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On the generalized Ball bases

Jorge Delgado, Juan Manuel Peña
2006 Advances in Computational Mathematics  
In this paper, we analyze some shape preserving and stability properties of these bases. We prove that the Wang-Ball basis is strictly monotonicity preserving for all m.  ...  However, it is not geometrically convexity preserving and is not totally positive for m > 3, in contrast with the Said-Ball basis.  ...  In this paper we show that the known good shape preserving properties of the Said-Ball basis for the representation of polynomial curves of degree m when m is odd also hold for even m.  ... 
doi:10.1007/s10444-004-7636-x fatcat:4p7dpyjuercx7pc4qvph26mmlq

Page 6597 of Mathematical Reviews Vol. , Issue 88m [page]

1988 Mathematical Reviews  
The function s is expressed as a linear combina- tion of B-spline basis functions and is required to satisfy certain properties relating to its shape.  ...  It is briefly described how such a shape-preserving spline approximant to given data can be ob- tained.  ... 

Construction of Cubic Trigonometric Curves with an Application of Curve Modelling

Abdul Majeed, Mehwish Naureen, Muhammad Abbas, Kenjiro T. Miura
2022 Mathematics  
Some open and closed curves from TBS and trigonometric rational B-spline (TRBS) are generated to test the applicability of the suggested technique, and the influence of the shape parameter is also noted  ...  This paper introduces new trigonometric basis functions (TBF) in polynomial and rational form with two shape parameters (SPs).  ...  Acknowledgments: This research was supported by the Department of Mechanical Engineering, Shizuoka University, Hamamatsu, Shizuoka 432-8561, Japan.  ... 
doi:10.3390/math10071087 fatcat:mo2lj3kyo5d7xabc7dnnf3te44

Morphophoric POVMs, generalised qplexes, and 2-designs [article]

Wojciech Słomczyński, Anna Szymusiak
2020 arXiv   pre-print
(basis) and the outer (primal) polytopes between which the generalised qplex is sandwiched.  ...  We study the class of quantum measurements with the property that the image of the set of quantum states under the measurement map transforming states into probability distributions is similar to this  ...  Acknowledgements We thank Anna Szczepanek for numerous remarks that improve the readability of the paper.  ... 
arXiv:1911.12456v4 fatcat:boxfar5yavbpllnobaj5dbje2q

A multisided C2 B-spline patch over extraordinary vertices in quadrilateral meshes

Gerben J. Hettinga, Jiří Kosinka
2020 Computer-Aided Design  
Acknowledgement We gratefully acknowledge the support of NVIDIA Corporation with the donation of the Titan V GPU used for this research.  ...  We have chosen for the representation that stays the closest to the original B-spline basis functions, because of their good shape properties.  ...  The surfaces are affine invariant, preserve the convex hull property, and edits to the control mesh have local influence.  ... 
doi:10.1016/j.cad.2020.102855 fatcat:7g6dflkklzditm7zpgehe4syym

Morphophoric POVMs, generalised qplexes, and 2-designs

Wojciech Słomczyński, Anna Szymusiak
2020 Quantum  
(basis) and the outer (primal) polytopes between which the generalised qplex is sandwiched.  ...  We study the class of quantum measurements with the property that the image of the set of quantum states under the measurement map transforming states into probability distributions is similar to this  ...  Acknowledgements We thank Anna Szczepanek for numerous remarks that improve the readability of the paper.  ... 
doi:10.22331/q-2020-09-30-338 fatcat:por5m76xmbat3iaay6tavgfqpi

Linear embeddings of low-dimensional subsets of a Hilbert space to Rm

Gilles Puy, Mike Davies, Remi Gribonval
2015 2015 23rd European Signal Processing Conference (EUSIPCO)  
Defining appropriate random linear projections, we propose two constructions of linear maps that have the restricted isometry property (RIP) on the secant set of M with high probability.  ...  The first one is optimal in the sense that it only needs a number of projections essentially proportional to the intrinsic dimension of M to satisfy the RIP.  ...  Let us highlight that the shape of p is thus governed by the shape of the projection of the chords x 1 − x 2 on Φ and not the projection of the vectors in M themselves.  ... 
doi:10.1109/eusipco.2015.7362427 dblp:conf/eusipco/PuyDG15 fatcat:2uuxzyunbfav7f3bd266ah7cmu

Page 1577 of Mathematical Reviews Vol. , Issue 92c [page]

1992 Mathematical Reviews  
(MAL-USM) Shape preserving properties of the generalised Ball basis. Comput. Aided Geom. Design 8 (1991), no. 2, 115-121.  ...  Finally they discuss the advantages and disadvantages of the Ball basis as compared to the Bernstein basis. S.  ... 

