On Solutions of Holonomic Divided-Difference Equations on Non-Uniform Lattices

The main aim of this paper is the development of suitable bases (replacing the power basis x^n (n\in\IN_\le 0) which enable the direct series representation of orthogonal polynomial systems on non-uniform lattices (quadratic lattices of a discrete or a q-discrete variable). We present two bases of this type, the first of which allows to write solutions of arbitrary divided-difference equations in terms of series representations extending results given in [16] for the q-case. Furthermore it enables the representation of the Stieltjes function which can be used to prove the equivalence between the Pearson equation for a given linear functional and the Riccati equation for the formal Stieltjes function. If the Askey-Wilson polynomials are written in terms of this basis, however, the coefficients turn out to be not q-hypergeometric. Therefore, we present a second basis, which shares several relevant properties with the first one. This basis enables to generate the defining representation of the Askey-Wilson polynomials directly from their divided-difference equation. For this purpose the divided-difference equation must be rewritten in terms of suitable divided-difference operators developed in [5], see also [6].

Unified modified divided difference implementation of Adams and BDF formulas /

"March 1980."

Characterization theorem for classical orthogonal polynomials on non-uniform lattices: The functional approach

Using the functional approach, we state and prove a characterization theorem for classical orthogonal polynomials on non-uniform lattices (quadratic lattices of a discrete or a q-discrete variable) including the Askey-Wilson polynomials. This theorem proves the equivalence between seven characterization properties, namely the Pearson equation for the linear functional, the second-order divided-difference equation, the orthogonality of the derivatives, the Rodrigues formula, two types of structure relations,and the Riccati equation for the formal Stieltjes function.

Steffensen Methods for Solving Generalized Equations

2000 Mathematics Subject Classification: 65G99, 65K10, 47H04.

Ponseti Method: Does Age at the Beginning of Treatment Make a Difference?

The Ponseti method is reportedly effective for treating clubfoot in children up to 9 years of age. However, whether age at the beginning of treatment influences the rate of successful correction and the rate of relapse is unknown. We therefore retrospectively reviewed 68 consecutive children with 102 idiopathic clubfeet treated by the Ponseti technique in four Portuguese hospitals. We followed patients a minimum of 30 months (mean, 41.4 months; range, 30–61 months). The patients were divided into two groups according to their age at the beginning of treatment; Group I was younger than 6 months and Group II was older than 6 months. All feet(100%) were initially corrected and no feet required extensive surgery regardless of age at the beginning of treatment. There were no differences between Groups I and II in the number of casts, tenotomies, success in terms of rate of initial correction, rate of recurrence, and rate of tibialis anterior transference. The rate of the Ponseti method in avoiding extensive surgery was 100% in Groups I and II; relapses occurred in 8% of the feet in younger and older children. Level of Evidence: Level II, prognostic study. See the Guidelines for Authors for a complete description of levels of evidence.

The difference between the basal metabolic rate and the sleeping metabolic rate in Japanese.

Previous studies have demonstrated the difference between the basal metabolic rate (BMR) and the sleeping metabolic rate (SMR): however, the difference in the Japanese population has not yet been explored. This study examined the relationship between the BMR and SMR in ninety-four healthy Japanese subjects (37 males and 57 females, 39 +/- 12 y of age and 22.0 +/- 7.4% body fat) in a respiratory chamber. The SMR was significantly lower than the BMR (1416 +/- 245 vs. 1492 +/- 256 kcal/d): however, there was a highly significant correlation between the two (r = 0.867; p < 0.001). The ratio of SMR/BMR largely varied among individuals (0.95 +/-0.08, 8.4% of the coefficient of variation). The ratio was significantly lower in males than in females (0.93 +/- 0.10 vs. 0.97 +/- 0.06, p < 0.05). None of the anthropometric measures (age, weight, body mass index, body surface area or percent body fat) correlated with the ratio. These results showed that SMR was 95%, of BMR on average in a healthy Japanese group. However, when applied over a longer time period (24 h or more), the difference tends to become negligible for most analyses in a group. Although the difference between SMR and BMR will induce a 5% gap of physical activity level defined as the total energy expenditure divided by the BMR or SMR, this factor seems to have little practical importance in epidemiological research.

