9,298 research outputs found
Polar Varieties, Real Equation Solving and Data-Structures: The hypersurface case
In this paper we apply for the first time a new method for multivariate
equation solving which was developed in \cite{gh1}, \cite{gh2}, \cite{gh3} for
complex root determination to the {\em real} case. Our main result concerns the
problem of finding at least one representative point for each connected
component of a real compact and smooth hypersurface. The basic algorithm of
\cite{gh1}, \cite{gh2}, \cite{gh3} yields a new method for symbolically solving
zero-dimensional polynomial equation systems over the complex numbers. One
feature of central importance of this algorithm is the use of a
problem--adapted data type represented by the data structures arithmetic
network and straight-line program (arithmetic circuit). The algorithm finds the
complex solutions of any affine zero-dimensional equation system in non-uniform
sequential time that is {\em polynomial} in the length of the input (given in
straight--line program representation) and an adequately defined {\em geometric
degree of the equation system}. Replacing the notion of geometric degree of the
given polynomial equation system by a suitably defined {\em real (or complex)
degree} of certain polar varieties associated to the input equation of the real
hypersurface under consideration, we are able to find for each connected
component of the hypersurface a representative point (this point will be given
in a suitable encoding). The input equation is supposed to be given by a
straight-line program and the (sequential time) complexity of the algorithm is
polynomial in the input length and the degree of the polar varieties mentioned
above.Comment: Late
Polar Varieties and Efficient Real Elimination
Let be a smooth and compact real variety given by a reduced regular
sequence of polynomials . This paper is devoted to the
algorithmic problem of finding {\em efficiently} a representative point for
each connected component of . For this purpose we exhibit explicit
polynomial equations that describe the generic polar varieties of . This
leads to a procedure which solves our algorithmic problem in time that is
polynomial in the (extrinsic) description length of the input equations and in a suitably introduced, intrinsic geometric parameter, called
the {\em degree} of the real interpretation of the given equation system .Comment: 32 page
Polar Varieties and Efficient Real Equation Solving: The Hypersurface Case
The objective of this paper is to show how the recently proposed method by
Giusti, Heintz, Morais, Morgenstern, Pardo \cite{gihemorpar} can be applied to
a case of real polynomial equation solving. Our main result concerns the
problem of finding one representative point for each connected component of a
real bounded smooth hypersurface. The algorithm in \cite{gihemorpar} yields a
method for symbolically solving a zero-dimensional polynomial equation system
in the affine (and toric) case. Its main feature is the use of adapted data
structure: Arithmetical networks and straight-line programs. The algorithm
solves any affine zero-dimensional equation system in non-uniform sequential
time that is polynomial in the length of the input description and an
adequately defined {\em affine degree} of the equation system. Replacing the
affine degree of the equation system by a suitably defined {\em real degree} of
certain polar varieties associated to the input equation, which describes the
hypersurface under consideration, and using straight-line program codification
of the input and intermediate results, we obtain a method for the problem
introduced above that is polynomial in the input length and the real degree.Comment: Late
The intrinsic complexity of parametric elimination methods
This paper is devoted to the complexity analysis of a particular property,
called "algebraic robustness" owned by all known symbolic methods of parametric
polynomial equation solving (geometric elimination). It is shown that any
parametric elimination procedure which owns this property must neccessarily
have an exponential sequential time complexity.Comment: LaTeX, 12 pages. To appear in Proc. of WAIT'97, Buenos Aires,
Argentina, 199
Laughter as a Priming Agent for Change
The purpose of this study was to analyze the importance of laughter as a factor in influencing employee job satisfaction ratings. The Job Satisfaction Survey (Spector, 1985, 1997) and pulses of laughter were used in this study. To explore the relationship between laughter and job satisfaction, results of the Job Satisfaction Survey (Spector, 1994) were collected quarterly (four times a year) for three consecutive years, beginning six months prior to the start of the two-year study and six months post. The study sample was composed of 545 employees (34% male, 66% female) operating out of 10 employee-owned retail chain locations across Midwestern United States. A quasi-experimental, time-series research model, utilizing a one-way repeated measure multivariate analysis of variance (MANOVA) was used in this study. The MANOVA determined significant differences existed. Further studies should be carried out in different settings to shed light on the versatility of laughter on job satisfaction and laughter pulses as a means of non-participatory intervention.
Keywords: job satisfaction, supraliminal laughter, occupational stress, employee assistance program (EAP), mental health, counseling, priming, non-participatory interventions, counselor educatio
Spirituality in late adulthood
MacDonald\u27s Expressions of Spirituality Inventory was used to examine spirituality in late adulthood using a sample of 30 people (22 women, 8 men) whose mean age was 72.6 yr. While average scores are higher on scales measuring spiritual and religious beliefs and practices for the sample than for a standardization group of undergraduate students with a mean age of 21.0 yr., means are lower on scales measuring paranormal beliefs. Low scores on death anxiety are correlated only with Existential Well-being and age. And, while some religious behaviors such as frequent religious practice, prayer, and church attendance are correlated with some of the dimensions of spirituality, many of the scores on the Expressions of Spirituality Inventory scales are independent of self-reported religious behaviors
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