Entropies from Coarse-graining: Convex Polytopes vs. Ellipsoids

Nikos Kalogeropoulos
2015 Entropy  
Our discussion is motivated by and confined to the behaviour of Hamiltonian systems of many degrees of freedom.  ...  We examine the Boltzmann/Gibbs/Shannon S_BGS and the non-additive Havrda-Charvát / Daróczy/Cressie-Read/Tsallis S_q and the Kaniadakis κ-entropy S_κ from the viewpoint of coarse-graining, symplectic capacities  ...  , generalised shapes which are symmetric convex polytopes.  ... 
doi:10.3390/e17096329 fatcat:zcj224zbrnfnvima6mm2vywrq4

The dual of non-extremal area: differential entropy in higher dimensions [article]

Vijay Balasubramanian, Charles Rabideau
2018 arXiv   pre-print
Then we propose a new formula in terms of an integral of shape derivatives of the entanglement entropy of ball shaped regions.  ...  The Ryu-Takayanagi formula relates entanglement entropy in a field theory to the area of extremal surfaces anchored to the boundary of a dual AdS space.  ...  property that the boundaries of nearby balls intersect at two points.  ... 
arXiv:1812.06985v1 fatcat:l4uhvz3pczeyjn3qfu6u3laisq

The dual of non-extremal area: differential entropy in higher dimensions

Vijay Balasubramanian, Charles Rabideau
2020 Journal of High Energy Physics  
Then we propose a new formula in terms of an integral of shape derivatives of the entanglement entropy of ball shaped regions.  ...  The Ryu-Takayanagi formula relates entanglement entropy in a field theory to the area of extremal surfaces anchored to the boundary of a dual AdS space.  ...  VB and CR acknowledge support from the Simons Foundation (# 385592, VB) through the It From Qubit Simons Collaboration, and the US Department of Energy contract # FG02-05ER-41367.  ... 
doi:10.1007/jhep09(2020)051 fatcat:tceambvolbcelojmzgsycck2uq

Dichromatic State Sum Models for Four-Manifolds from Pivotal Functors

Manuel Bärenz, John Barrett
2017 Communications in Mathematical Physics  
A family of invariants of smooth, oriented four-dimensional manifolds is defined via handle decompositions and the Kirby calculus of framed link diagrams.  ...  Derivations of state space dimensions of TQFTs arising from the state sum model agree with recent calculations of ground state degeneracies in Walker-Wang models.  ...  participants of the Oxford "TQFTea seminar" and the workshop "Higher TQFT and categorical quantum mechanics" at the Erwin Schrödinger Institute in Vienna for helpful discussions and correspondence.  ... 
doi:10.1007/s00220-017-3012-9 fatcat:2zqstilyl5gcrkuheqghd63teq

Generalised Hermite constants, Voronoi theory and heights on flag varieties

Bertrand Meyer
2009 Bulletin de la Société Mathématique de France  
This paper explores the study of the general Hermite constant associated to the general linear group and its irreducible representations, as defined by T. Watanabe in [Wat00] .  ...  To that end, a height, which naturally applies to flag varieties, is built and notions of perfection and eutaxy characterising extremality are introduced.  ...  Namely, this basis where (e i ) 1 i n is a basis of E and T a Young tableau, i.e. a diagram of shape λ, inscribed with numbers chosen in [[1, n]], the inscription of which are strictly increasing along  ... 
doi:10.24033/bsmf.2571 fatcat:js5lafwyvraddo7wkpelclfcza

PDE-Driven Adaptive Morphology for Matrix Fields [chapter]

Bernhard Burgeth, Michael Breuß, Luis Pizarro, Joachim Weickert
2009 Lecture Notes in Computer Science  
Numerical experiments performed on synthetic and realworld data confirm the gap-closing and line-completing qualities of the proposed method.  ...  Recently, morphological partial differential equations (PDEs) for dilation and erosion known for grey scale images have been extended to three dimensional fields of symmetric positive definite matrices  ...  Acknowledgement The financial support of the German Academic Exchange Service (DAAD) for the third author is gratefully acknowledged.  ... 
doi:10.1007/978-3-642-02256-2_21 fatcat:3h6iql2gvndi3ass7pftslfogq

BMO on shapes and sharp constants [article]

Galia Dafni, Ryan Gibara
2019 arXiv   pre-print
We consider a very general definition of BMO on a domain in R^n, where the mean oscillation is taken with respect to a basis of shapes, i.e. a collection of open sets covering the domain.  ...  For the standard bases of shapes consisting of balls or cubes (classic BMO), or rectangles (strong BMO), we review known results, such as the boundedness of rearrangements and its consequences.  ...  Acknowledgements The authors would like to thank Almut Burchard for discussions that initiated much of the investigation that lead to this paper.  ... 
arXiv:1905.00144v1 fatcat:ocvj3wj3qrcoflblvfa6burowe
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