Increased risks of early sexual initiators: time makes a difference.

BACKGROUND: Years since onset of sexual intercourse (YSSI) is a rarely used variable when studying adolescents- sexual outcomes. The aim of this study is to evaluate the influence of YSSI on the adverse sexual outcomes of early sexual initiators.METHODS: Data were drawn from the 2002 Swiss Multicenter Adolescent Survey on Health database, a nationally representative cross-sectional survey including 7429 adolescents in post mandatory school aged 16-20 years. Only adolescents reporting sexual intercourse (SI) were included (N=4388; 45% females) and divided by age of onset of SI (early initiators, age<16: N=1469, 44% females; and late initiators, age?16: N=2919, 46% females). Analyses were done separately by gender. Groups were compared for personal characteristics at the bivariate level. We analyzed three sexual outcomes (?4 sexual partners, pregnancy and non-use of condom at last SI) controlling for all significant personal variables with two logistic regressions first using age, then YSSI as one of the confounding variables. Results are given as adjusted odds ratios (aOR) using lSI as the reference category.RESULTS: After adjusting for YSSI instead of age, negative sexual outcomes among early initiators were no longer significant, except for multiple sexual partners among females, although at a much lower level. Early initiators were less likely to report non-use of condom at last SI when adjusting for YSSI (females: aOR=0.59 [0.44-0.79]; p<0.001; males aOR=0.71 [0.50-1.00]; p=0.053).CONCLUSION: YSSI is an important explanatory variable when studying adolescents- sexuality and needs to be included in future research on adolescents- sexual health.

Youths carrying a weapon or using a weapon in a fight: what makes the difference?

The objective of this study was to characterize weapon-carrying adolescents and to assess whether weapon carriers differ from weapon users. Data were drawn from a cross-sectional school-based survey of 7548 adolescents aged 16-20 years in Switzerland. Youths carrying a weapon were compared with those who do not. Subsequently, weapon carriers were divided into those who had used it in a fight and those who had not. Individual, family, school and social factors were analyzed using bivariate and stepwise multivariate analysis. For both genders, delinquent behavior and being victim of physical violence were associated with weapon carrying. For males, quarreling while intoxicated, being an apprentice, being sensation seekers, having a tattoo, having a poor relationship with parents and practicing unsafe sex were also related to weapon carrying. Compared with weapon carriers, female weapon users were more likely to be regular smokers. Male weapon users were foreign born, urban and apprentices; had poor school connectedness; practiced unsafe sex and quarreled while intoxicated. Carrying a weapon is a relatively frequent behavior among youths in Switzerland and a sizeable proportion of weapon carriers have used it in a fight. Weapon carrying should be part of the clinical assessment and preventive counseling of adolescents. Preventive programs specific for at-risk youth groups need to be developed.

Increased risks of early sexual initiators: time makes a difference

BACKGROUND: Years since onset of sexual intercourse (YSSI) is a rarely used variable when studying adolescents- sexual outcomes. The aim of this study is to evaluate the influence of YSSI on the adverse sexual outcomes of early sexual initiators. METHODS: Data were drawn from the 2002 Swiss Multicenter Adolescent Survey on Health database, a nationally representative cross-sectional survey including 7429 adolescents in post mandatory school aged 16-20 years. Only adolescents reporting sexual intercourse (SI) were included (N=4388; 45% females) and divided by age of onset of SI (early initiators, age<16: N=1469, 44% females; and late initiators, age≥16: N=2919, 46% females). Analyses were done separately by gender. Groups were compared for personal characteristics at the bivariate level. We analyzed three sexual outcomes (≥4 sexual partners, pregnancy and non-use of condom at last SI) controlling for all significant personal variables with two logistic regressions first using age, then YSSI as one of the confounding variables. Results are given as adjusted odds ratios (aOR) using lSI as the reference category. RESULTS: After adjusting for YSSI instead of age, negative sexual outcomes among early initiators were no longer significant, except for multiple sexual partners among females, although at a much lower level. Early initiators were less likely to report non-use of condom at last SI when adjusting for YSSI (females: aOR=0.59 [0.44-0.79]; p<0.001; males aOR=0.71 [0.50-1.00]; p=0.053). CONCLUSION: YSSI is an important explanatory variable when studying adolescents- sexuality and needs to be included in future research on adolescents- sexual health.

