An elementary rectifiability lemma and some applications

We generalize a classical theorem of Besicovitch, showing that, for any positive integers $k<n$, if $E\subset \mathbb R^n$ is a Souslin set which is not $\mathcal{H}^k$-$\sigma$-finite, then $E$ contains a purely unrectifiable closed set $F$ with $0< \mathcal{H}^k (F) < \infty$. Therefore, if $E\subset \mathbb R^n$ is a Souslin set with the property that every closed subset with finite $\mathcal{H}^k$ measure is $k$-rectifiable, then $E$ is $k$-rectifiable. Our interest is motivated by recent studies of the structure of the singular sets of several objects in geometric analysis and we explain the usefulness of our lemma with some examples

Faber-Krahn inequalities, the Alt-Caffarelli-Friedman formula, and Carleson's ε2\varepsilon^2 conjecture in higher dimensions

The main aim of this article is to prove quantitative spectral inequalities for the Laplacian with Dirichlet boundary conditions. More specifically, we prove sharp quantitative stability for the Faber-Krahn inequality in terms of Newtonian capacities and Hausdorff contents of positive codimension, thus providing an answer to a question posed by De Philippis and Brasco. One of our results asserts that for any bounded domain $\Omega\subset\mathbb R^n$, $n\geq3$, with Lebesgue measure equal to that of the unit ball and whose first eigenvalue is $\lambda_\Omega$, denoting by $\lambda_B$ the first eigenvalue for the unit ball, for any $a\in (0,1)$ it holds $$\lambda_\Omega - \lambda_B \geq C(a) \,\inf_B \bigg(\sup_{t\in (0,1)} \frac1{H^{n-1}(\partial ((1-t) B))} \int_{\partial ((1-t) B)} \frac{\operatorname{Cap}_{n-2}(B(x,atr_B)\setminus \Omega)}{(t\,r_B)^{n-3}}\,dH^{n-1}(x)\bigg)^2,$$ where the infimum is taken over all balls $B$ with the same Lebesgue measure as $\Omega$ and $\operatorname{Cap}_{n-2}$ is the Newtonian capacity of homogeneity $n-2$. In fact, this holds for bounded subdomains of the sphere and the hyperbolic space, as well. In a second result, we also apply the new Faber-Krahn type inequalities to quantify the Hayman-Friedland inequality about the characteristics of disjoint domains in the unit sphere. Thirdly, we propose a natural extension of Carleson's $\varepsilon^2$-conjecture to higher dimensions in terms of a square function involving the characteristics of certain spherical domains, and we prove the necessity of the finiteness of such square function in the tangent points via the Alt-Caffarelli-Friedman monotonicity formula. Finally, we answer in the negative a question posed by Allen, Kriventsov and Neumayer in connection to rectifiability and the positivity set of the ACF monotonicity formula.Comment: In this version we also deal with the hyperbolic space. Further, we give a counterexample to a question of Allen, Kriventsov and Neumayer in connection to rectifiability and the positivity set of the ACF monotonicity formul

BARBELL ACCELERATION ANALYSIS ON VARIOUS INTENSITIES OF WEIGHTLIFTING

The purpose of this study was to examine how various intensity levels influence the peak barbell acceleration in weightlifting. USA weightlifting resident team members (n=9, men:5 & women:4) participated in this study. They performed two repetitions at intensities of 80, 85, and 90% of 1 repetition maximum (total six repetitions). The peak barbell acceleration was measured at the 2nd pull phase of the snatch/clean. A one-way repeated measure ANOVA was used to analyze the effects of the intensity levels (p = .05). The results showed that intensity has a significant effect on the peak barbell acceleration (F(2,16) = 11.49, p < .001). The peak barbell acceleration decreased as the intensity level increased (80%: 19.63±3.04, 85%: 16.78±3.56, 90%: 13.65±3.50). Comparison between elite and beginners or other power-oriented athletes can be considered in future studies

Prevalence and Patterns of Sexting among Ethnic Minority Urban High School Students

