and the critical exponents of the Poincaré series are the same, and the same is true if the geodesic stretch is equal to one.

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The finite-step realizability of the joint spectral radius of a pair of d×d matrices one of which being rank-one

Linear Algebra and its Applications ◽

10.1016/j.laa.2012.04.053 ◽

2012 ◽

Vol 437 (7) ◽

pp. 1548-1561 ◽

Cited By ~ 6

Author(s):

Xiongping Dai ◽

Yu Huang ◽

Jun Liu ◽

Mingqing Xiao

Keyword(s):

Spectral Radius ◽

Joint Spectral Radius ◽

Rank One ◽

Finite Step

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Nebraska Supreme Court Rules a Minor in Foster Care Seeking an Abortion Must Obtain Foster Parents Consent – In re Anonymous 5

American Journal of Law & Medicine ◽

10.1017/s0098858800000083 ◽

2014 ◽

Vol 40 (1) ◽

pp. 172-174

Author(s):

Tulsi A. Patel

Keyword(s):

Foster Care ◽

Supreme Court ◽

Foster Parents ◽

Care Seeking ◽

A Minor

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Rating Post-Operative Backs (Part I)

Guides Newsletter ◽

10.1001/amaguidesnewsletters.1997.julaug01 ◽

1997 ◽

Vol 2 (4) ◽

pp. 1-3

Author(s):

James B. Talmage

Keyword(s):

Spinal Stenosis ◽

Foot Drop ◽

Neurogenic Claudication ◽

Root Damage ◽

Fourth Edition ◽

Minor Strain ◽

Injury Model ◽

Strain Type ◽

A Minor ◽

Anterior Tibialis

Abstract The AMA Guides to the Evaluation of Permanent Impairment, Fourth Edition, uses the Injury Model to rate impairment in people who have experienced back injuries. Injured individuals who have not required surgery can be rated using differentiators. Challenges arise when assessing patients whose injuries have been treated surgically before the patient is rated for impairment. This article discusses five of the most common situations: 1) What is the impairment rating for an individual who has had an injury resulting in sciatica and who has been treated surgically, either with chemonucleolysis or with discectomy? 2) What is the impairment rating for an individual who has a back strain and is operated on without reasonable indications? 3) What is the impairment rating of an individual with sciatica and a foot drop (major anterior tibialis weakness) from L5 root damage? 4) What is the rating for an individual who is injured, has true radiculopathy, undergoes a discectomy, and is rated as Category III but later has another injury and, ultimately, a second disc operation? 5) What is the impairment rating for an older individual who was asymptomatic until a minor strain-type injury but subsequently has neurogenic claudication with severe surgical spinal stenosis on MRI/myelography? [Continued in the September/October 1997 The Guides Newsletter]

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Pelvic Impairments

Guides Newsletter ◽

10.1001/amaguidesnewsletters.2018.julaug02 ◽

2018 ◽

Vol 23 (4) ◽

pp. 9-10

Author(s):

James Talmage ◽

Jay Blaisdell

Keyword(s):

Pelvic Ring ◽

Reproductive Organs ◽

High Impact ◽

Pelvic Fractures ◽

Motor Dysfunction ◽

Impact Event ◽

Concomitant Injuries ◽

Rating Process ◽

Pass Through ◽

A Minor

Abstract Pelvic fractures are relatively uncommon, and in workers’ compensation most pelvic fractures are the result of an acute, high-impact event such as a fall from a roof or an automobile collision. A person with osteoporosis may sustain a pelvic fracture from a lower-impact injury such as a minor fall. Further, major parts of the bladder, bowel, reproductive organs, nerves, and blood vessels pass through the pelvic ring, and traumatic pelvic fractures that result from a high-impact event often coincide with damaged organs, significant bleeding, and sensory and motor dysfunction. Following are the steps in the rating process: 1) assign the diagnosis and impairment class for the pelvis; 2) assign the functional history, physical examination, and clinical studies grade modifiers; and 3) apply the net adjustment formula. Because pelvic fractures are so uncommon, raters may be less familiar with the rating process for these types of injuries. The diagnosis-based methodology for rating pelvic fractures is consistent with the process used to rate other musculoskeletal impairments. Evaluators must base the rating on reliable data when the patient is at maximum medical impairment and must assess possible impairment from concomitant injuries.

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The Effect of Path Length and Display Size on Memory for Spatial Information

Experimental Psychology (formerly Zeitschrift für Experimentelle Psychologie) ◽

10.1027/1618-3169/a000137 ◽

2012 ◽

Vol 59 (3) ◽

pp. 147-152 ◽

Cited By ~ 11

Author(s):

Katherine Guérard ◽

Sébastien Tremblay

Keyword(s):

Path Length ◽

Potential Role ◽

Spatial Information ◽

Recall Performance ◽

Minor Role ◽

Length Effect ◽

Serial Memory ◽

Fixed Reference ◽

A Minor

In serial memory for spatial information, some studies showed that recall performance suffers when the distance between successive locations increases relatively to the size of the display in which they are presented (the path length effect; e.g., Parmentier et al., 2005) but not when distance is increased by enlarging the size of the display (e.g., Smyth & Scholey, 1994). In the present study, we examined the effect of varying the absolute and relative distance between to-be-remembered items on memory for spatial information. We manipulated path length using small (15″) and large (64″) screens within the same design. In two experiments, we showed that distance was disruptive mainly when it is varied relatively to a fixed reference frame, though increasing the size of the display also had a small deleterious effect on recall. The insertion of a retention interval did not influence these effects, suggesting that rehearsal plays a minor role in mediating the effects of distance on serial spatial memory. We discuss the potential role of perceptual organization in light of the pattern of results.

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