On the equivalence between MV-algebras and ll-groups with strong unit

In "A new proof of the completeness of the Lukasiewicz axioms"} (Transactions of the American Mathematical Society, 88) C.C. Chang proved that any totally ordered $MV$-algebra $A$ was isomorphic to the segment $A \cong \Gamma(A^*, u)$ of a totally ordered $l$-group with strong unit $A^*$. This was done by the simple intuitive idea of putting denumerable copies of $A$ on top of each other (indexed by the integers). Moreover, he also show that any such group $G$ can be recovered from its segment since $G \cong \Gamma(G, u)^*$, establishing an equivalence of categories. In "Interpretation of AF $C^*$-algebras in Lukasiewicz sentential calculus" (J. Funct. Anal. Vol. 65) D. Mundici extended this result to arbitrary $MV$-algebras and $l$-groups with strong unit. He takes the representation of $A$ as a sub-direct product of chains $A_i$, and observes that $A \overset {} {\hookrightarrow} \prod_i G_i$ where $G_i = A_i^*$. Then he let $A^*$ be the $l$-subgroup generated by $A$ inside $\prod_i G_i$. He proves that this idea works, and establish an equivalence of categories in a rather elaborate way by means of his concept of good sequences and its complicated arithmetics. In this note, essentially self-contained except for Chang's result, we give a simple proof of this equivalence taking advantage directly of the arithmetics of the the product $l$-group $\prod_i G_i$, avoiding entirely the notion of good sequence.Comment: 6 page

Experiences of Burnout Among Adolescent Female Gymnasts: Three Case Studies

Within the current study, the process of adolescent burnout is considered in relation to perceived contributors, symptoms, consequences, and subsequently, effective and ineffective coping strategies. Through case studies, the researchers sought the burnout experiences of three competitive female gymnasts. Participants were selected based on scores obtained from Raedeke and Smith’s (2001) Athlete Burnout Questionnaire. To gain a comprehensive understanding of the process, athlete data were considered in tandem with interviews from at least one parent and one coach. Transcribed data were segmented into meaning units, coded into a hierarchy of themes and verified by each respondent. Despite common trends among the participants, differences were also found in relation to symptoms, contributors, and the progression of the condition. Implications are provided for the athlete/parent/coach triad and also for sport psychologists

Representation theory of MV-algebras

In this paper we develop a general representation theory for MV-algebras. We furnish the appropriate categorical background to study this problem. Our guide line is the theory of classifying topoi of coherent extensions of universal algebra theories. Our main result corresponds, in the case of MV-algebras and MV-chains, to the representation of commutative rings with unit as rings of global sections of sheaves of local rings. We prove that any MV-algebra is isomorphic to the MV-algebra of all global sections of a sheaf of MV-chains on a compact topological space. This result is intimately related to McNaughton’s theorem, and we explain why our representation theorem can be viewed as a vast generalization of McNaughton’s theorem. In spite of the language used in this abstract, we have written this paper in the hope that it can be read by experts in MV-algebras but not in sheaf theory, and conversely.Fil: Dubuc, Eduardo Julio. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Poveda, Yuri A.. Universidad Tecnologica de Pereira; Colombi

A Tentative List of the Land Snails of Georgia, U.S.A.

Because of their high ecological and conservation value, and because we know so little about the group, we compiled a systematic if tentative list of land snails from the state of Georgia. After gleaning a list of species from a monograph on the land snails of eastern United States, written by Leslie Hubricht in 1985, we realized that many species whose ecological requirements are found in Georgia had not been documented there. Therefore, we developed a qualitative model to predict the likelihood that these candidate species occur in Georgia and would eventually be documented. We tested the model with collections data from nine natural history museums and found that the model nonrandomly predicted the species that were collected after the publication of Hubricht’s work. Our searches revealed 214 species of land snails collected in Georgia that exist in museums. Our model predicted that another 68 species are likely occur in the state and await documentation. There are at least 10 species of exotic snails within Georgia’s borders, some of them invasive. We consider our list of land snails in Georgia tentative but useful because of our systematic approach. It is our hope that more researchers will consider Georgia land snails as a model for studying systematics, evolution, ecology, and conservation

Occurrence of the orange wheat blossom midge [Diptera :Cecidomyiidae] in Quebec and its incidence on wheat grain microflora

À l'été 1995, on a prélevé des échantillons de blé (Triticum aestivum) dans des champs de diverses régions agricoles du Québec. La présence de larves de la cécidomyie orangée du blé (Sitodiplosis mosellana) fut quantifiée et une évaluation qualitative et quantitative de la microflore des grains fut réalisée. Les pertes moyennes de rendement causées par les larves de la cécidomyie du blé furent estimée à 6,3%. Le pourcentage des épis infestés fut significativement corrélé avec la contamination bactérienne et fongique des grains (r = 0,79). La présence spécifique du Fusarium graminearum dans les grains de blé fut aussi significativement corrélée avec le nombre de larves par épi (r= 0,67) ou par épillet (r= 0,67). Il appert que la cécidomyie du blé pourrait jouer un rôle dans la dissémination du F. graminearum.Samples of wheat spikes (Triticum aestivum) were collected in the summer of 1995 from different crop districts in Quebec and the occurrence of orange wheat blossom midge (Sitodiplosis mosellana) and seed microflora were determined. Estimated yield loss caused by wheat midge larvae averaged 6.3%. The percentage of infested spikes was significantly correlated with total seed contamination by fungi and bacteria (r = 0.79). The specific occurrence of Fusarium graminearum in grains was also significantly correlated with number of larvae per spike (r = 0.67) or per spikelet (r = 0.67). Consequently, the wheat midge might play a role in dissemination of F. graminearum

Development and validation of clinical profiles of patients hospitalized due to behavioral and psychological symptoms of dementia.

