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The complex numbers
 Journal of Formalized Mathematics
, 1990
"... Summary. We define the set C of complex numbers as the set of all ordered pairs z = 〈a,b 〉 where a and b are real numbers and where addition and multiplication are defined. We define the real and imaginary parts of z and denote this by a = ℜ(z), b = ℑ(z). These definitions satisfy all the axioms for ..."
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Cited by 118 (1 self)
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Summary. We define the set C of complex numbers as the set of all ordered pairs z = 〈a,b 〉 where a and b are real numbers and where addition and multiplication are defined. We define the real and imaginary parts of z and denote this by a = ℜ(z), b = ℑ(z). These definitions satisfy all the axioms
The Complex Numbers
"... Summary. We define the set of complex numbers as the set of all ordered pairs z = 〈a, b 〉 where a and b are real numbers and where addition and multiplication are defined. We define the real and imaginary parts of z and denote this by a = ℜ(z), b = ℑ(z). These definitions satisfy all the axioms fo ..."
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Summary. We define the set of complex numbers as the set of all ordered pairs z = 〈a, b 〉 where a and b are real numbers and where addition and multiplication are defined. We define the real and imaginary parts of z and denote this by a = ℜ(z), b = ℑ(z). These definitions satisfy all the axioms
The architecture of complexity
 Proceedings of the American Philosophical Society
, 1962
"... A number of proposals have been advanced in recent years for the development of “general systems theory ” that, abstracting from properties peculiar to physical, biological, or social systems, would be applicable to all of them. 1 We might well feel that, while the goal is laudable, systems of such ..."
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Cited by 772 (1 self)
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A number of proposals have been advanced in recent years for the development of “general systems theory ” that, abstracting from properties peculiar to physical, biological, or social systems, would be applicable to all of them. 1 We might well feel that, while the goal is laudable, systems
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, ..."
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Cited by 845 (12 self)
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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
Error and attack tolerance of complex networks
, 2000
"... Many complex systems display a surprising degree of tolerance against errors. For example, relatively simple organisms grow, persist and reproduce despite drastic pharmaceutical or environmental interventions, an error tolerance attributed to the robustness of the underlying metabolic network [1]. C ..."
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Cited by 1013 (7 self)
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Many complex systems display a surprising degree of tolerance against errors. For example, relatively simple organisms grow, persist and reproduce despite drastic pharmaceutical or environmental interventions, an error tolerance attributed to the robustness of the underlying metabolic network [1
Coupled hidden Markov models for complex action recognition
, 1996
"... We present algorithms for coupling and training hidden Markov models (HMMs) to model interacting processes, and demonstrate their superiority to conventional HMMs in a vision task classifying twohanded actions. HMMs are perhaps the most successful framework in perceptual computing for modeling and ..."
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Cited by 501 (22 self)
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and classifying dynamic behaviors, popular because they offer dynamic time warping, a training algorithm, and a clear Bayesian semantics. However, the Markovian framework makes strong restrictive assumptions about the system generating the signalthat it is a single process having a small number of states
A volumetric method for building complex models from range images,”
 in Proceedings of the 23rd annual conference on Computer graphics and interactive techniques. ACM,
, 1996
"... Abstract A number of techniques have been developed for reconstructing surfaces by integrating groups of aligned range images. A desirable set of properties for such algorithms includes: incremental updating, representation of directional uncertainty, the ability to fill gaps in the reconstruction, ..."
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Cited by 1020 (17 self)
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Abstract A number of techniques have been developed for reconstructing surfaces by integrating groups of aligned range images. A desirable set of properties for such algorithms includes: incremental updating, representation of directional uncertainty, the ability to fill gaps in the reconstruction
1. Extension of Complex Numbers
"... Abstract: Complex numbers are an extension of the real number system and can be written in the form a + bi, where a and b are both real numbers and i = √( 1). The quaternions are just an extension of this complex number form. It was observed that Mixed Numbers are also the extension of complex numb ..."
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Abstract: Complex numbers are an extension of the real number system and can be written in the form a + bi, where a and b are both real numbers and i = √( 1). The quaternions are just an extension of this complex number form. It was observed that Mixed Numbers are also the extension of complex
A standardized set of 260 pictures: Norms for name agreement, image agreement, familiarity, and visual complexity
 JOURNAL OF EXPERIMENTAL PSYCHOLOGY: HUMAN LEARNING AND MEMORY
, 1980
"... In this article we present a standardized set of 260 pictures for use in experiments investigating differences and similarities in the processing of pictures and words. The pictures are blackandwhite line drawings executed according to a set of rules that provide consistency of pictorial represent ..."
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Cited by 663 (1 self)
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representation. The pictures have been standardized on four variables of central relevance to memory and cognitive processing: name agreement, image agreement, familiarity, and visual complexity. The intercorrelations among the four measures were low, suggesting that the) ' are indices of different
The unity and diversity of executive functions and their contributions to complex “Frontal Lobe” tasks: a latent variable analysis
 COGNIT PSYCHOL
, 2000
"... This individual differences study examined the separability of three often postulated executive functions—mental set shifting ("Shifting"), information updating and monitoring ("Updating"), and inhibition of prepotent responses ("Inhibition")—and their roles in complex ..."
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Cited by 696 (9 self)
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This individual differences study examined the separability of three often postulated executive functions—mental set shifting ("Shifting"), information updating and monitoring ("Updating"), and inhibition of prepotent responses ("Inhibition")—and their roles in complex
Results 1  10
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69,889