COMMUTATIVE AUTOMORPHIC LOOPS OF ORDER p(3)

A loop is said to be automorphic if its inner mappings are automorphisms. For a prime p, denote by A(p) the class of all 2-generated commutative automorphic loops Q possessing a central subloop Z congruent to Z(p) such that Q/Z congruent to Z(p) x Z(p). Upon describing the free 2-generated nilpotent class two commutative automorphic loop and the free 2-generated nilpotent class two commutative automorphic p-loop F-p in the variety of loops whose elements have order dividing p(2) and whose associators have order dividing p, we show that every loop of A(p) is a quotient of F-p by a central subloop of order p(3). The automorphism group of F-p induces an action of GL(2)(p) on the three-dimensional subspaces of Z(F-p) congruent to (Z(p))(4). The orbits of this action are in one-to-one correspondence with the isomorphism classes of loops from A(p). We describe the orbits, and hence we classify the loops of A(p) up to isomorphism. It is known that every commutative automorphic p-loop is nilpotent when p is odd, and that there is a unique commutative automorphic loop of order 8 with trivial center. Knowing A(p) up to isomorphism, we easily obtain a classification of commutative automorphic loops of order p(3). There are precisely seven commutative automorphic loops of order p(3) for every prime p, including the three abelian groups of order p(3).

Rounding of a first-order quantum phase transition to a strong-coupling critical point

We investigate the effects of quenched disorder on first-order quantum phase transitions on the example of the N-color quantum Ashkin-Teller model. By means of a strong-disorder renormalization group, we demonstrate that quenched disorder rounds the first-order quantum phase transition to a continuous one for both weak and strong coupling between the colors. In the strong-coupling case, we find a distinct type of infinite-randomness critical point characterized by additional internal degrees of freedom. We investigate its critical properties in detail and find stronger thermodynamic singularities than in the random transverse field Ising chain. We also discuss the implications for higher spatial dimensions as well as unusual aspects of our renormalization-group scheme. DOI: 10.1103/PhysRevB.86.214204

Occurrence of asthma symptoms and of airflow obstruction in amateur swimmers between 8 and 17 years of age

Objective: To determine the prevalence of asthma symptoms and of airflow obstruction in amateur swimmers between 8 and 17 years of age, as well as to assess the awareness of asthma and asthma management among these swimmers, their parents, and their coaches. Methods: Our sample comprised 1,116 amateur swimmers who completed a modified version of the International Study of Asthma and Allergies in Childhood written questionnaire, to which questions regarding the reasons to initiate swimming and regarding asthma management had been added. In addition, the participants underwent spirometry prior to a swimming competition. Results: The prevalence of asthma symptoms in the last 12 months was 11.5%, and 327 (29.4%) of the participants reported "wheezing or whistling" in the past. Of the 223 swimmers who reported "asthma ever" or "bronchitis ever", only 102 (45.7%) reported having ever been treated: the most common "treatment" was swimming (in 37.3%), and only 12.7% used inhaled corticosteroids. Of the 254 participants (22.7%) with airflow obstruction, only 52 (20.5%) reported having asthma symptoms. Conclusions: Asthma symptoms are present in amateur swimmers, and a considerable number of such swimmers have airflow obstruction without symptoms. It is therefore likely that the prevalence of asthma is underestimated in this population. It is worrisome that, in our study sample, the swimmers previously diagnosed with asthma were not using the recommended treatments for asthma. The clinical implications of these findings underscore the importance of implementing educational measures for amateur swimmers, as well as for their parents and coaches, to help them recognize asthma symptoms and the consequent risks in the sports environment, in order to allow prompt diagnosis and early clinical intervention.

Healing of a tooth with an overinstrumented apex, extensive transportation and periapical lesion using a 5 mm calcium hydroxide apical plug: an 8-year follow-up report

Besides the risk of filling material extrusion throughout the apex, a satisfactory apical seal can be difficult to achieve in canals with open apices or iatrogenic enlargements of the apical constriction. These situations pose a challenge to root canal filling. This paper describes the root canal filling of a maxillary right canine with an overinstrumented apex, complete loss of the apical stop, extensive canal transportation and apical periodontitis. A 5 mm calcium hydroxide apical plug was placed before root canal filling. The plug was made by soaking paper points with saline, dipping the points in calcium hydroxide powder and then applying it to the apex several times, until a consistent apical plug was obtained. The canal was then irrigated with saline in order to remove any residual calcium hydroxide from the root canal walls, dried with paper points and obturated with an inverted #80 gutta-percha cone and zinc oxide-eugenol based sealer by the lateral condensation technique. An 8-year radiographic follow-up showed formation of mineralized tissue sealing the apical foramen, apical remodeling and no signs of apical periodontitis.