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Special Functions
, 2013
"... The computation of special functions has important implications throughout engineering and the physical sciences. Nonlinear special functions include the solutions of integrable partial differential equations and the Painleve ́ transcendents. Many problems in water wave theory, nonlinear optics and ..."
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The computation of special functions has important implications throughout engineering and the physical sciences. Nonlinear special functions include the solutions of integrable partial differential equations and the Painleve ́ transcendents. Many problems in water wave theory, nonlinear optics
THE SPECIAL FUNCTION
, 2005
"... Abstract. The purpose of the work is to furnish a complete study of a discrete and special function, discovered by the author and named with the Arabian letter � �(Shin) 1. It includes three other papers, published in the international journal ”Kragujevac Journal of Mathematics”. The methods, the te ..."
Abstract
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Cited by 2 (2 self)
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Abstract. The purpose of the work is to furnish a complete study of a discrete and special function, discovered by the author and named with the Arabian letter � �(Shin) 1. It includes three other papers, published in the international journal ”Kragujevac Journal of Mathematics”. The methods
Smooth minimization of nonsmooth functions
- Math. Programming
, 2005
"... In this paper we propose a new approach for constructing efficient schemes for nonsmooth convex optimization. It is based on a special smoothing technique, which can be applied to the functions with explicit max-structure. Our approach can be considered as an alternative to black-box minimization. F ..."
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Cited by 523 (1 self)
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In this paper we propose a new approach for constructing efficient schemes for nonsmooth convex optimization. It is based on a special smoothing technique, which can be applied to the functions with explicit max-structure. Our approach can be considered as an alternative to black-box minimization
Greedy Function Approximation: A Gradient Boosting Machine
- Annals of Statistics
, 2000
"... Function approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest{descent minimization. A general gradient{descent \boosting" paradigm is developed for additi ..."
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Cited by 1000 (13 self)
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for additive expansions based on any tting criterion. Specic algorithms are presented for least{squares, least{absolute{deviation, and Huber{M loss functions for regression, and multi{class logistic likelihood for classication. Special enhancements are derived for the particular case where the individual
Special Functions
"... We define here some functions of numbers that you will frequently use in computing practice and theory. factorial function, n! If n is a positive integer, the factorial n! is defined to be n! = n n−1 �2⋅1. So, for example 3! = 3⋅2 ⋅ 1 = 6 ..."
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We define here some functions of numbers that you will frequently use in computing practice and theory. factorial function, n! If n is a positive integer, the factorial n! is defined to be n! = n n−1 �2⋅1. So, for example 3! = 3⋅2 ⋅ 1 = 6
The rate-distortion function for source coding with side information at the decoder
- IEEE Trans. Inform. Theory
, 1976
"... Abstract-Let {(X,, Y,J}r = 1 be a sequence of independent drawings of a pair of dependent random variables X, Y. Let us say that X takes values in the finite set 6. It is desired to encode the sequence {X,} in blocks of length n into a binary stream*of rate R, which can in turn be decoded as a seque ..."
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Cited by 1060 (1 self)
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sequence { 2k}, where zk E %, the reproduction alphabet. The average distorjion level is (l/n) cl = 1 E[D(X,,z&, where D(x, $ 2 0, x E I, 2 E J, is a pre-assigned distortion measure. The special assumption made here is that the decoder has access to the side information {Yk}. In this paper we determine
Topics in special functions
, 2001
"... The authors survey recent results in special functions, particularly the gamma function and the Gaussian hypergeometric function. ..."
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Cited by 11 (2 self)
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The authors survey recent results in special functions, particularly the gamma function and the Gaussian hypergeometric function.
Separation of ownership and control
- JOURNAL OF LAW AND ECONOMICS
, 1983
"... This paper analyzes the survival of organizations in which decision agents do not bear a major share of the wealth effects of their decisions. This is what the literature on large corporations calls separation of âownershipâ and âcontrol.â Such separation of decision and risk bearing functio ..."
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Cited by 1661 (8 self)
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functions is also common to organizations like large professional partnerships, financial mutuals and nonprofits. We contend that separation of decision and risk bearing functions survives in these organizations in part because of the benefits of specialization of management and risk bearing but also
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