Existence Results for Some Damped Second-Order Volterra Integro-Differential Equations

In this paper we make a subtle use of operator theory techniques and the well-known Schauder fixed-point principle to establish the existence of pseudo-almost automorphic solutions to some second-order damped integro-differential equations with pseudo-almost automorphic coefficients. In order to illustrate our main results, we will study the existence of pseudo-almost automorphic solutions to a structurally damped plate-like boundary value problem.Comment: 20 pages. arXiv admin note: substantial text overlap with arXiv:1402.563

Euler-like recurrences for smallest parts functions

We obtain recurrences for smallest parts functions which resemble Euler's recurrence for the ordinary partition function. The proofs involve the holomorphic projection of non-holomorphic modular forms of weight 2

Classical elliptic current algebras

In this paper we discuss classical elliptic current algebras and show that there are two different choices of commutative test function algebras on a complex torus leading to two different elliptic current algebras. Quantization of these classical current algebras give rise to two classes of quantized dynamical quasi-Hopf current algebras studied by Enriquez-Felder-Rubtsov and Arnaudon-Buffenoir-Ragoucy-Roche-Jimbo-Konno-Odake-Shiraishi. Different degenerations of the classical elliptic algebras are considered. They yield different versions of rational and trigonometric current algebras. We also review the averaging method of Faddeev-Reshetikhin, which allows to restore elliptic algebras from the trigonometric ones

Conformally equivariant quantization: Existence and uniqueness

We prove the existence and the uniqueness of a conformally equivariant symbol calculus and quantization on any conformally flat pseudo-Riemannian manifold (M,\rg). In other words, we establish a canonical isomorphism between the spaces of polynomials on $T^*M$ and of differential operators on tensor densities over $M$, both viewed as modules over the Lie algebra \so(p+1,q+1) where $p+q=\dim(M)$. This quantization exists for generic values of the weights of the tensor densities and compute the critical values of the weights yielding obstructions to the existence of such an isomorphism. In the particular case of half-densities, we obtain a conformally invariant star-product.Comment: LaTeX document, 32 pages; improved versio

Ultrafilter and Constructible topologies on spaces of valuation domains

Let $K$ be a field and let $A$ be a subring of $K$. We consider properties and applications of a compact, Hausdorff topology called the "ultrafilter topology" defined on the space Zar$(K|A)$ of all valuation domains having $K$ as quotient field and containing $A$. We show that the ultrafilter topology coincides with the constructible topology on the abstract Riemann-Zariski surface Zar$(K|A)$. We extend results regarding distinguished spectral topologies on spaces of valuation domains.Comment: Comm. Algebra (accepted for publication

The burden of breast cancer in Italy: mastectomies and quadrantectomies performed between 2001 and 2008 based on nationwide hospital discharge records.

BACKGROUND: Where population coverage is limited, the exclusive use of Cancer Registries might limit ascertainment of incident cancer cases. We explored the potentials of Nationwide hospital discharge records (NHDRs) to capture incident breast cancer cases in Italy. METHODS: We analyzed NHDRs for mastectomies and quadrantectomies performed between 2001 and 2008. The average annual percentage change (AAPC) and related 95% Confidence Interval (CI) in the actual number of mastectomies and quadrantectomies performed during the study period were computed for the full sample and for subgroups defined by age, surgical procedure, macro-area and singular Region. Re-admissions of the same patients were separately presented. RESULTS: The overall number of mastectomies decreased, with an AAPC of -2.1% (-2.3 -1.8). This result was largely driven by the values observed for women in the 45 to 64 and 65 to 74 age subgroups (-3.0%, -3.4 -3.6 and -3.3%, -3.8 -2.8, respectively). We observed no significant reduction in mastectomies for women in the remaining age groups. Quadrantectomies showed an overall +4.7 AAPC (95%CI:4.5-4.9), with no substantial differences by age. Analyses by geographical area showed a remarkable decrease in mastectomies, with inter-regional discrepancies possibly depending upon variability in mammography screening coverage and adherence. Quadrantectomies significantly increased, with Southern Regions presenting the highest average rates. Data on repeat admissions within a year revealed a total number of 46,610 major breast surgeries between 2001 and 2008, with an overall +3.2% AAPC (95%CI:2.8-3.6). CONCLUSIONS: In Italy, NHDRs might represent a valuable supplemental data source to integrate Cancer Registries in cancer surveillance

Social connections and risk of incident mild cognitive impairment, dementia, and mortality in 13 longitudinal cohort studies of ageing

