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Generalized Minkowski sets for the regularization of inverse problems [article]

Bas Peters, Felix J. Herrmann
2019 arXiv   pre-print
Many works on inverse problems in the imaging sciences consider regularization via one or more penalty functions or constraint sets.  ...  We generalize the Minkowski set, such that the model parameters are the sum of two components, each of which is constrained to an intersection of sets.  ...  We propose the generalized Minkowski constraint set for the regularization of inverse problems as Definition 1 (Generalized Minkowski Set).  ... 
arXiv:1903.03942v1 fatcat:4bhwoeehl5cu7h2m4hxcohh4na

Inversive Planes, Minkowski Planes and Regular Sets of Points

Gloria Rinaldi
2001 European journal of combinatorics (Print)  
New examples of regular sets of points for the Miquelian inversive planes of order q, q a prime power, q ≥ 7, are found and connections between such planes and certain Minkowski planes of order q 2 are  ...  The existence of a regular set S for the Minkowski plane M(q 2 , σ ), with S contained in a block, is equivalent to the existence of a regular setS for the group P L(2, q 2 ) acting on G F(q 2 ) ∪ {∞}  ...  In this paper, bearing in mind the Miquelian inversive plane of order q, M(q), is embeddable in each known Minkowski plane of order q 2 (see [19] ), we intend to find new examples of regular sets for  ... 
doi:10.1006/eujc.1999.0468 fatcat:jwmkktmag5afxl5lfnkg4xlgfa

Group morphology with convolution algebras

Mikola Lysenko, Saigopal Nelaturi, Vadim Shapiro
2010 Proceedings of the 14th ACM Symposium on Solid and Physical Modeling - SPM '10  
We show that group morphology is a proper setting for unifying, formulating and solving a number of important problems, including translational and rotational configuration space problems, mechanism workspace  ...  In particular, we show that all Minkowski product and quotient operations may be represented implicitly as sublevel sets of the same real-valued convolution function.  ...  ACKNOWLEDGMENTS The authors are grateful to John Uicker for pointing out the spherical 4-bar chain example.  ... 
doi:10.1145/1839778.1839781 dblp:conf/sma/LysenkoNS10 fatcat:vogfma2qejebjeqboigz5hfwae

Harmonic measure in convex domains

David Jerison
1989 Bulletin of the American Mathematical Society  
The proof of Theorem 1 depends by way of Caffarelli's methods on the entire development of regularity theory in the Minkowski problem. We would like to thank L.  ...  This is analogous to the Brunn-Minkowski inequality, which leads to uniqueness in the generalized Minkowski problem (see [3] ). gives the conformai mapping <S> from the upper half-plane H = {z e C: Imz  ... 
doi:10.1090/s0273-0979-1989-15823-0 fatcat:lfkhxca4l5gtdoy633aj5gq47m

Page 3866 of Mathematical Reviews Vol. , Issue 2004e [page]

2004 Mathematical Reviews  
(RS-K UBT; Krasnodar) Direct regularization of the inversion of real-valued Laplace transforms. (English summary) Inverse Problems 19 (2003), no. 3, 573-583.  ...  Summary: “The paper presents a regularization method for the inversion of real-valued Laplace transforms.  ... 

The Feynman problem for the Klein–Gordon equation

Christian Gérard, Michał Wrochna
2022 Séminaire Laurent Schwartz — EDP et applications  
We report on the well-posedness of the Feynman problem for the Klein-Gordon equation on asymptotically Minkowski spacetimes.  ...  Furthermore, the inverse is shown to coincide with the Duistermaat-Hörmander Feynman parametrix modulo smoothing terms.  ...  Support from the grant ANR-16-CE40-0012-01 is gratefully acknowledged. Séminaire Laurent-Schwartz -EDP et applications Institut des hautes études scientifiques, 2019-2020 Exposé n o IV, 1-10  ... 
doi:10.5802/slsedp.140 fatcat:mtgyn7eaanggdddfzu7p62p5e4

The Feynman problem for the Klein-Gordon equation [article]

Christian Gérard, Michał Wrochna
2020 arXiv   pre-print
We report on the well-posedness of the Feynman problem for the Klein-Gordon equation on asymptotically Minkowski spacetimes.  ...  Furthermore, the inverse is shown to coincide with the Duistermaat-H\"ormander Feynman parametrix modulo smoothing terms.  ...  In other words, one needs ways to control regularity of solutions of an inhomogeneous problem P u = f in terms of asymptotic data, and the invertibility properties are also tied to the decay at spatial  ... 
arXiv:2003.14404v1 fatcat:famc6kajf5eyjgi47sj3o5vikm


Daniela Velichová
2013 Scientific Proceedings. Faculty of Mechanical Engineering  
Paper brings few ideas about a concept of Minkowski combinations of point sets, which can be defined as generalisation of set operations defined on point sets in the Euclidean space, Minkowski sum and  ...  Presented algebraic tool for modelling point sets determined by defined vector operations can be used in geometric modeling, in applied computer graphics, or for solving other problems in vector analysis  ...  Minkowski linear combination of two point sets can be then regarded as a certain generalization of Minkowski sum, defined as Minkowski sum of scalar multiples of these two sets. Definition 4.  ... 
doi:10.2478/stu-2013-0009 fatcat:rse6k67fsvbi5pmgaluo4q7nym