Nonautonomous difference equations with applications

This work is divided in two parts. In the first part we develop the theory of discrete nonautonomous dynamical systems. In particular, we investigate skew-product dynamical system, periodicity, stability, center manifold, and bifurcation. In the second part we present some concrete models that are used in ecology/biology and economics. In addition to developing the mathematical theory of these models, we use simulations to construct graphs that illustrate and describe the dynamics of the models. One of the main contributions of this dissertation is the study of the stability of some concrete nonlinear maps using the center manifold theory. Moreover, the second contribution is the study of bifurcation, and in particular the construction of bifurcation diagrams in the parameter space of the autonomous Ricker competition model. Since the dynamics of the Ricker competition model is similar to the logistic competition model, we believe that there exists a certain class of two-dimensional maps with which we can generalize our results. Finally, using the Brouwer’s fixed point theorem and the construction of a compact invariant and convex subset of the space, we present a proof of the existence of a positive periodic solution of the nonautonomous Ricker competition model.

Genetic trends in the expected progeny difference of the asymptotic weight of Nelore females

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Combined training (aerobic plus strength) potentiates a reduction in body fat but demonstrates no difference on the lipid profile in postmenopausal women when compared to aerobic training with a similar training load

The aim of this study was to verify the effects of aerobic and combined training on the body composition and lipid profile of obese postmenopausal women and to analyze which of these models is more effective after equalizing the training load. Sixty five postmenopausal women (age=61.0±6.3 years) were divided into three groups: Aerobic Training (AT,n= 15), Combined Training (CT,[strength+aerobic],n=32) and control group (CG,n=18). Their body composition: upper body fat (TF), fat mass (FM), percentage of fat mass and fat free mass (FFM) were estimated by DXA. The lipid profile, total cholesterol, HDL-cholesterol and LDL-cholesterol were assessed. There was a statistically significant difference in the TF (AT= -4.4 %, CT= -4.4%, and CG= 1.0%, p= 0.001) and FFM (AT= 1.7%, CT= 2.6%, and CG= -1.4%, p= 0.0001) between the experimental and the control groups. Regarding the percentage of body fat, there was a statistically significant difference only between the CT and CG groups (AT= -2.8%, CT= -3.9% and CG= 0.31%, p= 0.004). When training loads were equalized, the aerobic and combined training decreased core fat and increased fat-free mass, but only the combined training potentiated a reduction in percentage of body fat in obese postmenopausal women after the training program. HDL-c levels increased in the combined group and the chol/HDL ratio (atherogenic index) decreased in the aerobic group, however, there were no significant differences between the intervention programs. Taken together, both the exercise training programs were effective for improving body composition and inducing an anti-atherogenic status.

A Divided City in a Common Market: EU Citizenship and Everyday Instrumentalities on the Polish-German Border

Based on an ethnographic case study in the border cities of Frankfurt (Oder), Germany and Słubice, Poland, this article explores the construction and maintenance of ethnic difference within the transnational economic and social spaces created by the European Union's common market. Through an examination of three domains of cross-border citizenship practice - shopping and consumption, housing and work - this article argues that even as the European Union deploys policies aimed at creating de-territorialised and supranational forms of identity and citizenship, economic asymmetries and hierarchies of value embedded within these policies grant rights differentially in ways that continue to be linked to ethnicity and nationality.

