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Functions and their basic properties
 JOURNAL OF FORMALIZED MATHEMATICS
, 2003
"... The definitions of the mode Function and the graph of a function are introduced. The graph of a function is defined to be identical with the function. The following concepts are also defined: the domain of a function, the range of a function, the identity function, the composition of functions, the ..."
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Cited by 1336 (32 self)
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The definitions of the mode Function and the graph of a function are introduced. The graph of a function is defined to be identical with the function. The following concepts are also defined: the domain of a function, the range of a function, the identity function, the composition of functions
Reflections on Language.
, 1975
"... This article reviews, and rethinks, a few leading themes of the biolinguistic program since its inception in the early 1950s, at each stage influenced by developments in the biological sciences. The following also discusses how the questions now entering the research agenda develop in a natural way ..."
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Cited by 968 (2 self)
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This article reviews, and rethinks, a few leading themes of the biolinguistic program since its inception in the early 1950s, at each stage influenced by developments in the biological sciences. The following also discusses how the questions now entering the research agenda develop in a natural
Quantum Gravity
, 2004
"... We describe the basic assumptions and key results of loop quantum gravity, which is a background independent approach to quantum gravity. The emphasis is on the basic physical principles and how one deduces predictions from them, at a level suitable for physicists in other areas such as string theor ..."
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Cited by 572 (11 self)
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We describe the basic assumptions and key results of loop quantum gravity, which is a background independent approach to quantum gravity. The emphasis is on the basic physical principles and how one deduces predictions from them, at a level suitable for physicists in other areas such as string
The irreducibility of the space of curves of given genus
 Publ. Math. IHES
, 1969
"... Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k ~ ..."
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Cited by 506 (2 self)
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approach however is closest to Severi's incomplete proof ([Se], Anhang F; the error is on pp. 344345 and seems to be quite basic) and follows a suggestion of Grothendieck for using the result in char. o to deduce the result in char. p. The basis of both Severi's and Grothendieck's ideas
The English Noun Phrase in its Sentential Aspect
 PH.D. DISSERTATION MIT
, 1987
"... This dissertation is a defense of the hypothesis that the noun phrase is headed by a functional element (i.e., "nonlexical" category) D, identified with the determiner. In this way, the structure of the noun phrase parallels that of the sentence, which is headed by Infl(ection), under ass ..."
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Cited by 532 (4 self)
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assumptions now standard within the GovernmentBinding (GB) framework. The central empirical problem addressed is the question of the proper analysis of the socalled "Possing" gerund in English. This construction possesses simultaneously many properties of sentences, and many properties of noun
Theory of Elasticity,
, 1951
"... ABSTRACT The knowledge of the insitu stress field in rock masses is in general of crucial importance in various areas of geoengineering, such as mining or civil underground excavations, hydrocarbon extraction, CO2 storage, hydraulic fracture operations, etc. In the context of the Finite Element ..."
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Cited by 710 (1 self)
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Method, the insitu stress conditions should be incorporated in the analysis following the generation of the FE mesh and prior to the consideration of the actions due to the engineering design The method described in this paper involves basically two steps. In the first one a first estimate
PrivacyPreserving Data Mining
, 2000
"... A fruitful direction for future data mining research will be the development of techniques that incorporate privacy concerns. Specifically, we address the following question. Since the primary task in data mining is the development of models about aggregated data, can we develop accurate models with ..."
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Cited by 844 (3 self)
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A fruitful direction for future data mining research will be the development of techniques that incorporate privacy concerns. Specifically, we address the following question. Since the primary task in data mining is the development of models about aggregated data, can we develop accurate models
What Can Economists Learn from Happiness Research?
 FORTHCOMING IN JOURNAL OF ECONOMIC LITERATURE
, 2002
"... Happiness is generally considered to be an ultimate goal in life; virtually everybody wants to be happy. The United States Declaration of Independence of 1776 takes it as a selfevident truth that the “pursuit of happiness” is an “unalienable right”, comparable to life and liberty. It follows that e ..."
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Cited by 545 (24 self)
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Happiness is generally considered to be an ultimate goal in life; virtually everybody wants to be happy. The United States Declaration of Independence of 1776 takes it as a selfevident truth that the “pursuit of happiness” is an “unalienable right”, comparable to life and liberty. It follows
Compressive sampling
, 2006
"... Conventional wisdom and common practice in acquisition and reconstruction of images from frequency data follow the basic principle of the Nyquist density sampling theory. This principle states that to reconstruct an image, the number of Fourier samples we need to acquire must match the desired res ..."
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Cited by 1441 (15 self)
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Conventional wisdom and common practice in acquisition and reconstruction of images from frequency data follow the basic principle of the Nyquist density sampling theory. This principle states that to reconstruct an image, the number of Fourier samples we need to acquire must match the desired
Predictive reward signal of dopamine neurons
 Journal of Neurophysiology
, 1998
"... Schultz, Wolfram. Predictive reward signal of dopamine neurons. is called rewards, which elicit and reinforce approach behavJ. Neurophysiol. 80: 1–27, 1998. The effects of lesions, receptor ior. The functions of rewards were developed further during blocking, electrical selfstimulation, and drugs ..."
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Cited by 747 (12 self)
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of rewards, and rons show phasic activations after primary liquid and food rewards and conditioned, rewardpredicting visual and auditory stimuli. the availability of rewards determines some of the basic They show biphasic, activationdepression responses after stimuli parameters of the subject’s life
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