Lattice calculation of hadronic tensor of the nucleon

Jian Liang, Keh-Fei Liu, Yi-Bo Yang, M. Della Morte, P. Fritzsch, E. Gámiz Sánchez, C. Pena Ruano
2018 EPJ Web of Conferences  
We used the Backus-Gilbert reconstruction method to address the inverse Laplace transformation for the analytic continuation from the Euclidean to the Minkowski space.  ...  We report an attempt to calculate the deep inelastic scattering structure functions from the hadronic tensor calculated on the lattice.  ...  T ) for each ν 0 and for each ν 0 Eq. (9) always holds, then we can have the value of the function ω(ν) at arbitrary ν, which means that the inverse problem is solved.  ... 
doi:10.1051/epjconf/201817514014 fatcat:f45cqafrgfb75b5sckcutf6l7a

The Inverse Kakeya Problem [article]

Sergio Cabello, Otfried Cheong, Michael Gene Dobbins
2019 arXiv   pre-print
We prove that the largest convex shape that can be placed inside a given convex shape Q ⊂R^d in any desired orientation is the largest inscribed ball of Q.  ...  The ball is the unique solution, except when maximizing the perimeter in the two-dimensional case.  ...  Minkowski sums For two convex shapes P and Q in R d , the Minkowski sum P + Q is the set {p + q | p ∈ P, q ∈ Q}.  ... 
arXiv:1912.08477v1 fatcat:r5u7i4xl7bbgxhjvqwqhkbelji

A bound for the perimeter of inner parallel bodies

Simon Larson
2016 Journal of Functional Analysis  
The proof, which is straightforward, is based on the construction of an extremal set for a certain optimization problem and the use of basic properties of mixed volumes.  ...  We provide a sharp lower bound for the perimeter of the inner parallel sets of a convex body Ω.  ...  A great deal of gratitude is owed Professor Ari Laptev for valuable discussions and for proposing the study of the problem at hand.  ... 
doi:10.1016/j.jfa.2016.02.022 fatcat:3662hu35uvfl3pnja7r3s3faly

Regularization of Kepler problem inκ-spacetime

Partha Guha, E. Harikumar, N. S. Zuhair
2016 Journal of Mathematical Physics  
First, we perform a Moser-type regularization and then we proceed for the Ligon-Schaaf regularization to our problem. In particular, generalizing Heckman-de Laat (J.  ...  Symplectic Geom. 10, (2012), 463-473) in the noncommutative context we show that the Ligon-Schaaf regularization map follows from an adaptation of the Moser regularization can be generalized to the Kepler  ...  PG would like to thank the Tudor Ratiu very much for discussion and ongoing collaboration on geometry of Kepler equation.  ... 
doi:10.1063/1.4966552 fatcat:z7ztakpvlbfbziug7fwqx3hklu

The Three Reflections Theorem Revisited

Gunter Weiss
2018 KoG  
A consequence of the presented results are further generalisations of the 3RT, e.g. in planes with Minkowski metric, affine or projective 3-space, or in circle geometries.  ...  For the Euclidean case and its non-Euclidean counterparts this property is automatically fulfilled. From the projective geometry point of view a (skew) reflection is nothing but a harmonic homology.  ...  Acknowledgement The author thanks Prof. E. Jurkin and the reviewer(s) for valuable help and hints.  ... 
doi:10.31896/k.22.5 fatcat:xh7nuledhnfthec5dvuxfm2ywq

Probabilist Set Inversion using Pseudo-Intervals Arithmetic

Abdelouahab KENOUFI
2014 TEMA  
One introduces the <span>psi</span>-algorithm, which performs set inversion of functions and exhibits some numerical examples developed with the python programming langage<!--EndFragment--></pre>.  ...  for its associated vector space.  ...  SET INVERSION One of the most recurrent problem arising in sciences and engineering is to perform adjustments of a system in order to get the desired performances.  ... 
doi:10.5540/tema.2014.015.01.0097 fatcat:uykdg7vu7jfzpb3apegr4eufoi

Orlicz-Minkowski flows [article]

Paul Bryan, Mohammad N. Ivaki, Julian Scheuer
2020 arXiv   pre-print
Moreover, employing a parabolic approximation method, we give new proofs of some of the existence results for the general Orlicz-Minkowski problems; the L_p versions are the even L_p-Minkowski problem  ...  As an application, we obtain old and new results for the regular even Orlicz-Minkowski problems; the corresponding L_p version is the even L_p-Minkowski problem for p>-n-1.  ...  Acknowledgment PB was supported by the ARC within the research grant "Analysis of fully non-linear geometric problems and differential equations", number DE180100110. MI was supported by a Jerrold E.  ... 
arXiv:2005.00143v1 fatcat:jvvbc4arsrdkze3475c2yf3q7e
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