Although sexting among U.S. youth has received much popular media attention, there are only limited data on its prevalence among ethnic minority youth. This study, therefore, specifically examined the prevalence and patterns of sexting (sending and/or receiving a nude or semi-nude picture/video or a sexual text-only message) among a sample of black and Hispanic youth. Data from 1,034 tenth graders from a large, urban school district in southeast Texas were used to calculate the prevalence of sexting by gender-race/ethnicity. Overlap among sexting behaviors was also examined. Electronic surveys were administered via an audio-computer-assisted self-interview on laptop computers. Prevalence estimates were obtained, and chi-square analyses were conducted to compare the distribution of sexting behaviors by gender-race/ethnicity subgroups. More than 20% of students reported sending either a nude or semi-nude picture/video or a sexual text-only message (jointly referred to as a sext ), and more than 30% reported receiving a sext. Sexts were also frequently shared with unintended recipients. Black males and females reported similar prevalence estimates for sexting behaviors. However, they were more likely than Hispanic males to participate in some sexting behaviors. Hispanic females reported the lowest estimates for sexting behaviors for all gender-race/ethnicity subgroups. Many youth who sent or received a nude or semi-nude picture/video were also likely to have sent or received sexual text-only messages. The results of this study indicate that sexting is prevalent among ethnic minority youth. However, more research is needed to understand the specific context and circumstances around which sexting occurs in this population

Hemoglobin A1c improvements and better diabetes-specific quality of life among participants completing diabetes self-management programs: A nested cohort study

BACKGROUND: Numerous primary care innovations emphasize patient-centered processes of care. Within the context of these innovations, greater understanding is needed of the relationship between improvements in clinical endpoints and patient-centered outcomes. To address this gap, we evaluated the association between glycosylated hemoglobin (HbA(1c)) and diabetes-specific quality of life among patients completing diabetes self-management programs. METHODS: We conducted a retrospective cohort study nested within a randomized comparative effectiveness trial of diabetes self-management interventions in 75 diabetic patients. Multiple linear regression models were developed to examine the relationship between change in HbA(1c) from baseline to one-year follow-up and Diabetes-39 (a diabetes-specific quality of life measure) at one year. RESULTS: HbA(1c) levels improved for the overall cohort from baseline to one-year follow-up (t (74) = 3.09, p = .0029). One-year follow up HbA(1c) was correlated with worse overall quality of life (r = 0.33, p = 0.004). Improvements in HbA(1c) from baseline to one-year follow-up were associated with greater D-39 diabetes control (β = 0.23, p = .04) and D-39 sexual functioning (β = 0.25, p = .03) quality of life subscales. CONCLUSIONS: Improvements in HbA(1c) among participants completing a diabetes self-management program were associated with better diabetes-specific quality of life. Innovations in primary care that engage patients in self-management and improve clinical biomarkers, such as HbA(1c), may also be associated with better quality of life, a key outcome from the patient perspective

Fluoxetine during Development Reverses the Effects of Prenatal Stress on Depressive-Like Behavior and Hippocampal Neurogenesis in Adolescence

Depression during pregnancy and the postpartum period is a growing health problem, which affects up to 20% of women. Currently, selective serotonin reuptake inhibitor (SSRIs) medications are commonly used for treatment of maternal depression. Unfortunately, there is very little research on the long-term effect of maternal depression and perinatal SSRI exposure on offspring development. Therefore, the aim of this study was to determine the role of exposure to fluoxetine during development on affective-like behaviors and hippocampal neurogenesis in adolescent offspring in a rodent model of maternal depression. To do this, gestationally stressed and non-stressed Sprague-Dawley rat dams were treated with either fluoxetine (5 mg/kg/day) or vehicle beginning on postnatal day 1 (P1). Adolescent male and female offspring were divided into 4 groups: 1) prenatal stress+fluoxetine exposure, 2) prenatal stress+vehicle, 3) fluoxetine exposure alone, and 4) vehicle alone. Adolescent offspring were assessed for anxiety-like behavior using the Open Field Test and depressive-like behavior using the Forced Swim Test. Brains were analyzed for endogenous markers of hippocampal neurogenesis via immunohistochemistry. Results demonstrate that maternal fluoxetine exposure reverses the reduction in immobility evident in prenatally stressed adolescent offspring. In addition, maternal fluoxetine exposure reverses the decrease in hippocampal cell proliferation and neurogenesis in maternally stressed adolescent offspring. This research provides important evidence on the long-term effect of fluoxetine exposure during development in a model of maternal adversity

