المؤلفون: Laschos, Vaios, Mielke, Alexander

مصطلحات موضوعية: article, ddc:510, 51Fxx, Geometry on cones -- local angle condition -- K-semiconcavity -- Hellinger-Kantorovich -- Spherical Hellinger-Kantorovich

الوصف: By studying general geometric properties of cone spaces, we prove the existence of a distance on the space of Probability measures that turns the Hellinger--Kantorovich space into a cone space over the space of probabilities measures. Here we exploit a natural two-parameter scaling property of the Hellinger-Kantorovich distance. For the new space, we obtain a full characterization of the geodesics. We also provide new geometric properties for the original space, including a two-parameter rescaling and reparametrization of the geodesics, local-angle condition and some partial K-semiconcavity of the squared distance, that it will be used in a future paper to prove existence of gradient flows.

العلاقة: https://doi.org/10.20347/WIAS.PREPRINT.2458Test; https://archive.wias-berlin.de/receive/wias_mods_00002502Test; https://archive.wias-berlin.de/servlets/MCRFileNodeServlet/wias_derivate_00002415/wias_preprints_2458.pdfTest; http://www.wias-berlin.de/publications/wias-publ/run.jsp?template=abstract&type=Preprint&year=2017&number=2458Test

الإتاحة: https://doi.org/10.20347/WIAS.PREPRINT.2458Test
https://archive.wias-berlin.de/receive/wias_mods_00002502Test
https://archive.wias-berlin.de/servlets/MCRFileNodeServlet/wias_derivate_00002415/wias_preprints_2458.pdfTest
http://www.wias-berlin.de/publications/wias-publ/run.jsp?template=abstract&type=Preprint&year=2017&number=2458Test

المؤلفون: Dipierro, Serena, Savin, Ovidiu, Valdinoci, Enrico

مصطلحات موضوعية: article, ddc:510, 35R11, 35R35, 49Q20, 49Q05, Fractional perimeter -- minimization problem -- monotonicity formula -- classification of cones

الوصف: We consider a nonlocal free boundary problem built by a fractional Dirichlet norm plus a fractional perimeter. Among other results, we prove a monotonicity formula for the minimizers, glueing lemmata, uniform energy bounds, convergence results, a regularity theory for the planar cones and a trivialization result for the flat case. Several classical free boundary problems are limit cases of the one that we consider in this paper.

العلاقة: https://doi.org/10.20347/WIAS.PREPRINT.2042Test; https://archive.wias-berlin.de/receive/wias_mods_00002110Test; https://archive.wias-berlin.de/servlets/MCRFileNodeServlet/wias_derivate_00002024/wias_preprints_2042.pdfTest; http://www.wias-berlin.de/publications/wias-publ/run.jsp?template=abstract&type=Preprint&year=2014&number=2042Test

الإتاحة: https://doi.org/10.20347/WIAS.PREPRINT.2042Test
https://archive.wias-berlin.de/receive/wias_mods_00002110Test
https://archive.wias-berlin.de/servlets/MCRFileNodeServlet/wias_derivate_00002024/wias_preprints_2042.pdfTest
http://www.wias-berlin.de/publications/wias-publ/run.jsp?template=abstract&type=Preprint&year=2014&number=2042Test

المؤلفون: Mielke, Alexander, Laschos, Vaios

مصطلحات موضوعية: article, ddc:510, Geometry on cones -- local angle condition -- K-semiconcavity -- Hellinger-Kantorovich -- Spherical Hellinger-Kantorovich

الوصف: By studying general geometric properties of cone spaces, we prove the existence of a distance on the space of Probability measures that turns the Hellinger--Kantorovich space into a cone space over the space of probabilities measures. Here we exploit a natural two-parameter scaling property of the Hellinger-Kantorovich distance. For the new space, we obtain a full characterization of the geodesics. We also provide new geometric properties for the original space, including a two-parameter rescaling and reparametrization of the geodesics, local-angle condition and some partial K-semiconcavity of the squared distance, that it will be used in a future paper to prove existence of gradient flows.

