Chapter 1. Mod p Arithmetic, Group Theory and Cryptography

Keyword(s):  
1993 ◽  
Vol 02 (02) ◽  
pp. 141-148 ◽  
Author(s):  
HUGH M. HILDEN ◽  
MARIA TERESA LOZANO ◽  
JOSÉ MARIA MONTESINOS-AMILIBIA

Let (p/q, n) be the orbifold with cyclic isotropy of order n and with singular set the 2-bridge knot or link p/q where p and q are relatively prime numbers, q is odd, q is less than p, and q is not congruent to ±1 mod p (i.e. p/q is any non toroidal 2-bridge knot or link). We show that the orbifold fundamental group π1(p/q, n) is universal for n any multiple of 12. This means that if Γ is any such group, it can be thought of as a discrete group of hyperbolic isometries of hyperbolic 3-space ℍ3, and then, given any closed, oriented 3-manifold M, there exists a subgroup of finite index G of Γ such that M is homeomorphic to G\ℍ3. Since we have shown elsewhere that the group π1(5/3, 12) is an arithmetic group, it follows that there exists an orbifold, namely (5/3, 12), whose singular set is a knot, the figure eight, and whose fundamental group is both arithmetic and universal.


2000 ◽  
Vol 5 (5) ◽  
pp. 4-5

Abstract Spinal cord (dorsal column) stimulation (SCS) and intraspinal opioids (ISO) are treatments for patients in whom abnormal illness behavior is absent but who have an objective basis for severe, persistent pain that has not been adequately relieved by other interventions. Usually, physicians prescribe these treatments in cancer pain or noncancer-related neuropathic pain settings. A survey of academic centers showed that 87% of responding centers use SCS and 84% use ISO. These treatments are performed frequently in nonacademic settings, so evaluators likely will encounter patients who were treated with SCS and ISO. Does SCS or ISO change the impairment associated with the underlying conditions for which these treatments are performed? Although the AMA Guides to the Evaluation of Permanent Impairment (AMA Guides) does not specifically address this question, the answer follows directly from the principles on which the AMA Guides impairment rating methodology is based. Specifically, “the impairment percents shown in the chapters that consider the various organ systems make allowance for the pain that may accompany the impairing condition.” Thus, impairment is neither increased due to persistent pain nor is it decreased in the absence of pain. In summary, in the absence of complications, the evaluator should rate the underlying pathology or injury without making an adjustment in the impairment for SCS or ISO.


2000 ◽  
Vol 5 (6) ◽  
pp. 1-7
Author(s):  
Christopher R. Brigham ◽  
James B. Talmage ◽  
Leon H. Ensalada

Abstract The AMA Guides to the Evaluation of Permanent Impairment (AMA Guides), Fifth Edition, is available and includes numerous changes that will affect both evaluators who and systems that use the AMA Guides. The Fifth Edition is nearly twice the size of its predecessor (613 pages vs 339 pages) and contains three additional chapters (the musculoskeletal system now is split into three chapters and the cardiovascular system into two). Table 1 shows how chapters in the Fifth Edition were reorganized from the Fourth Edition. In addition, each of the chapters is presented in a consistent format, as shown in Table 2. This article and subsequent issues of The Guides Newsletter will examine these changes, and the present discussion focuses on major revisions, particularly those in the first two chapters. (See Table 3 for a summary of the revisions to the musculoskeletal and pain chapters.) Chapter 1, Philosophy, Purpose, and Appropriate Use of the AMA Guides, emphasizes objective assessment necessitating a medical evaluation. Most impairment percentages in the Fifth Edition are unchanged from the Fourth because the majority of ratings currently are accepted, there is limited scientific data to support changes, and ratings should not be changed arbitrarily. Chapter 2, Practical Application of the AMA Guides, describes how to use the AMA Guides for consistent and reliable acquisition, analysis, communication, and utilization of medical information through a single set of standards.


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