Results 1  10
of
48,245
A characterization of complex Hilbert spaces
 Bull. London Math. Soc
, 1970
"... Throughout what follows let X # {0} be a complex Banach space with norm   , and let 0$(X) be the Banach algebra of all continuous linear operators mapping X into itself (with norm also denoted by   ). An operator S e 3S{X) will be called Vidavhermitian provided \\I + itS\ \ = l+o(t) as t ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Throughout what follows let X # {0} be a complex Banach space with norm   , and let 0$(X) be the Banach algebra of all continuous linear operators mapping X into itself (with norm also denoted by   ). An operator S e 3S{X) will be called Vidavhermitian provided \\I + itS\ \ = l+o(t) as t
Commutativity up to a factor of bounded operators in complex Hilbert space
 Proc.R.Soc.Lond.,Ser.AMath.Phys.Eng.Sci
"... We explore commutativity up to a factor, AB = λBA, for bounded operators in a complex Hilbert space. Conditions on the possible values of the factor λ are formulated and shown to depend on spectral properties of the operators involved. Commutativity up to a unitary factor is considered for pairs of ..."
Abstract

Cited by 14 (0 self)
 Add to MetaCart
We explore commutativity up to a factor, AB = λBA, for bounded operators in a complex Hilbert space. Conditions on the possible values of the factor λ are formulated and shown to depend on spectral properties of the operators involved. Commutativity up to a unitary factor is considered for pairs
SOME REVERSES OF THE CONTINUOUS TRIANGLE INEQUALITY FOR BOCHNER INTEGRAL OF VECTORVALUED FUNCTIONS IN COMPLEX HILBERT SPACES
, 2004
"... Abstract. Some reverses of the continuous triangle inequality for Bochner integral of vectorvalued functions in complex Hilbert spaces are given. Applications for complexvalued functions are provided as well. 1. ..."
Abstract
 Add to MetaCart
Abstract. Some reverses of the continuous triangle inequality for Bochner integral of vectorvalued functions in complex Hilbert spaces are given. Applications for complexvalued functions are provided as well. 1.
Combining Word Semantics within Complex Hilbert Space for Information Retrieval
"... Abstract. Complex numbers are a fundamental aspect of the mathematical formalism of quantum physics. Quantumlike models developed outside physics often overlooked the role of complex numbers. Specifically, previous models in Information Retrieval (IR) ignored complex numbers. We argue that to adva ..."
Abstract
 Add to MetaCart
complex valued Hilbert spaces, and thus where terms, documents and queries are represented as complexvalued vectors. The proposal consists of integrating distributional semantics evidence within the real component of a term vector; whereas, ontological information is encoded in the imaginary component
The space complexity of approximating the frequency moments
 JOURNAL OF COMPUTER AND SYSTEM SCIENCES
, 1996
"... The frequency moments of a sequence containing mi elements of type i, for 1 ≤ i ≤ n, are the numbers Fk = �n i=1 mki. We consider the space complexity of randomized algorithms that approximate the numbers Fk, when the elements of the sequence are given one by one and cannot be stored. Surprisingly, ..."
Abstract

Cited by 845 (12 self)
 Add to MetaCart
The frequency moments of a sequence containing mi elements of type i, for 1 ≤ i ≤ n, are the numbers Fk = �n i=1 mki. We consider the space complexity of randomized algorithms that approximate the numbers Fk, when the elements of the sequence are given one by one and cannot be stored. Surprisingly
Monotone Complexity
, 1990
"... We give a general complexity classification scheme for monotone computation, including monotone spacebounded and Turing machine models not previously considered. We propose monotone complexity classes including mAC i , mNC i , mLOGCFL, mBWBP , mL, mNL, mP , mBPP and mNP . We define a simple ..."
Abstract

Cited by 2825 (11 self)
 Add to MetaCart
We give a general complexity classification scheme for monotone computation, including monotone spacebounded and Turing machine models not previously considered. We propose monotone complexity classes including mAC i , mNC i , mLOGCFL, mBWBP , mL, mNL, mP , mBPP and mNP . We define a
The particel swarm: Explosion, stability, and convergence in a multidimensional complex space
 IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTION
"... The particle swarm is an algorithm for finding optimal regions of complex search spaces through interaction of individuals in a population of particles. Though the algorithm, which is based on a metaphor of social interaction, has been shown to perform well, researchers have not adequately explained ..."
Abstract

Cited by 852 (10 self)
 Add to MetaCart
The particle swarm is an algorithm for finding optimal regions of complex search spaces through interaction of individuals in a population of particles. Though the algorithm, which is based on a metaphor of social interaction, has been shown to perform well, researchers have not adequately
A theory of shape by space carving
 In Proceedings of the 7th IEEE International Conference on Computer Vision (ICCV99), volume I, pages 307– 314, Los Alamitos, CA
, 1999
"... In this paper we consider the problem of computing the 3D shape of an unknown, arbitrarilyshaped scene from multiple photographs taken at known but arbitrarilydistributed viewpoints. By studying the equivalence class of all 3D shapes that reproduce the input photographs, we prove the existence of a ..."
Abstract

Cited by 566 (14 self)
 Add to MetaCart
of a special member of this class, the photo hull, that (1) can be computed directly from photographs of the scene, and (2) subsumes all other members of this class. We then give a provablycorrect algorithm, called Space Carving, for computing this shape and present experimental results on complex
Spacetime block codes from orthogonal designs
 IEEE Trans. Inform. Theory
, 1999
"... Abstract — We introduce space–time block coding, a new paradigm for communication over Rayleigh fading channels using multiple transmit antennas. Data is encoded using a space–time block code and the encoded data is split into � streams which are simultaneously transmitted using � transmit antennas. ..."
Abstract

Cited by 1524 (42 self)
 Add to MetaCart
space–time block codes for both real and complex constellations for any number of transmit antennas. These codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as PAM. For an arbitrary complex constellation such as PSK
Mean shift: A robust approach toward feature space analysis
 In PAMI
, 2002
"... A general nonparametric technique is proposed for the analysis of a complex multimodal feature space and to delineate arbitrarily shaped clusters in it. The basic computational module of the technique is an old pattern recognition procedure, the mean shift. We prove for discrete data the convergence ..."
Abstract

Cited by 2395 (37 self)
 Add to MetaCart
A general nonparametric technique is proposed for the analysis of a complex multimodal feature space and to delineate arbitrarily shaped clusters in it. The basic computational module of the technique is an old pattern recognition procedure, the mean shift. We prove for discrete data
Results 1  10
of
48,245