1,721,136 research outputs found
A representation formula for slice regular functions over slice-cones in several variables
No full textThe aim of this paper is to extend the so called slice analysis to a general case in which the codomain is a real vector space of even dimension, i.e. is of the form R2n. This is a new setting which contains and encompasses in a nontrivial way other cases already studied in the literature and which requires new tools. To this end, we define a cone WCd in [End(R2n)]d and we extend the slice topology τs to this cone. Slice regular functions can be defined on open sets in (τs,WCd) and a number of results can be proved in this framework, among which a representation formula. This theory can be applied to some real algebras, called left slice complex structure algebras. These algebras include quaternions, octonions, Clifford algebras and real alternative ∗ -algebras but also left-alternative algebras and sedenions, thus providing brand new settings in slice analysis
Extension theorem and representation formula in non-axially-symmetric domains for slice regular functions
Get PDFSlice analysis is a generalization of the theory of holomorphic functions of one complex variable to quaternions. Among the new phenomena which appear in this context, there is the fact that the convergence domain of f(q) = Sigma(n is an element of N) (q - p)*(n)a(n), given by a sigma-ball Sigma(p, r), is not open in H unless p is an element of R. This motivates us to investigate, in this article, what is a natural topology for slice regular functions. It turns out that the natural topology is the so-called slice topology, which is different from the Euclidean topology and nicely adapts to the slice structure of quaternions. We extend the function theory of slice regular functions to any domains in the slice topology. Many fundamental results in the classical slice analysis for axially symmetric domains fail in our general setting. We can even construct a counterexample to show that a slice regular function in a domain cannot be extended to an axially symmetric domain. In order to provide positive results we need to consider so-called path-slice functions instead of slice functions. Along these lines, we can establish an extension theorem and a representation formula in a slice domain
Slice quaternionic analysis in two variables
No full textSlice quaternionic analysis in two variables is a generalization of the theory of several complex variables to quaternions. This study relies on the theory of stem functions and the theory of holomorphic functions in two complex variables. Our approach is to introduce holomorphicity for stem functions in terms of two commutative complex structures. It turns out that, locally, a function which is slice regular corresponds exactly to the Taylor series of two ordered quaternions, with the coefficients on the right. The Hartogs phenomenon holds in our setting; however, its proof is subtle due to some topological obstacles. We overcome them by showing that holomorphic stem functions preserve the property of being intrinsic after extension
Generational Differences in Age-Specific Dementia Prevalence Rates
Get PDFImportance: Dementia is a significant public health challenge, with its prevalence expected to increase as life expectancy continues to extend globally. Objective: To estimate generational differences in age-specific dementia prevalence across the US, Europe, and England. Design, Setting, and Participants: This cross-sectional study used data from 1994 to 2021 from the United States Health and Retirement Study (HRS), from 2004 to 2020 from the Survey of Health, Ageing and Retirement in Europe (SHARE), and from 2002 to 2019 from the English Longitudinal Study of Ageing (ELSA). Statistical analysis was performed from May 2023 to February 2025. Main Outcomes and Measures: First, 2 different methods - the validated algorithm and machine learning techniques as the robustness check - were used to identify respondents with probable dementia. Then the status of dementia was used to estimate the association of cohort with dementia status by age-period-cohort methodology. Results: Of the 99420 individuals (mean [SD] age, 79.1 [6.2] years; 59.2% women) in the HRS dataset, 21069 (21.2%) were included in this study; of the 83580 individuals (mean [SD] age, 78.6 [5.9] years; 54.7% women) in the SHARE dataset, 32490 (38.9%) were included in this study; and of the 31384 individuals (mean [SD] age, 77.9 [5.6] years; 55.8% women) in the ELSA dataset, 8878 (28.3%) were included in this study. Focusing on people aged 71 years or older and controlling for age and period effects, birth cohorts born more recently were less likely to develop dementia in all 3 regions, albeit at different rates (point estimate for 1944-1948 vs 1919-1923 cohorts: US, -0.55 [95% CI, -0.77 to -0.34] vs -0.18 [95% CI, -0.25 to -0.10]; Europe, -1.49 [95% CI, -1.72 to -1.27] vs -0.24 [95% CI, -0.35 to -0.13]; and England, -0.48 [95% CI, -0.89 to -0.08] vs -0.23 [95% CI, -0.38 to -0.07]). This decreasing trend was more pronounced among women than men (point estimate in 1944-1948 for women vs men: US, -0.55 [95% CI, -0.86 to -0.30] vs -0.48 [95% CI, -0.84 to -0.13]; Europe, -1.50 [95% CI, -1.80 to -1.21] vs -1.34 [95% CI, -1.70 to -0.99]; and England, -0.76 [95% CI, -1.30 to -0.23] vs -0.07 [95% CI, -0.69 to 0.54]); the point estimates for men in England were not statistically significant. Conclusions and Relevance: In this cross-sectional study examining generational differences in age-specific dementia prevalence across the US, Europe, and England, we found that individuals from more recent birth cohorts had lower proportions of people with dementia. Work of this kind is relevant to plan for health and long-term care policy and workforce requirements across these regions now and into the future
Weak Slice Regular Functions on the n-Dimensional Quadratic Cone of Octonions
Get PDFIn the literature on slice analysis in the hypercomplex setting, there are two main approaches to define slice regular functions in one variable: one consists in requiring that the restriction to any complex plane is holomorphic (with the same complex structure of the complex plane), the second one makes use of stem and slice functions. So far, in the setting of several hypercomplex variables, only the second approach has been considered, i.e. the one based on stem functions. In this paper, we use instead the first definition on the so-called n-dimensional quadratic cone of octonions. These two approaches yield the same class of slice regular functions on axially symmetric slice-domains, however, they are different on other types of domains. We call this new class of functions weak slice regular. We show that there exist weak slice regular functions which are not slice regular in the second approach. Moreover, we study various properties of these functions, including a Taylor expansion
A New Approach to Slice Analysis Via Slice Topology
Get PDFIn this paper we summarize some known facts on slice topology in the quaternionic case, and we deepen some of them by proving new results and discussing some examples. We then show, following Dou et al. (A representation formula for slice regular functions over slice-cones in several variables, arXiv:2011.13770, 2020), how this setting allows us to generalize slice analysis to the general case of functions with values in a real left alternative algebra, which includes the case of slice monogenic functions with values in Clifford algebra. Moreover, we further extend slice analysis, in one and several variables, to functions with values in a Euclidean space of even dimension. In this framework, we study the domains of slice regularity, we prove some extension properties and the validity of a Taylor expansion for a slice regular function
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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