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Page 973 of American Mathematical Society. Proceedings of the American Mathematical Society Vol. 12, Issue 6
[page]

1961
*
American Mathematical Society. Proceedings of the American Mathematical Society
*

Let V

*and*V’ be real or complex*linear*spaces*and*F a separating family of*linear*functionals on V’. ... Denote by #’ the weak-F*topology*on V’;*and*let S be a subset of V which spans it linearly, S’ a t/-compact subset of V’, $ the set of*linear*transformations of V into V’ which map S into S’,*and*¢ the ...##
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Page 501 of Mathematical Reviews Vol. 57, Issue 2
[page]

1979
*
Mathematical Reviews
*

R. 3810
Some new

*linear**topological*spaces (of operators), with trivial*and*non-trivial duals. Nanta Math. 10 (1977), no. 1, 72-76. ... Two compatible locally convex (LC)*topologies*7, 7, on E are termed G-equivalent if the spaces P(E, 7), G)*and*L((E, 72), G) of continuous*linear*maps coincide. ...##
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Comparison of ReLU and linear saturated activation functions in neural network for universal approximation

2019
*
2019 22nd International Conference on Process Control (PC19)
*

This paper aims to compare two

doi:10.1109/pc.2019.8815057
fatcat:dcl5l4dglrewtjpnjk6t346goq
*types*of*linear*based functions -symmetric*linear*saturated function*and*the rectifier*linear*unit (ReLU) function as activation functions of the feedforward neural network ...*Topologies*with one hidden layer*and*the combination of defined quantities of hidden layer neurons in the feedforward neural network are used. ... To be more specific, a comparison of symmetric*linear*saturated*and*rectified*linear*unit activation functions for the purposes of nonlinear system*approximation*is examined. ...##
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Linear-size approximations to the vietoris-rips filtration

2012
*
Proceedings of the 2012 symposuim on Computational Geometry - SoCG '12
*

Use packing arguments to get

doi:10.1145/2261250.2261286
dblp:conf/compgeom/Sheehy12
fatcat:a2hiocle7zdktpybotlj7uitwe
*linear*size. Union trick eliminates zigzag. The Future Distance to a measure? Other*types*of simplification. ... Use packing arguments to get*linear*size. Union trick eliminates zigzag. The Future Distance to a measure? Other*types*of simplification. Construct the net-tree in O(n log n) time. ... Persistence Diagrams describe the changes in*topology*corresponding to changes in scale. d ∞ B = max i |p i − q i | ∞ Bottleneck Distance In*approximate*persistence diagrams, birth*and*death times differ ...##
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Scaling the Topology of Symmetric, Second-Order Planar Tensor Fields
[chapter]

2003
*
Mathematics and Visualization
*

This results in a simplified

doi:10.1007/978-3-642-55787-3_10
fatcat:nyzpi3wnrfhx3hgeigjtjlxf74
*topology**and*a clarified depiction, though globally maintaining the qualitative properties of the original data. ... The whole process can be seen as a scaling of the*topological*information that neglects details of small scale*and*only retains their structural aspect in the large. ... Furthermore, we would like to thank Tom Bobach, Holger Burbach, Stefan Clauss, Jan Frey, Aragorn Rockstroh, René Schätzl*and*Thomas Wischgoll for their programming efforts. ...##
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Approximation Properties of Locally Convex Spaces and the Problem of Uniqueness of the Trace of a Linear Operator
[article]

2011
*
arXiv
*
pre-print

A number of

arXiv:1108.1721v1
fatcat:7hqa4knnwzfwbay2xwwxwi7dwy
*approximation*-*type*properties of locally convex spaces*and*relations between these properties are considered in Section 3. ... We prove that the uniqueness problem has a positive solution if E possesses the "bounded*approximation*property." Preliminary information*and*results are presented in Section 2. ...*Approximation*-*type*properties of locally convex spaces 3.1. ...##
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Page 4967 of Mathematical Reviews Vol. , Issue 83m
[page]

1983
*
Mathematical Reviews
*

Studying the duality between Lp.s.