Development of the prenatal health inventory of behaviors (PHI-B)

textHealth promoting behaviors have a critical influence on outcomes during pregnancy, at delivery, and on life-long health in women. Despite the significance of these behaviors, scientifically sound and comprehensive measures of health behaviors during pregnancy and preconception are lacking. The purpose of this study was to develop a comprehensive, psychometrically sound inventory to measure women’s health behaviors associated with the preconception and pregnancy time periods. The study was divided into four phases. Phase I focused on conceptualization of prenatal health behavior utilizing Rubin’s construct of maternal tasks and an extensive literature review. Critical domains and definitions of healthy behavior associated with pregnancy were generated. During Phase II items representing these domains were developed with help of perinatal experts and construction of the inventory took place. Phase III consisted of a pilot study. Individual pregnant women, as well as two groups of pregnant women, completed the inventory and critiqued it for readability, redundancy, format, cultural sensitivity, and completion time. Based on their comments and item analysis, the inventory, renamed the Prenatal Health Inventory of Behaviors (PHI-B), consisted of 45 items. Phase IV was the main study to test reliability and validity of the PHI-B in a multi-ethnic sample of 333 pregnant women. During this phase the PHI-B demonstrated satisfactory internal consistency reliability for the scale as a whole (coefficient alpha = .82), but coefficient alphas for the theorized domain subscales ranged from poor to adequate. Preliminary factor analysis and a content validity index failed to support the theorized domain subscales. Further factor analysis revealed a five-factor solution, somewhat dissimilar from the original theorized domains of health behavior. These five factors were named Surveillance of Health, Good Health Practices, Ensuring Safety, Balancing Health, and Adherence. Evidence of test-retest reliability for these factor-analytic based subscales was found. Evidence of concurrent validity was provided by obtaining Pearson correlations between scores of well-being, depression, and physical discomforts, while evidence of convergent and divergent validity of the inventory was found with a general measure of health behaviors and a measure of social desirability, respectively. Assessing factor-analytic subscales for hypothesis-based construct validity revealed interesting associations, particularly for stress management and depressive symptoms.Nursin

Hispanic Mothers' and High School Girls' Perceptions of Cervical Cancer, Human Papilloma Virus, and the Human Papilloma Virus Vaccine

AbstractPurposeCervical cancer incidence and mortality are higher for Hispanic women than for women in other population groups. However, the incidence could be reduced if teenaged Hispanic girls received the human papillomavirus (HPV) vaccine before they become sexually active. Unfortunately, few Hispanic girls receive this vaccine, which prevents cervical cancer. This study assessed Hispanic mothers' and girls' perceptions about cervical cancer, HPV, and the HPV vaccine. Results show factors that affect whether Hispanic high school girls receive the vaccine.MethodsTwenty-four Hispanic mothers and 28 Hispanic girls from an urban school district in southeast Texas each participated in one of eight focus groups. Bilingual moderators facilitated the mothers' groups in English and Spanish and the girls' groups in English. We analyzed transcripts of the discussions and identified themes using the grounded theory approach.ResultsOur analysis found several themes that affect whether Hispanic girls get the HPV vaccine: gaps in knowledge; fears and concerns about the vaccine; sociocultural communication practices; and decision-making about HPV vaccination. Both mothers and girls had limited knowledge about cervical cancer, HPV, and the vaccine. Some girls who received the vaccine said they wished their mothers had involved them in making the decision.ConclusionsFindings may help in developing school or community-based educational programs for Hispanic families. Such programs should provide information on the HPV vaccine and the link between HPV and cervical cancer, and they should assist mothers and girls in communicating to make informed decisions about the vaccine