العلاقة: 1096-0783 -- J. Funct. Anal. -- Journal of Functional Analysis -- 1469633-2 -- https://www.sciencedirect.com/journal/journal-of-functional-analysisTest; https://doi.org/10.1016/j.jfa.2018.12.013Test; https://archive.wias-berlin.de/receive/wias_mods_00005379Test

الإتاحة: https://doi.org/10.1016/j.jfa.2018.12.013Test
https://archive.wias-berlin.de/receive/wias_mods_00005379Test

المؤلفون: Henrion, René, Seeger, Alberto

مصطلحات موضوعية: article, ddc:510, 46B10, 46B20, 52A41, Convex cone -- circumradius -- inradius -- condition number -- eccentricity -- simplicial cones

الوصف: We discuss some extremality issues concerning the circumradius, the inradius, and the condition number of a closed convex cone in $\mathbb{R}^n$. The condition number refers to the ratio between the circumradius and the inradius. We also study the eccentricity of a closed convex cone, which is a coefficient that measures to which extent the circumcenter differs from the incenter.

العلاقة: https://doi.org/10.20347/WIAS.PREPRINT.1594Test; https://archive.wias-berlin.de/receive/wias_mods_00002926Test; https://archive.wias-berlin.de/servlets/MCRFileNodeServlet/wias_derivate_00002831/wias_preprints_1594.pdfTest; http://www.wias-berlin.de/publications/wias-publ/run.jsp?template=abstract&type=Preprint&year=2011&number=1594Test

الإتاحة: https://doi.org/10.20347/WIAS.PREPRINT.1594Test
https://archive.wias-berlin.de/receive/wias_mods_00002926Test
https://archive.wias-berlin.de/servlets/MCRFileNodeServlet/wias_derivate_00002831/wias_preprints_1594.pdfTest
http://www.wias-berlin.de/publications/wias-publ/run.jsp?template=abstract&type=Preprint&year=2011&number=1594Test

المؤلفون: Henrion, René, Outrata, Jiří

مصطلحات موضوعية: article, ddc:510, 49J52, 90C31, limitng normal cone -- convex polyhedra -- union of polyhedral cones

الوصف: The paper provides formulae for calculating the limiting normal cone introduced by Mordukhovich to a finite union of convex polyhedra. In the first part, special cases of independent interest are considered (almost disjoint cones, half spaces, orthants). The second part focusses on unions of general polyhedra. Due to the local nature of the normal cone, one may restrict considerations without loss of generality to finite unions of polyhedral cones. First, an explicit formula for the normal cone is provided in the situation of two cones. An algorithmic approach is presented along with a refined, more efficient formula. Afterwards, a general formula for the union of N cones is derived. Finally, an application to the stability analysis of a special type of probabilistic constraints is provided.

العلاقة: https://doi.org/10.20347/WIAS.PREPRINT.1146Test; https://archive.wias-berlin.de/receive/wias_mods_00001469Test; https://archive.wias-berlin.de/servlets/MCRFileNodeServlet/wias_derivate_00001387/wias_preprints_1146.pdfTest; http://www.wias-berlin.de/publications/wias-publ/run.jsp?template=abstract&type=Preprint&year=2006&number=1146Test

الإتاحة: https://doi.org/10.20347/WIAS.PREPRINT.1146Test
https://archive.wias-berlin.de/receive/wias_mods_00001469Test
https://archive.wias-berlin.de/servlets/MCRFileNodeServlet/wias_derivate_00001387/wias_preprints_1146.pdfTest
http://www.wias-berlin.de/publications/wias-publ/run.jsp?template=abstract&type=Preprint&year=2006&number=1146Test

المؤلفون: Jourani, Abderrahim

مصطلحات موضوعية: article, ddc:510, 49J52, nonsmooth analysis -- compactly epi-lipschitzian sets -- locally compact cones

الوصف: The paper is devoted to the study of the so-called compactly epi-Lipschitzian sets. These sets are needed for many aspects of generalized differentiation, particulary for necessary optimality conditions, stability of mathematical programming problems and calculus rules for subdifferentials and normal cones. We present general conditions under which sets defined by general constraints are compactly epi-Lipschitzian. This allows us to show how the compact epi-Lipschitzness properties behave under set intersections.

