Inertia groups and smooth structures on quaternionic projective spaces

This paper deals with certain results on the number of smooth structures on quaternionic projective spaces, obtained through the computation of inertia groups and their analogues, which in turn are computed using techniques from stable homotopy theory. We show that the concordance inertia group is trivial in dimension 20, but there are many examples in high dimensions where the concordance inertia group is non-trivial. We extend these to computations of concordance classes of smooth structures. These have applications to 3-sphere actions on homotopy spheres and tangential homotopy structures.

Inertia, group conformity and customer loyalty in healthcare in the information age

PurposeThe purpose is to analyse the influence of inertia and group conformity on loyalty in healthcare.Design/methodology/approachStructural equation model developed from the literature and tested with cross-sectional data from a patient online survey.FindingsInertia is a significant antecedent of loyalty and has a stronger effect in healthcare than in other service sectors. Group conformity has no significant effect in healthcare.Research ImplicationsThe strength of the impact of inertia [group conformity] on loyalty depends on the importance of the customer need that the service industry satisfies, in Maslow's hierarchy of needs. Where inertia (stability need) is equally or more [less] important than the customer need, the influence of inertia on loyalty should be positive and strong [weak or insignificant]. In services that satisfy needs more [equally or less] important than group conformity (belonging need), there may be an insignificant [significant] influence of group conformity on customer loyalty, even [especially] in credence services.Practical implicationsHealthcare providers can exploit the stronger effect of inertia in healthcare through development of inertia-based loyalty policies. Regulatory authorities should be vigilant to ensure that these policies are not detrimental to patients. ‘Inert’ patients must become responsible for assessing their loyalties. Authorities and reference groups must stimulate customer loyalty assessments, and assist by providing impartial information.Originality/valueThis is the first study to address the influence of inertia and group conformity on loyalty in the healthcare sector and, from the perspective of Maslow's hierarchy of needs, it is the first to do so in any service sector.

Therapeutic inertia and intensified treatment in diabetes mellitus prescription patterns: A nationwide population-based study in Taiwan

Objective To measure therapeutic inertia by characterizing prescription patterns using secondary data obtained from the nationwide diabetes mellitus pay-for-performance (DM-P4P) programme in Taiwan. Methods Using reimbursement claims from Taiwan’s National Health Insurance Research Database, a nationwide retrospective cohort study was undertaken of patients with diabetes mellitus who participated in the DM-P4P programme from 2006–2008. Glycosylated haemoglobin results were used to evaluate modifications in therapy in response to poor diabetes control. Prescription patterns were used to assign patients to either a therapeutic inertia group or an intensified treatment group. Therapeutic inertia was defined as the failure to act on a known problem. Results The research sample comprised of 168 876 patients with diabetes mellitus who had undergone 899 135 tests. Of these, 37.4% (336 615 visits) of prescriptions were for a combination of two types of drug and 27.7% (248 788 visits) were for a combination of three types of drug. The proportion of patients in the intensified therapy group who were prescribed more than two types of drug was considerably higher than that in the therapeutic inertia group. Conclusion In many cases in the therapeutic inertia group only a single type of hypoglycaemic drug was prescribed or the dosage remained unchanged.

LOCAL MOVE IDENTITIES FOR THE ALEXANDER POLYNOMIALS OF HIGH-DIMENSIONAL KNOTS AND INERTIA GROUPS

As analogues of the well-known skein relations for the Alexander and the Jones polynomials for classical links, we present three relations that hold among invariants of high dimensional knots differing by "local moves". Two are for the Alexander polynomials and the other is for the Arf-invariants, the inertia group and the bP-subgroup.

Totally Real Rigid Elements and Galois Theory

Abelian closed subgroups of the Galois group of the pythagorean closure of a formally real field are described by means of the inertia group of suitable valuation rings.

Addendum: Π-principal hereditary orders (Nagoya Math. J. 32 (1968), 41–65)

Let R denote a complete discrete rank one valuation ring of unequal characteristic, and let p denote the characteristic of the residue class field R̅ of R. Consider the integral closure S of R in a finite Galois extension K of the quotient field k of R. Recall (see Prop. 1.1 of [3]) that the inertia group G0 of K over k is a semi-direct product G0 = J × Gp, where J is a cyclic group of order relatively prime to p and Gp is a normal p-subgroup of G.