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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 ...
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. ...
2019 22nd International Conference on Process Control (PC19)
This paper aims to compare two 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. ...doi:10.1109/pc.2019.8815057 fatcat:dcl5l4dglrewtjpnjk6t346goq
Use packing arguments to get 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 ...doi:10.1145/2261250.2261286 dblp:conf/compgeom/Sheehy12 fatcat:a2hiocle7zdktpybotlj7uitwe
Mathematics and Visualization
This results in a simplified 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. ...doi:10.1007/978-3-642-55787-3_10 fatcat:nyzpi3wnrfhx3hgeigjtjlxf74
A number of 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. ...arXiv:1108.1721v1 fatcat:7hqa4knnwzfwbay2xwwxwi7dwy
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. ...
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 ...
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 ... 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 ...doi:10.1016/0021-9045(84)90049-2 fatcat:kf77dmajpnbvhciotcv4sejnha
Chapters I I , I I I , IV, 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. ...doi:10.1017/s0004972700009989 fatcat:p46unlbyunaapma2t3l6cpi2jy
(Compact) 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). ...doi:10.1016/j.topol.2017.11.001 fatcat:un7tc5b7lvar5hftlg3q6r32mm
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 ¥**. ...
Roughly speaking, an isolated hypersurface singularity is called 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. ...doi:10.1112/jlms/jdq011 fatcat:qttuutxdvbdhtbz5xkeoqndwhm
We present an algorithm that allows stream surfaces to recognize 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. ...doi:10.1111/j.1467-8659.2009.01672.x fatcat:3yqi2mmhcnevngqs2y7mui54zu
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 ), (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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