Patients hospitalized on acute psychogeriatric wards are a heterogeneous population. Cluster analysis is a useful statistical method for partitioning a sample of patients into well separated groups of patients who present common characteristics. Several patient profile studies exist, but they are not adapted to acutely hospitalized psychogeriatric patients with cognitive impairment. The present study aims to partition patients hospitalized due to behavioral and psychological symptoms of dementia into profiles based on a global evaluation of mental health using cluster analysis. Using nine of the 13 items from the Health of the Nation Outcome Scales for elderly people (HoNOS65+), data were collected from a sample of 542 inpatients with dementia who were hospitalized between 2011 and 2014 in acute psychogeriatric wards of a Swiss university hospital. An optimal clustering solution was generated to represent various profiles, by using a mixed approach combining hierarchical and non-hierarchical (k-means) cluster analyses associated with a split-sample cross-validation. The quality of the clustering solution was evaluated based on a cross-validation, on a k-means method with 100 random initial seeds, on validation indexes, and on clinical interpretation. The final solution consisted of four clinically distinct and homogeneous profiles labeled (1) BPSD-affective, (2) BPSD-functional, (3) BPSD-somatic and (4) BPSD-psychotic according to their predominant clinical features. The four profiles differed in cognitive status, length of hospital stay, and legal admission status. In the present study, clustering methods allowed us to identify four profiles with distinctive characteristics. This clustering solution may be developed into a classification system that may allow clinicians to differentiate patient needs in order to promptly identify tailored interventions and promote better allocation of available resources

Poisson algebras for non-linear field theories in the Cahiers topos

We develop an approach to construct Poisson algebras for non-linear scalar field theories that is based on the Cahiers topos model for synthetic differential geometry. In this framework the solution space of the field equation carries a natural smooth structure and, following Zuckerman's ideas, we can endow it with a presymplectic current. We formulate the Hamiltonian vector field equation in this setting and show that it selects a family of observables which forms a Poisson algebra. Our approach provides a clean splitting between geometric and algebraic aspects of the construction of a Poisson algebra, which are sufficient to guarantee existence, and analytical aspects that are crucial to analyze its properties

Multiscale Computation with Interpolating Wavelets

Multiresolution analyses based upon interpolets, interpolating scaling functions introduced by Deslauriers and Dubuc, are particularly well-suited to physical applications because they allow exact recovery of the multiresolution representation of a function from its sample values on a finite set of points in space. We present a detailed study of the application of wavelet concepts to physical problems expressed in such bases. The manuscript describes algorithms for the associated transforms which, for properly constructed grids of variable resolution, compute correctly without having to introduce extra grid points. We demonstrate that for the application of local homogeneous operators in such bases, the non-standard multiply of Beylkin, Coifman and Rokhlin also proceeds exactly for inhomogeneous grids of appropriate form. To obtain less stringent conditions on the grids, we generalize the non-standard multiply so that communication may proceed between non-adjacent levels. The manuscript concludes with timing comparisons against naive algorithms and an illustration of the scale-independence of the convergence rate of the conjugate gradient solution of Poisson's equation using a simple preconditioning, suggesting that this approach leads to an O(n) solution of this equation.Comment: 33 pages, figures available at http://laisla.mit.edu/muchomas/Papers/nonstand-figs.ps . Updated: (1) figures file (figs.ps) now appear with the posting on the server; (2) references got lost in the last submissio

Structure of shells in complex networks

In a network, we define shell $\ell$ as the set of nodes at distance $\ell$ with respect to a given node and define $r_\ell$ as the fraction of nodes outside shell $\ell$. In a transport process, information or disease usually diffuses from a random node and reach nodes shell after shell. Thus, understanding the shell structure is crucial for the study of the transport property of networks. For a randomly connected network with given degree distribution, we derive analytically the degree distribution and average degree of the nodes residing outside shell $\ell$ as a function of $r_\ell$. Further, we find that $r_\ell$ follows an iterative functional form $r_\ell=\phi(r_{\ell-1})$, where $\phi$ is expressed in terms of the generating function of the original degree distribution of the network. Our results can explain the power-law distribution of the number of nodes $B_\ell$ found in shells with $\ell$ larger than the network diameter $d$, which is the average distance between all pairs of nodes. For real world networks the theoretical prediction of $r_\ell$ deviates from the empirical $r_\ell$. We introduce a network correlation function $c(r_\ell)\equiv r_{\ell+1}/\phi(r_\ell)$ to characterize the correlations in the network, where $r_{\ell+1}$ is the empirical value and $\phi(r_\ell)$ is the theoretical prediction. $c(r_\ell)=1$ indicates perfect agreement between empirical results and theory. We apply $c(r_\ell)$ to several model and real world networks. We find that the networks fall into two distinct classes: (i) a class of {\it poorly-connected} networks with $c(r_\ell)>1$, which have larger average distances compared with randomly connected networks with the same degree distributions; and (ii) a class of {\it well-connected} networks with $c(r_\ell)<1$