1,721,102 research outputs found
An interview with Lars-Erik Persson
No full textOn the occasion of his 65th birthday, we had an interview with Professor Lars-Erik Persson. We present several questions in this interview together with his answers. Some of the answers are indeed surprising also to us who know him wellValiderad; 2010; 20100509 (ysko)</p
Lars-Erik Persson - the man and his work
No full textOn the occasion of Lars-Erik Persson's 65th birthday there was organized a conference Analysis, Inequalities and Homogenization Theory (AIHT), which was held at Lule a University of Technology in June 8-11, 2009, in Lulea-Sweden. The first plenary lecture had the title above and here I present an abbreviated form of this lecture.Validerad; 2010; 20100509 (ysko)</p
Lars-Erik Persson - the man and his work
No full textHis life and mathematics in interpolation theory and inequalities will be presented. Special attention will be taken to our long cooperation (23 years) and joint results. Let me mention here 2 books written jointly: 1. L. Larsson, L. Maligranda, J. E. Peˇcari´c and L. E. Persson, Multiplicative Inequalities of Carlson Type and Interpolation, World Scientific, Singapore 2006, xiv+201 pp. (ISBN: 981-256-708-9).2. A. Kufner, L. Maligranda and L. E. Persson, The Hardy inequality - About its History and Some Related Results, Vydavatelski Servis Publishing House, Pilsen 2007, 162 pp. (ISBN: 978-80-86843-15-5).MR2351524 (2008j:26001) (Reviewer: B. Muckenhoupt).Of course, description about his life with many photos, some sories and jokes will be included.</p
Viscosity solutions of fully nonlinear PDEs
No full textI discuss in talk the Cauchy problem for fully nonlinear and possibly degenerate parabolic equations of the form ut + F(t, x, u,Du,D2u) = 0 set in QT = (0, T] × Rn. The delicate uniqueness issue is the main topic. Since the PDE is set in an unbounded set, it is, generally speaking, necessary to impose restrictons on the growth on the solution to prove uniqueness. However, I mention uniqueness results without any restrictions, for (i) the inviscid Hamilon-Jacobi equation ut + H(t, x,Du) = 0 or for (ii) the viscous equation ut+ 1 2 |Du|2+V (x)-"u = 0. A result for the Isaacs equation under an exponential growth condition on the solution is also given.</p
On the two-dimensional Hardy inequality [Elektronisk resurs]
No full textThe two-dimensional Hardy operator is characteried with two conditions. In the case were one of the weightfunctions is of product typeone of the conditions is a pure constant, so the reslut coincide with earlier results.</p
On the two-dimensional Hardy inequality
No full textThe two-dimensional Hardy operator is characteried with two conditions. In the case were one of the weightfunctions is of product typeone of the conditions is a pure constant, so the reslut coincide with earlier results.Godkänd; 2009; 20090612 (evan)</p
Compactness of embedding between Sobolev type spaces with multiweighted derivatives
No full textWe consider a new Sobolev type function space called the space with multiweighted derivatives. As basis for this space serves some differential operators containing weight functions. We establish necessary and sufficient conditions for the boundedness and compactness of the embedding between the spaces with multiweighted derivatives in different selections of weights.</p
Statistical and Knowledge Supported Visualization of Multivariate data
No full textIn the present work we have selected a collection of statistical and mathematical tools useful for the exploration of multivariate data and we present them in a form that is meant to be particularly accessible to a classically trained mathematician. We give self contained and streamlined introductions to principal component analysis, multidimensional scaling and statistical hypothesis testing. Within the presented mathematical framework we then propose a general exploratory methodology for the investigation of real world high dimensional datasets that builds on statistical and knowledge supported visualizations. We exemplify the proposed methodology by applying it to several different genomewide DNA-microarray datasets. The exploratory methodology should be seen as an embryo that can be expanded and developed in many directions. As an example we point out some recent promising advances in the theory for random matrices that, if further developed, potentially could provide practically useful and theoretically well founded estimations of information content in dimension reducing visualizations. We hope that the present work can serve as an introduction to, and help to stimulate more research within, the interesting and rapidly expanding field of data exploration
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe 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
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