Numerical approximate computations can solve large and complex problems *** have the advantage of high *** they only give approximate results,whereas we need exact results in some *** is a gap between approximate comp...
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Numerical approximate computations can solve large and complex problems *** have the advantage of high *** they only give approximate results,whereas we need exact results in some *** is a gap between approximate computations and exact results. In this paper,we build a bridge by which exact results can be obtained by numerical approximate computations.
Given a polynomial with symbolic/literal coefficients,a complete discrimination system is a set of explicit expressions in terms of the coefficients,which is sufficient for determining the numbers and multiplicities o...
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Given a polynomial with symbolic/literal coefficients,a complete discrimination system is a set of explicit expressions in terms of the coefficients,which is sufficient for determining the numbers and multiplicities of the real and imaginary *** it is of great significance,such a criterion for root-classification has never been given for polynomials with degrees greater than *** lack of efficient tools in this aspect extremely prevents computer implementations for Tarski’s and other methods in automated theorem *** remedy this defect,a generic algorithm is proposed to produce a complete discrimination system for a polynomial with any *** result has extensive applications in various fields,and its efficiency was demonstrated by computer implementations.
By applying the Fourier analysis, we study the spectral properties of R- filters. Further, we prove that R-filters are a generalization of least squares polynomial adjustment, and we give the geometric interpretation ...
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By applying the Fourier analysis, we study the spectral properties of R- filters. Further, we prove that R-filters are a generalization of least squares polynomial adjustment, and we give the geometric interpretation of R-filters.
In some fields such as Mathematics Mechanization, automatedreasoning and Trustworthy Computing, etc., exact results are needed. Symbolic computations are used to obtain the exact results. Symbolic computations are of...
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In some fields such as Mathematics Mechanization, automatedreasoning and Trustworthy Computing, etc., exact results are needed. Symbolic computations are used to obtain the exact results. Symbolic computations are of high complexity. In order to improve the situation, exact interpolating methods are often proposed for the exact results and approximate interpolating methods for the ap- proximate ones. In this paper, the authors study how to obtain exact interpolation polynomial with rational coefficients by approximate interpolating methods.
In existent researches of trustworthiness-based grid access control systems, an important question has not been resolved well: what types of historical behaviors should be chosen to measure trustworthiness. An access ...
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Dixon Resultant method can eliminate many variables simultaneously. It is often used to solve a system of polynomial equations. However, the Dixon matrix is often singular, and the Dixon Resultant vanishes identically...
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By means of dimension-decreasing method and cell-decomposition,a practical algorithm is proposed to decide the positivity of a certain class of symmetric polynomials,the numbers of whose elements are *** is a class of...
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By means of dimension-decreasing method and cell-decomposition,a practical algorithm is proposed to decide the positivity of a certain class of symmetric polynomials,the numbers of whose elements are *** is a class of mechanically decidable problems beyond Tarski *** implement the algorithm,a program nprove written in maple is developed which can decide the positivity of these polynomials rapidly.
For a generic loop: while (constraints) {updates} it is well known that the termination problem is undecidable in general, even for a simple class of polynomial programs. If the constraints or the updating function in...
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Through a detailed analysis of the theoretical basis for MOOCs in terms of educational learning theories, this paper attempts at finding the corresponding relationship between the theories and MOOCs, which not only th...
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ISBN:
(纸本)9789881925367
Through a detailed analysis of the theoretical basis for MOOCs in terms of educational learning theories, this paper attempts at finding the corresponding relationship between the theories and MOOCs, which not only theoretically explains the reasons why MOOCs exceed all the previous education models, but also empirically proves it with voluminous facts and data. The author conducts this research in the hope of enlightening the online education platform of other types. Besides, this paper provides the model framework and strategy to multidimensional educational review based on MOOCs. The model and strategy are applicable not only to MOOCs, the large-scale online education, but also to various online education platforms.
A class of integral inequalities is transformed into homogeneous symmetric polynomial inequalities beyond Tarski model,where the number of elements of the polynomial,say n,is also a variable and the coefficients are f...
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A class of integral inequalities is transformed into homogeneous symmetric polynomial inequalities beyond Tarski model,where the number of elements of the polynomial,say n,is also a variable and the coefficients are functions of *** is closely associated with some open problems formulated recently by Yang et *** Timofte's dimension-decreasing method for symmetric polynomial inequalities,combined with the inequality-proving package BOTTEMA and a program of implementing the method known as successive difference substitution,we provide a procedure for deciding the nonnegativity of the corresponding polynomial inequality such that the original integral inequality is mechanically decidable;otherwise,a counterexample will be *** effectiveness of the algorithm is illustrated by some more examples.
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