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3.1 Signature for Real Vector Spaces.............................. 4
"... The theory of real vector spaces, norms and derivatives of functions between normed vector spaces as required for formal modelling of some physical theories. Created 2004/07/15 ..."
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The theory of real vector spaces, norms and derivatives of functions between normed vector spaces as required for formal modelling of some physical theories. Created 2004/07/15
The HahnBanach Theorem for Real Vector Spaces
, 2011
"... The HahnBanach Theorem is one of the most fundamental results in functional analysis. We present a fully formal proof of two versions of the theorem, one for general linear spaces and another for normed spaces. This development is based on simplytyped classical settheory, as provided by ..."
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Cited by 5 (1 self)
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The HahnBanach Theorem is one of the most fundamental results in functional analysis. We present a fully formal proof of two versions of the theorem, one for general linear spaces and another for normed spaces. This development is based on simplytyped classical settheory, as provided by
The Real Vector Spaces of Finite Sequences are Finite Dimensional
, 2009
"... In this paper we show the finite dimensionality of real linear spaces with their carriers equal R^n. We also give the standard basis of such spaces. For the set R^n we introduce the concepts of linear manifold subsets and orthogonal subsets. The cardinality of orthonormal basis of discussed spaces ..."
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Cited by 3 (2 self)
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In this paper we show the finite dimensionality of real linear spaces with their carriers equal R^n. We also give the standard basis of such spaces. For the set R^n we introduce the concepts of linear manifold subsets and orthogonal subsets. The cardinality of orthonormal basis of discussed
Equivariant Ktheory of real vector spaces and real projective spaces
 TOPOLOGY AND ITS APPLICATIONS 122 (2002) 531–546
, 2002
"... ... (V) of the Thom space of a real vector bundle has been done successfully only under some spinoriality conditions [1], thanks to a clever use of the Atiyah–Singer index theorem (even if G is a finite group). One purpose of this paper is to fill this gap, at least for real vector spaces (considere ..."
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Cited by 5 (2 self)
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... (V) of the Thom space of a real vector bundle has been done successfully only under some spinoriality conditions [1], thanks to a clever use of the Atiyah–Singer index theorem (even if G is a finite group). One purpose of this paper is to fill this gap, at least for real vector spaces
EQUIVARIANT KTHEORY OF FINITE DIMENSIONAL REAL VECTOR SPACES
, 903
"... Abstract. We give a general formula for the equivariant complex Ktheory K ∗ G (V) of a finite dimensional real linear space V equipped with a linear action of a compact group G in terms of the representation theory of a certain double cover of G. Using this general formula, we give explicit computa ..."
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Cited by 5 (0 self)
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computations in various interesting special cases. In particular, as an application we obtain explicit formulas for the Ktheory of C ∗ r (GL(n, R)), the reduced group C*algebra of GL(n, R). Let G be a compact group acting linearly on the real vector space V. In this paper we want to give explicit formulas
Collusionresistant Fingerprints Based on the Use of Superimposed Codes in Real Vector Spaces
"... Abstract—In this work we propose the use of random superimposed codes as sequences for collusionresistant fingerprints. This approach seems to be more suitable in comparison with the use of some other regular sequences (as WBEsequences) against watermark removal attacks. Sphere decoding algorithm ..."
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Abstract—In this work we propose the use of random superimposed codes as sequences for collusionresistant fingerprints. This approach seems to be more suitable in comparison with the use of some other regular sequences (as WBEsequences) against watermark removal attacks. Sphere decoding algorithm is used for tracing traitors. The performance evaluation of the proposed method is presented. Simulation results show a good efficiency of the proposed codes. Index Terms—Digital fingerprints, collusion attacks, superimposed codes, sphere decoding algorithm. I.
ELA NATURAL GROUP ACTIONS ON TENSOR PRODUCTS OF THREE REAL VECTOR SPACES WITH FINITELY MANY ORBITS ∗
"... Abstract. Let G be the direct product of the general linear groups of three real vector spaces U, V, W of dimensions l, m, n (2 ≤ l ≤ m ≤ n<∞). Consider the natural action of G on the tensor product of these spaces. The number of Gorbits in X is finite if and only if l =2andm = 2 or 3. In these ..."
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Abstract. Let G be the direct product of the general linear groups of three real vector spaces U, V, W of dimensions l, m, n (2 ≤ l ≤ m ≤ n<∞). Consider the natural action of G on the tensor product of these spaces. The number of Gorbits in X is finite if and only if l =2andm = 2 or 3
Support Vector Machine Active Learning with Applications to Text Classification
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2001
"... Support vector machines have met with significant success in numerous realworld learning tasks. However, like most machine learning algorithms, they are generally applied using a randomly selected training set classified in advance. In many settings, we also have the option of using poolbased acti ..."
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Cited by 729 (5 self)
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Support vector machines have met with significant success in numerous realworld learning tasks. However, like most machine learning algorithms, they are generally applied using a randomly selected training set classified in advance. In many settings, we also have the option of using pool
A practical guide to support vector classification
, 2010
"... The support vector machine (SVM) is a popular classification technique. However, beginners who are not familiar with SVM often get unsatisfactory results since they miss some easy but significant steps. In this guide, we propose a simple procedure which usually gives reasonable results. ..."
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Cited by 787 (7 self)
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The support vector machine (SVM) is a popular classification technique. However, beginners who are not familiar with SVM often get unsatisfactory results since they miss some easy but significant steps. In this guide, we propose a simple procedure which usually gives reasonable results.
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