العلاقة: https://doi.org/10.20347/WIAS.PREPRINT.651Test; https://archive.wias-berlin.de/receive/wias_mods_00001041Test; https://archive.wias-berlin.de/servlets/MCRFileNodeServlet/wias_derivate_00000960/wias_preprints_651.pdfTest; http://www.wias-berlin.de/publications/wias-publ/run.jsp?template=abstract&type=Preprint&year=2001&number=651Test

الإتاحة: https://doi.org/10.20347/WIAS.PREPRINT.651Test
https://archive.wias-berlin.de/receive/wias_mods_00001041Test
https://archive.wias-berlin.de/servlets/MCRFileNodeServlet/wias_derivate_00000960/wias_preprints_651.pdfTest
http://www.wias-berlin.de/publications/wias-publ/run.jsp?template=abstract&type=Preprint&year=2001&number=651Test

المؤلفون: Peterhof, Daniela, Recke, Lutz

مصطلحات موضوعية: article, ddc:510, 58E07, 58E09, 34A26, Forced symmetry breaking -- bifurcation from solution orbits -- G-invariant implicit function theorem -- locking cones -- principle of reduced stability

الوصف: We consider abstract forced symmetry breaking problems of the type F(x,λ) = y, x ≈ O(x0), λ ≈ λ0, y ≈ O. It is supposed that for all λ the maps F(·,λ) are equivariant with respect to representations of a given compact Lie group, that F(x0, λ0) = 0 and, hence, that F(x,λ0) = 0 for all elements x of the group orbit O(x0) of x0. We look for solutions x which bifurcate from the solution family O(x0) as λ and y move away from λ0 and zero, respectively. Especially, we describe the number of different solutions x (for fixed control parameters λ and y), their dynamic stability, their asymptotic behavior for y tending to zero and the structural stability of all these results. Further, generalizations are given to problems of the type F(x,λ) = y(x,λ), x ≈ O(x0), λ ≈ λ0, y(x,λ) ≈ 0. This work is a generalization of results of J. K. HALE, P. T'ABOAS , A. VANDERBAUWHEDE and E. DANCER to such extend that the conclusions are applicable to forced frequency locking problems for rotating and modulated wave solutions of certain S1-equivariant evolution equations which arise in laser modeling.

العلاقة: https://doi.org/10.20347/WIAS.PREPRINT.256Test; https://archive.wias-berlin.de/receive/wias_mods_00000610Test; https://archive.wias-berlin.de/servlets/MCRFileNodeServlet/wias_derivate_00000521/wias_preprints_256.pdfTest; http://www.wias-berlin.de/publications/wias-publ/run.jsp?template=abstract&type=Preprint&year=1996&number=256Test

الإتاحة: https://doi.org/10.20347/WIAS.PREPRINT.256Test
https://archive.wias-berlin.de/receive/wias_mods_00000610Test
https://archive.wias-berlin.de/servlets/MCRFileNodeServlet/wias_derivate_00000521/wias_preprints_256.pdfTest
http://www.wias-berlin.de/publications/wias-publ/run.jsp?template=abstract&type=Preprint&year=1996&number=256Test

المؤلفون: Laschos, Vaios, Mielke, Alexander

مصطلحات موضوعية: article, ddc:510, 51Fxx, Geometry on cones -- local angle condition -- K-semiconcavity -- Hellinger-Kantorovich -- Spherical Hellinger-Kantorovich

الوصف: By studying general geometric properties of cone spaces, we prove the existence of a distance on the space of Probability measures that turns the Hellinger--Kantorovich space into a cone space over the space of probabilities measures. Here we exploit a natural two-parameter scaling property of the Hellinger-Kantorovich distance. For the new space, we obtain a full characterization of the geodesics. We also provide new geometric properties for the original space, including a two-parameter rescaling and reparametrization of the geodesics, local-angle condition and some partial K-semiconcavity of the squared distance, that it will be used in a future paper to prove existence of gradient flows.

