Heuristic methods for operations with algebraic numbers

Author(s):  
Keith O. Geddes ◽  
Gaston H. Gonnet ◽  
Trevor J. Smedley
2018 ◽  
Vol 28 (5) ◽  
pp. 1527-1532
Author(s):  
Hristo Patev

In this first work, out of the total of twenty-four, are considered: Integrative approach, interdisciplinary relations and transnational language in the technical and economic fundament of engineering and management, for the purpose of competitive innovation and successful business. Approaches to develop the innovation with a high degree of complexity. Interactive heuristic methods and algorithms for inventive activity, for inspiring and developing new industrial products and services for households and production systems. Implementing an effective business vocabulary for organizational renewal. Introduction of gaming and "art" methods in innovation management. Intensifying innovation activities through an attempt to introduce artificial intelligence into teamwork, with simultaneous implementation of an engineering and non-engineering approach.


2008 ◽  
Author(s):  
Suresh Sethi ◽  
Chelliah Sriskandarajah ◽  
Giri Kumar Tayi ◽  
M. R. Rao
Keyword(s):  

2010 ◽  
Vol 06 (01) ◽  
pp. 69-87 ◽  
Author(s):  
ALISON MILLER ◽  
AARON PIXTON

We extend results of Bringmann and Ono that relate certain generalized traces of Maass–Poincaré series to Fourier coefficients of modular forms of half-integral weight. By specializing to cases in which these traces are usual traces of algebraic numbers, we generalize results of Zagier describing arithmetic traces associated to modular forms. We define correspondences [Formula: see text] and [Formula: see text]. We show that if f is a modular form of non-positive weight 2 - 2 λ and odd level N, holomorphic away from the cusp at infinity, then the traces of values at Heegner points of a certain iterated non-holomorphic derivative of f are equal to Fourier coefficients of the half-integral weight modular forms [Formula: see text].


1984 ◽  
Vol 8 (3) ◽  
pp. 211-214
Author(s):  
S.K. Goyal ◽  
Amiya K. Chakravarty
Keyword(s):  

Author(s):  
Sylwia Agata Bęczkowska ◽  
Iwona Grabarek

This article discusses the issues related to the safety for the transport of dangerous goods by road. Research on accidents in transport unambiguously points to the human factor, which is the most responsible for causing accidents. Determining the causes of driver unreliability in the human−vehicle−environment system requires thorough research. Unfortunately, in this case, experimental research with human involvement is limited in scope. This leaves modeling and simulation of the behavior of the human factor, i.e., the driver transporting dangerous goods. The human being, because of its complexity, is a challenging element to parameterize. The literature presents various attempts to model human actions. Herein, the authors used heuristic methods, specifically fuzzy set techniques, to build a human factor model. In these models, human actions were specified using a verbal or linguistic description. The specificity of the fuzzy sets allowed for “naturally” limiting the “precision” in describing human behavior. The model was built based on the author’s questionnaire and expert research, based on which individual features were selected. Then, the traits were assigned appropriate states. The output parameter of the model was λL—the intensity of human error. The obtained values of the intensity of the accident caused by the driver’s error were implemented into the author’s method of risk assessment. They constituted one of the factors determining the probability of an accident in the transport of dangerous goods, which allowed for determining the optimal route for the transport of these goods characterized by the lowest risk of an undesirable event on the route. The article presents the model’s assumptions, structure, and the features included in the model, all of which have the most significant influence on shaping the intensity of human error. The results of the simulation studies showed a diversified effect of the analyzed characteristics on the driver’s efficiency.


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