WTC2005-63646 ELLIPTICAL CONTACT AREA BETWEEN ELASTIC BODIES BOUNDED BY HIGH ORDER SURFACES

ABSTRACT Hertz theory fails when contacting surfaces are expressed by a sum of even polynomials of higher powers than two. An alternative analytical solution implies the knowledge of contact area. In the case of elliptical domains, there are some published proposals for the correlation between pressure distribution and surface normal displacement. This paper identifies the class of high order surfaces which lead to elliptical contact domains and solves a contact between fourth order surfaces

WTC2005-63646 ELLIPTICAL CONTACT AREA BETWEEN ELASTIC BODIES BOUNDED BY HIGH ORDER SURFACES

ABSTRACT Hertz theory fails when contacting surfaces are expressed by a sum of even polynomials of higher powers than two. An alternative analytical solution implies the knowledge of contact area. In the case of elliptical domains, there are some published proposals for the correlation between pressure distribution and surface normal displacement. This paper identifies the class of high order surfaces which lead to elliptical contact domains and solves a contact between fourth order surfaces

The Impact of Individual Depressive Symptoms on Impairment of Psychosocial Functioning

abstract: Previous studies have established that scores on Major Depressive Disorder scales are correlated with measures of impairment of psychosocial functioning. It remains unclear, however, whether individual depressive symptoms vary in their effect on impairment, and if so, what the magnitude of these differences might be. We analyzed data from 3,703 depressed outpatients in the first treatment stage of the Sequenced Treatment Alternatives to Relieve Depression (STAR*D) study. Participants reported on the severity of 14 depressive symptoms, and stated to what degree their depression impaired psychosocial functioning (in general, and in the five domains work, home management, social activities, private activities, and close relationships). We tested whether symptoms differed in their associations with impairment, estimated unique shared variances of each symptom with impairment to assess the degree of difference, and examined whether symptoms had variable impacts across impairment domains. Our results show that symptoms varied substantially in their associations with impairment, and contributed to the total explained variance in a range from 0.7% (hypersomnia) to 20.9% (sad mood). Furthermore, symptoms had significantly different impacts on the five impairment domains. Overall, sad mood and concentration problems had the highest unique associations with impairment and were among the most debilitating symptoms in all five domains. Our findings are in line with a growing chorus of voices suggesting that symptom sum-scores obfuscate relevant differences between depressed patients and that substantial rewards will come from close attention to individual depression symptoms.The article is published at http://journals.plos.org/plosone/article?id=10.1371/journal.pone.009031

Measuring Relations Between Concepts In Conceptual Spaces

The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a high-dimensional space and concepts are represented by regions in this space. Our recent mathematical formalization of this framework is capable of representing correlations between different domains in a geometric way. In this paper, we extend our formalization by providing quantitative mathematical definitions for the notions of concept size, subsethood, implication, similarity, and betweenness. This considerably increases the representational power of our formalization by introducing measurable ways of describing relations between concepts.Comment: Accepted at SGAI 2017 (http://www.bcs-sgai.org/ai2017/). The final publication is available at Springer via https://doi.org/10.1007/978-3-319-71078-5_7. arXiv admin note: substantial text overlap with arXiv:1707.05165, arXiv:1706.0636

Coupling of symmetric operators and the third Green identity

The principal aim of this paper is to derive an abstract form of the third Green identity associated with a proper extension $T$ of a symmetric operator $S$ in a Hilbert space $\mathfrak H$, employing the technique of quasi boundary triples for $T$. The general results are illustrated with couplings of Schr\"{o}dinger operators on Lipschitz domains on smooth, boundaryless Riemannian manifolds.Comment: 26 page