INTRODUCTION: Previous meta-analyses have linked social connections and mild cognitive impairment, dementia, and mortality. However, these used aggregate data from North America and Europe and examined a limited number of social connection markers. METHODS: We used individual participant data (N = 39271, Mage  = 70.67 (40-102), 58.86% female, Meducation  = 8.43 years, Mfollow-up  = 3.22 years) from 13 longitudinal ageing studies. A two-stage meta-analysis of Cox regression models examined the association between social connection markers with our primary outcomes. RESULTS: We found associations between good social connections structure and quality and lower risk of incident mild cognitive impairment (MCI); between social structure and function and lower risk of incident dementia and mortality. Only in Asian cohorts, being married/in a relationship was associated with reduced risk of dementia, and having a confidante was associated with reduced risk of dementia and mortality. DISCUSSION: Different aspects of social connections - structure, function, and quality - are associated with benefits for healthy aging internationally. HIGHLIGHTS: Social connection structure (being married/in a relationship, weekly community group engagement, weekly family/friend interactions) and quality (never lonely) were associated with lower risk of incident MCI. Social connection structure (monthly/weekly friend/family interactions) and function (having a confidante) were associated with lower risk of incident dementia. Social connection structure (living with others, yearly/monthly/weekly community group engagement) and function (having a confidante) were associated with lower risk of mortality. Evidence from 13 longitudinal cohort studies of ageing indicates that social connections are important targets for reducing risk of incident MCI, incident dementia, and mortality. Only in Asian cohorts, being married/in a relationship was associated with reduced risk of dementia, and having a confidante was associated with reduced risk of dementia and mortality

Age-related cognitive decline and associations with sex, education and apolipoprotein E genotype across ethnocultural groups and geographic regions: a collaborative cohort study

Background: The prevalence of dementia varies around the world, potentially contributed to by international differences in rates of age-related cognitive decline. Our primary goal was to investigate how rates of age-related decline in cognitive test performance varied among international cohort studies of cognitive aging. We also determined the extent to which sex, educational attainment, and apolipoprotein E e4 allele (APOE*4) carrier status were associated with decline. Methods and findings: We harmonized longitudinal data for 14 cohorts from 12 countries (Australia, Brazil, France, Greece, Hong Kong, Italy, Japan, Singapore, Spain, South Korea, United Kingdom, United States), for a total of 42, 170 individuals aged 54–105 y (42% male), including 3.3% with dementia at baseline. The studies began between 1989 and 2011, with all but three ongoing, and each had 2–16 assessment waves (median = 3) and a follow-up duration of 2–15 y. We analyzed standardized Mini-Mental State Examination (MMSE) and memory, processing speed, language, and executive functioning test scores using linear mixed models, adjusted for sex and education, and meta-analytic techniques. Performance on all cognitive measures declined with age, with the most rapid rate of change pooled across cohorts a moderate -0.26 standard deviations per decade (SD/decade) (95% confidence interval CI] -0.35, -0.16], p < 0.001) for processing speed. Rates of decline accelerated slightly with age, with executive functioning showing the largest additional rate of decline with every further decade of age (-0.07 SD/decade, 95% CI -0.10, -0.03], p = 0.002). There was a considerable degree of heterogeneity in the associations across cohorts, including a slightly faster decline (p = 0.021) on the MMSE for Asians (-0.20 SD/decade, 95% CI -0.28, -0.12], p < 0.001) than for whites (-0.09 SD/decade, 95% CI -0.16, -0.02], p = 0.009). Males declined on the MMSE at a slightly slower rate than females (difference = 0.023 SD/decade, 95% CI 0.011, 0.035], p < 0.001), and every additional year of education was associated with a rate of decline slightly slower for the MMSE (0.004 SD/decade less, 95% CI 0.002, 0.006], p = 0.001), but slightly faster for language (-0.007 SD/decade more, 95% CI -0.011, -0.003], p = 0.001). APOE*4 carriers declined slightly more rapidly than non-carriers on most cognitive measures, with processing speed showing the greatest difference (-0.08 SD/decade, 95% CI -0.15, -0.01], p = 0.019). The same overall pattern of results was found when analyses were repeated with baseline dementia cases excluded. We used only one test to represent cognitive domains, and though a prototypical one, we nevertheless urge caution in generalizing the results to domains rather than viewing them as test-specific associations. This study lacked cohorts from Africa, India, and mainland China. Conclusions: Cognitive performance declined with age, and more rapidly with increasing age, across samples from diverse ethnocultural groups and geographical regions. Associations varied across cohorts, suggesting that different rates of cognitive decline might contribute to the global variation in dementia prevalence. However, the many similarities and consistent associations with education and APOE genotype indicate a need to explore how international differences in associations with other risk factors such as genetics, cardiovascular health, and lifestyle are involved. Future studies should attempt to use multiple tests for each cognitive domain and feature populations from ethnocultural groups and geographical regions for which we lacked data