Fusional vergence measurements for eso versus exo deviations: is there a difference?

Purpose: The aims of this study were to compare angle of deviation, fusional vergence measurements and fusion reserve ratio between esophoria and exophoria. Methods: A cross-sectional study was performed in children with best-corrected visual acuity of 0.0 LogMAR in either eye, compensated heterophoria within 10 prism dioptres (PD), full ocular rotations, presence of fusional vergence and stereopsis (60 seconds of arc or better). Fusional amplitudes were compared between angle of deviation (2, 4, 6, 8 and 10 PD) in esophoria and exophoria. The fusion reserve ratio was calculated (to assess the effect of the underlying angle of deviation) as fusional convergence divided by prism alternating cover test measurements. Results: Two-hundred and eleven children (7.65±1.16 years) were recruited to this study. Exophoria was most common for near (n=181; 85.8%) and distance (n=20; 9.5%). Esophoria was present in 22 children for near (10.4%) and in 1 child for distance (0.5%). No significant differences were found between fusional amplitudes and angle of deviation for near (p>0.05). Children with exophoria of 10PD had a slight, but not, significant (p=0.264) increase in fusional convergence from 2PD (19.95±5.09) to 10PD (26.67±5.77). In esophoric children the variation of fusional convergence was smaller from 2P (25.00±0.00) to 10PD (22.50±3.54) and non significant (p=0.185). The fusion reserve ratio was significantly smaller in children with higher deviations (i.e. 10PD) for both esophoria (p=0.003) and exophoria (p>0.001). The fusion reserve ratio ranged between 12.50 (2PD) and 2.25±0.35 (10PD) for esophoria and between 9.98±2.55 (2PD) and 2.67±0.58 (10PD) for exophoria. Conclusions: Angle of deviation is not an efficient measure to predict fusional amplitudes. The fusion reserve ratio appears to be a better measurement to assess the effect of the underlying angle of deviation on fusional convergence. More studies are necessary to understand better the relationship between fusion amplitudes and angle of deviation.

Microbial Evaluation Of Traumatized Teeth Treated With Triple Antibiotic Paste Or Calcium Hydroxide With 2% Chlorhexidine Gel In Pulp Revascularization.

Revascularization outcome depends on microbial elimination because apical repair will not happen in the presence of infected tissues. This study evaluated the microbial composition of traumatized immature teeth and assessed their reduction during different stages of the revascularization procedures performed with 2 intracanal medicaments. Fifteen patients (7-17 years old) with immature teeth were submitted to the revascularization procedures; they were divided into 2 groups according to the intracanal medicament used: TAP group (n = 7), medicated with a triple antibiotic paste, and CHP group (n = 8), dressed with calcium hydroxide + 2% chlorhexidine gel. Samples were taken before any treatment (S1), after irrigation with 6% NaOCl (S2), after irrigation with 2% chlorhexidine (S3), after intracanal dressing (S4), and after 17% EDTA irrigation (S5). Cultivable bacteria recovered from the 5 stages were counted and identified by means of polymerase chain reaction assay (16S rRNA). Both groups had colony-forming unit counts significantly reduced after S2 (P < .05); however, no significant difference was found between the irrigants (S2 and S3, P = .99). No difference in bacteria counts was found between the intracanal medicaments used (P = .95). The most prevalent bacteria detected were Actinomyces naeslundii (66.67%), followed by Porphyromonas endodontalis, Parvimonas micra, and Fusobacterium nucleatum, which were detected in 33.34% of the root canals. An average of 2.13 species per canal was found, and no statistical correlation was observed between bacterial species and clinical/radiographic features. The microbial profile of infected immature teeth is similar to that of primarily infected permanent teeth. The greatest bacterial reduction was promoted by the irrigation solutions. The revascularization protocols that used the tested intracanal medicaments were efficient in reducing viable bacteria in necrotic immature teeth.