*and*locally convex*linear**topological*spaces (1.c.t.s.) ... Author’s summary: “We consider some classes of*linear*pseudo-*topological*spaces (1.p.s.) which are important both in the theory itself*and*in its applications. ...##
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Page 4261 of Mathematical Reviews Vol. , Issue 87h
[page]

1987
*
Mathematical Reviews
*

In Part 1, Cristescu presents some classes of

*linear*operators on ordered*linear*spaces of various*types*, especially*topological*ordered*linear*spaces. ... Kajiwara, On the trace on C*-crossed products (Japanese) (pp. 110-117); Hideo Takemoto,*Approximate*innerness of positive*linear*maps of fac- tors of*type*II (pp. 118-127); Masamichi Hamana, Injective ...##
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A Weierstrass approximation theorem for topological vector spaces

1984
*
Journal of Approximation Theory
*

Before stating the main theorem let us make the following definition: A sequence of

doi:10.1016/0021-9045(84)90049-2
fatcat:kf77dmajpnbvhciotcv4sejnha
*linear*operators (t,) on a*topological*vector space has the Grothendieck*approximation*propety if*and*only if (1) each ... Let E*and*F be real Hausdorff*topological*vector spaces. ... Before stating the main theorem let us make the following definition: A sequence of*linear*operators (t,) on a*topological*vector space has the Grothendieck*approximation*propety if*and*only if (1) each ...##
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On the computational algorithms for time-lag optimal control problems

1985
*
Bulletin of the Australian Mathematical Society
*

Chapters I I , I I I , IV,

doi:10.1017/s0004972700009989
fatcat:p46unlbyunaapma2t3l6cpi2jy
*and*V deal with problems of the f i r s t*type**and*Chapter VI deals with problems of the second*type*. ... The*type*of convergence of this algorithm is as follows: ... of L^*and*in the almost everywhere*topology*. ...##
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Countable approximation of topological G -manifolds: Compact Lie groups G

2018
*
Topology and its Applications
*

(Compact)

doi:10.1016/j.topol.2017.11.001
fatcat:un7tc5b7lvar5hftlg3q6r32mm
*topological*G-manifolds have the G-homotopy*type*of (finite-dimensional) countable G-CW complexes (2.5). ... This partly generalizes Elfving's theorem for locally*linear*G-manifolds [Elf96], wherein the Lie group G is*linear*(such as compact). ... Elmar Vogt (Freie U Berlin) excited me further into classical*topology*(ANRs*and*Lemma 4.1). ...##
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Page 124 of American Mathematical Society. Bulletin of the American Mathematical Society Vol. 59, Issue 2
[page]

1953
*
American Mathematical Society. Bulletin of the American Mathematical Society
*

Both of these are special cases of

*linear**topological*spaces, spaces which are*linear**and*have a*topology*in which addi- tion*and*multiplication by real numbers is continuous,*and*which are determined ... For ¥* we have two*types*of weak convergence, that induced by %*and*that by ¥**. ...##
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On some generalizations of Newton non-degeneracy for hypersurface singularities

2010
*
Journal of the London Mathematical Society
*

Roughly speaking, an isolated hypersurface singularity is called

doi:10.1112/jlms/jdq011
fatcat:qttuutxdvbdhtbz5xkeoqndwhm
*topologically*Newton-non-degenerate (tNnd) if the local embedded*topological*singularity*type*can be restored from a collection of Newton ... For such singularities the classical formulas for the Milnor number*and*the zeta function of the Nnd hypersurface are generalized. ... Assume also that the directional*approximations*are of*linear**type*[Kerner06] , i.e. any representative of the*type*of C (i) can be brought to Γ i by*linear*transformations only. ...##
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Topology Aware Stream Surfaces

2010
*
Computer graphics forum (Print)
*

We present an algorithm that allows stream surfaces to recognize

doi:10.1111/j.1467-8659.2009.01672.x
fatcat:3yqi2mmhcnevngqs2y7mui54zu
*and*adapt to vector field*topology*. ... Standard stream surface algorithms either refine the surface uncontrolled near critical points which slows down the computation considerably*and*may lead to a poor surface*approximation*. ... Acknowledgments We wish to thank Markus Rütten from German Aerospace Center (DLR) in Göttingen for the Delta Wing dataset,*and*Ronald Peikert*and*VA Tech for the Draft Tube dataset. ...##
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Page 39 of American Mathematical Society. Proceedings of the American Mathematical Society Vol. 11, Issue 1
[page]

1960
*
American Mathematical Society. Proceedings of the American Mathematical Society
*

The answer is affirmative for the following

*types*of domain*and*range spaces: (i) both A*and*B are Hilbert spaces (see [2, p. 204]), (ii) both A*and*B are C[a, 6] (see [2, p. 222] or [3]), (iii) there ... Can T be*approximated*arbitrarily close in norm by bounded*linear*transformations whose ranges are finite dimen- sional (see [1, p. 49])? ...
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