Results 231 to 240 of about 255,069 (248)

Slice Hyperholomorphic Functions

2016
In the first section of this chapter we give a brief survey of the theory of slice hyperholomorphic functions, and we provide the basic results needed in the sequel. The theory is much more developed and we refer the reader to the Introduction to Part II of the present work for references. Then, the Sections from 6.2 to 6.5 focus on the functions slice
Daniel Alpay, Fabrizio Colombo, Irene Sabadini   +2 more
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Understanding function behaviors through program slicing

WPC '96. 4th Workshop on Program Comprehension, 2002
We present conditioned slicing as a general slicing framework for program comprehension. A conditioned slice consists of a subset of program statements which preserves the behavior of the original program with respect to a set of program executions. The set of initial states of the program that characterize these executions is specified in terms of a ...
A. DE LUCIA, FASOLINO, ANNA RITA, M. MUNRO   +2 more
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Adaptive slicing for functional slice inverse regression

Statistical Papers
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zheng, Linjuan, Liang, Beiting, Wang, Guochang   +2 more
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Rational Slice Hyperholomorphic Functions

2016
Rational functions play an important role in linear system theory, and in the noncommutative case we mention in particular the works [225, 264, 265]. We also mention [65], which is set in the framework of noncommutative probability. There the approach uses a topological algebra of a very special structure (dual of a countably normed nuclear space, with
Daniel Alpay, Fabrizio Colombo, Irene Sabadini   +2 more
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Slice Regular Functions: Algebra

2016
This chapter contains the definition and some basic results on slice regular functions. In particular, we discuss the subclass of slice regular intrinsic functions which possess additional properties. This subclass contains the transcendental functions like the quaternionic exponential, sine and cosine. We also introduce a suitable multiplication and a
Fabrizio Colombo, Irene Sabadini, Daniele C. Struppa   +2 more
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Slice Regular Functions: Analysis

2016
In this chapter we study the analytic properties of slice regular functions. We start by illustrating the Cauchy and Schwarz integral formulas as well as some consequences. Then we prove a version of the Riemann mapping theorem, we discuss the properties of the zeros of slice regular functions and the Ehrenpreis-Malgrange lemma.
Fabrizio Colombo, Irene Sabadini, Daniele C. Struppa   +2 more
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Sheaves of slice regular functions

Mathematische Nachrichten, 2012
AbstractSlice regular functions have been introduced in 20 as solutions of a special partial differential operator with variable coefficients. As such they do not naturally form a sheaf. In this paper we use a modified definition of slice regularity, see 21, to introduce the sheaf of slice regular functions with values in in the algebra of quaternions ...
COLOMBO, FABRIZIO, SABADINI, IRENE MARIA, D. C. Struppa   +2 more
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Robust functional sliced inverse regression

Statistical Papers, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Guochang, Zhou, Jianjun, Wu, Wuqing, Chen, Min   +3 more
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Influence Functions for Sliced Inverse Regression

Scandinavian Journal of Statistics, 2005
The sliced inverse regression is a technique of estimation of the best linear index coefficients \(\beta_i\) in a nonparametric regression model \(y=f(\beta_1x,\dots,\beta_k x,\varepsilon)\), where \(y\) is the response, \(x\) is the vector of regressors, \(f\) is an unknown regression function, and \(\varepsilon\) is an error term.
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Functional sliced inverse regression analysis

Statistics, 2003
Most of the usual multivariate methods have been extended to the context of functional data analysis. Our contribution concerns the study of sliced inverse regression (SIR) when the response variable is real but the regressor is a function. In the first part, we show how the relevant properties of SIR remain essentially the same in the functional ...
L. Ferré, A. F. Yao
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