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Now showing items 113 - 128 of 24623

  • Extremum of geometric functionals involving general L p $L_{p}$ -projection bodies

    Wang, Weidong   Wang, Jianye  

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  • pl dual curvature measures

    Erwin Lutwak   Deane Yang   Gaoyong Zhang  

    Abstract A new family of geometric Borel measures on the unit sphere is introduced. Special cases include the L p surface area measures (which extend the classical surface area measure of Aleksandrov and Fenchel & Jessen) and L p -integral curvature (which extends Alkesandrov's integral curvature) in the L p Brunn–Minkowski theory. It also includes the dual curvature measures (which are the duals of Federer's curvature measures) in the dual Brunn–Minkowski theory. This partially unifies the classical theory of mixed volumes and the newer theory of dual mixed volumes.
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  • Two weight L p estimates for paraproducts in non-homogeneous settings

    Lai, Jingguo   Treil, Sergei  

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  • Weighted L p estimates for rough bi-parameter Fourier integral operators

    Hong, Qing   Lu, Guozhen  

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  • Torres-Corzo J, Rangel-Castilla L, Nakaji P (eds) Neuroendoscopic surgery

    Cappabianca   Paolo  

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  • On the universal function for weighted spaces $L^{p}_{\mu}[0,1]$ , $p\geq 1$

    Grigoryan, Martin; Grigoryan, Tigran; Sargsyan, Artsrun  

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  • Lipscomb's L(A) Space Fractalized in l (p)(A)

    Mihail, Alexandru   Miculescu, Radu  

    In this paper, by using some of our new results concerning the shift space for an infinite IFS (see A. Mihail and R. Miculescu, The shift space for an infinite iterated function system, Math. Rep. Bucur. 11 (2009), 21-32), we show that, for an infinite set A, the embedded version of the Lipscomb space L(A) in l (p) (A), , with the metric induced from l (p) (A), denoted by , is the attractor of an infinite iterated function system comprising affine transformations of l (p) (A). In this way we provide a generalization of the positive answer that we gave to an open problem of J.C. Perry (see Lipscomb's universal space is the attractor of an infinite iterated function system, Proc. Amer. Math. Soc. 124 (1996), 2479-2489) in one of our previous works (see R. Miculescu and A. Mihail, Lipscomb space omega (A) is the attractor of an infinite IFS containing affine transformations of l (2)(A), Proc. Amer. Math. Soc. 136 (2008), 587-592). Moreover, as a byproduct, we provide a generalization of Corollary 15 from Perry's paper by proving that is a closed subset of l (p) (A).
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  • How the Classics Made Shakespeare || 6. S. P. Q. L.

    Bate, Jonathan  

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  • Behaviour of $L_{q}$ norms of the $\operatorname {sinc}_{p}$ function

    Edmunds, David E.   Melkonian, Houry  

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  • One-sided $L^p$ norm and best approximation in one-sided $L^p$ norm

    Yang   C.  

    Let f be a p integrable function on K, a compact subset of R, and mu a sigma-finite positive measure. For p > 1, the one-sided L(P) norm is defined as follows: parallel to f parallel to(p) = max {integral ({f>0}) (vertical bar f vertical bar pd mu))(1/p) , (integral(vertical bar f vertical bar pd mu)({f>0}))(1/p)} We first show that the above definition is indeed a norm and then study the best approximation in the one-sided LP norms. Among others, characterization and uniqueness of best approximation are discussed.
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  • Large deviations for high-dimensional random projections of l(p)(n)-balls

    Alonso-Gutierrez, David   Prochno, Joscha   Thaele, Christoph  

    The paper provides a description of the large deviation behavior for the Euclidean norm of projections of l(p)(n)-balls to high-dimensional random subspaces. More precisely, for each integer n >=3D 1, let k(n) is an element of{1,, n-1}, E-(n) be a uniform random k(n)-dimensional subspace of R-n and X-(n) be a random point that is uniformly distributed in the l(p)(n)-ball of R-n for some p is an element of[1, infinity]. Then the Euclidean norms parallel to P-E((n)) X-(n)parallel to(2) of the orthogonal projections are shown to satisfy a large deviation principle as the space dimension n tends to infinity. Its speed and rate function are identified, making thereby visible how they depend on p and the growth of the sequence of subspace dimensions k(n). As a key tool we prove a probabilistic representation of parallel to P-E((n)) X-(n)parallel to(2) which allows us to separate the influence of the parameter p and the subspace dimension k(n). (C) 2018 Elsevier Inc. All rights reserved.
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  • On the Null Space Constant for l(p) Minimization