العلاقة: https://doi.org/10.20347/WIAS.PREPRINT.2458Test; https://archive.wias-berlin.de/receive/wias_mods_00002502Test; https://archive.wias-berlin.de/servlets/MCRFileNodeServlet/wias_derivate_00002415/wias_preprints_2458.pdfTest; http://www.wias-berlin.de/publications/wias-publ/run.jsp?template=abstract&type=Preprint&year=2017&number=2458Test

الإتاحة: https://doi.org/10.20347/WIAS.PREPRINT.2458Test
https://archive.wias-berlin.de/receive/wias_mods_00002502Test
https://archive.wias-berlin.de/servlets/MCRFileNodeServlet/wias_derivate_00002415/wias_preprints_2458.pdfTest
http://www.wias-berlin.de/publications/wias-publ/run.jsp?template=abstract&type=Preprint&year=2017&number=2458Test

المؤلفون: Savin, Ovidiu, Dipierro, Serena, Valdinoci, Enrico

مصطلحات موضوعية: article, ddc:510, Fractional perimeter -- minimization problem -- monotonicity formula -- classification of cones

الوصف: Given $s,\sigma\in(0,1)$ and a bounded domain $\Omega\subset\mathbb{R}^n$, we consider the following minimization problem of $s$-Dirichlet--plus--$\sigma$-perimeter-type $ [u]_{ H^s(\mathbb{R}^{2n}\setminus(\Omega^c)^2) } + {\rm Per}_\sigma (\{u>0\},\Omega),$ where $[ \cdot]_{H^s}$ is the fractional Gagliardo seminorm and ${\rm Per}_\sigma$ is the fractional perimeter. Among other results, we prove a monotonicity formula for the minimizers, glueing lemmata, uniform energy bounds, convergence results, a regularity theory for the planar cones, and a trivialization result for the flat case. The classical free boundary problems are limit cases of the one that we consider in this paper, as $s\nearrow1$, $\sigma\nearrow1$, or $\sigma\searrow0$.

العلاقة: SIAM Journal on Mathematical Analysis -- 1095-7154 -- 0036-1410; https://doi.org/10.1137/140999712Test; https://archive.wias-berlin.de/receive/wias_mods_00005810Test

الإتاحة: https://doi.org/10.1137/140999712Test
https://archive.wias-berlin.de/receive/wias_mods_00005810Test

المؤلفون: Henrion, René, Seeger, Alberto

مصطلحات موضوعية: article, ddc:510, Convex cone -- circumradius -- inradius -- condition number -- eccentricity -- simplicial cones

الوصف: We discuss some extremality issues concerning the circumradius, the inradius, and the condition number of a closed convex cone in Rn. The condition number refers to the ratio between the circumradius and the inradius. We also study the eccentricity of a closed convex cone, which is a coefficient that measures to which extent the circumcenter differs from the incenter.

العلاقة: Mathematica Scandinavica -- Math. Scand. -- 1903-1807 -- 2858405-3 -- 0025-5521 -- 206411-X -- https://www.mscand.dk/aboutTest; https://doi.org/10.7146/math.scand.a-15190Test; https://archive.wias-berlin.de/receive/wias_mods_00004875Test

الإتاحة: https://doi.org/10.7146/math.scand.a-15190Test
https://archive.wias-berlin.de/receive/wias_mods_00004875Test