    Chen, Laming   Gu, Yuantao  

    The literature on sparse recovery often adopts the l(p) "norm" (p is an element of [0,1]) as the penalty to induce sparsity of the signal satisfying an underdetermined linear system. The performance of the corresponding l(p) minimization problem can be characterized by its null space constant. In spite of the NP-hardness of computing the constant, its properties can still help in illustrating the performance of l(p) minimization. In this letter, we show the strict increase of the null space constant in the sparsity level k and its continuity in the exponent p. We also indicate that the constant is strictly increasing in p with probability 1 when the sensing matrix A is randomly generated. Finally, we show how these properties can help in demonstrating the performance of l(p) minimization, mainly in the relationship between the the exponent p and the sparsity level k.
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  • \\(p\\)-Adic automorphic\\(L\\)-functions on\\(\\text {GL}(3)\\)

    Geroldinger   Angelika  

    We construct \(p\)-adic \(L\)-functions attached to cohomological cuspidal automorphic representations \(\pi \) of \(\text {GL}_3\) over \({\mathbb Q}\). These functions will be defined as \(p\)-adic Mellin transforms of \(h\)-admissible measures. Our strategy is to generalize the construction of \(p\)-adic \(L\)-functions given in Mahnkopf (Compos. Math. 124(3):253–304, 2000) for cuspidal representations of \(\text {GL}_3\) which are cohomological with respect to the trivial coefficient system. This mainly relies on Harder’s method of computing bounds for the denominators of certain Eisenstein cohomology classes, cf. Harder (Kohomologie Arithmetischer Gruppen, 1987). Finally, we establish a functional equation for the \(p\)-adic \(L\)-functions. This, in particular, requires the construction of \(p\)-adic \(L\)-functions attached to the critical integers on the right-hand side of the functional equation.
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  • A new characterization of L (2)(p) by NSE

    Jiang, Qinhui   Shao, Changguo  

    In this paper we give a new characterization of simple group L (2)(p) with p a prime by both its order and n s e(L (2)(p)), the set of numbers of elements of L (2)(p) with the same order.
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  • STABILITY OF UNCONDITIONAL SCHAUDER DECOMPOSITIONS IN l(p) SPACES

    Marchenko, Vitalii  

    We use the best constants in the Khintchine inequality to generalise a theorem of Kato ['Similarity for sequences of projections', Bull. Amer. Math. Soc. 73(6) (1967), 904-905] on similarity for sequences of projections in Hilbert spaces to the case of unconditional Schauder decompositions in l(p) spaces. We also sharpen a stability theorem of Vizitei ['On the stability of bases of subspaces in a Banach space', in: Studies on Algebra and Mathematical Analysis, Moldova Academy of Sciences (Kartja Moldovenjaska, Chisinau, 1965), 32-44; (in Russian)] in the case of unconditional Schauder decompositions in any Banach space.
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  • Facial expression recognition using\({l}_{p}\)-norm MKL multiclass-SVM

    Zhang, Xiao; Mahoor, Mohammad H.; Mavadati, S. Mohammad  

    Automatic recognition of facial expressions is an interesting and challenging research topic in the field of pattern recognition due to applications such as human-machine interface design and developmental psychology. Designing classifiers for facial expression recognition with high reliability is a vital step in this research. This paper presents a novel framework for person-independent expression recognition by combining multiple types of facial features via multiple kernel learning (MKL) in multiclass support vector machines (SVM). Existing MKL-based approaches jointly learn the same kernel weights with l(1)-norm constraint for all binary classifiers, whereas our framework learns one kernel weight vector per binary classifier in the multiclass-SVM with l(p)-norm constraints (p =3D 1), which considers both sparse and non-sparse kernel combinations within MKL. We studied the effect of lp-norm MKL algorithm for learning the kernel weights and empirically evaluated the recognition results of six basic facial expressions and neutral faces with respect to the value of "p". In our experiments, we combined two popular facial feature representations, histogram of oriented gradient and local binary pattern histogram, with two kernel functions, the heavy-tailed radial basis function and the polynomial function. Our experimental results on the CK+, MMI and GEMEP-FERA face databases as well as our theoretical justification show that this framework outperforms the state-of-the-art methods and the Simple MKL-based multiclass-SVM for facial expression recognition.
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