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This implies that a system is algebraically integrable (i.e., its eigenvalue problem is explicitly solvable in quadratures) if and only if the differential Galois group is commutative for generic eigenvalues.
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We apply this criterion of algebraic integrability to two examples: finite-zone potentials and the elliptic Calogero-Moser system.
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In the second example, we obtain a proof of the Chalyh-Veselov conjecture that the Calogero-Moser system with integer parameter is algebraically integrable, using the results of Felder and Varchenko.
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The least upper bound for the degrees of elements in a system of generators turns out to be independent of the number of vector variables.
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We consider 3-parametric polynomialsPμ*(x; q, t, s) which replace theAn-series interpolation Macdonald polynomialsPμ*(x; q, t) for theBCn-type root system.
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| In this paper is briefly described a source language as used in the compiling system ND-7301. The whole paper is divided into six sections. Section 1 is an introduction, in which are discussed the design background, the design objectives and the language structure. Section 2 consists of basic symbols, numbers, names, quantities and values. Section 3 consists of formulas and clauses. Section 4 describes declarations. Section 5 consists of programs, modules, comments, etc. In the last section are given two... In this paper is briefly described a source language as used in the compiling system ND-7301. The whole paper is divided into six sections. Section 1 is an introduction, in which are discussed the design background, the design objectives and the language structure. Section 2 consists of basic symbols, numbers, names, quantities and values. Section 3 consists of formulas and clauses. Section 4 describes declarations. Section 5 consists of programs, modules, comments, etc. In the last section are given two examples. Such a language may be used to describe user programs as well as systems programs. In the moduleparameter part and several clauses are also considered components to facilitate program debugging. | 本文扼要介绍了ND-7301编译系统中所用的初始语言。全文共分六节。第一节是引言,其中谈到这种语言的设计背景,设计目标,以及语言的结构。第二节是基本符号、数、名、量、值。第三节是公式和子句。第四节是说明。第五节是程序、模块、注解等。第六节给出了两个例子。本语言是一种既可用来写应用程序又可用来写系统程序的语言。在模块参数以及子句等部分还考虑了一些利于动态调试的成分。 | In this paper is briefly described a source language as used in the com- piling system ND-7301.The whole paper is divided into six sections.Section 1 is an introduction,in which are discussed the design background,the design objectives and the language structure.Section 2 consists of basic symbols,numbers,names,quantities and values.Section 3 consists of for- mulas and clauses.Section 4 describes declarations.Section 5 consists of programs,modules,comments,etc.In the last section are given two examples.... In this paper is briefly described a source language as used in the com- piling system ND-7301.The whole paper is divided into six sections.Section 1 is an introduction,in which are discussed the design background,the design objectives and the language structure.Section 2 consists of basic symbols,numbers,names,quantities and values.Section 3 consists of for- mulas and clauses.Section 4 describes declarations.Section 5 consists of programs,modules,comments,etc.In the last section are given two examples. Such a language may be used to describe user programs as well as systems programs. In the moduleparameter part and several clauses are also considered components to facilitate program debugging. | 本文扼要介绍了 ND-7301编译系统中所用的初始语言。全文共分六节。第一节是引言,其中谈到这种语言的设计背景,设计目标,以及语言的结构。第二节是基本符号、数、名、量、值。第三节是公式和子句。第四节是说明。第五节是程序、模块、注解等。第六节给出了两个例子。本语言是一种既可用来写应用程序又可用来写系统程序的语言。在模块参数以及子句等部分还考虑了一些利于动态调试的成分。 | In recent years advances in shipbuilding industry have stimulated considerable interest in the development and use of practical algorithms for the interpolation and approximation of points. A method for interpolating and fitting a curve through points is described here. Cubic polynomials in local coordinate systems are used to obtain an interpolating curve with continuous first and second derivatives.The nonlinear equations are rapidly solved by ordinary Newton iteration because the basic iterative step... In recent years advances in shipbuilding industry have stimulated considerable interest in the development and use of practical algorithms for the interpolation and approximation of points. A method for interpolating and fitting a curve through points is described here. Cubic polynomials in local coordinate systems are used to obtain an interpolating curve with continuous first and second derivatives.The nonlinear equations are rapidly solved by ordinary Newton iteration because the basic iterative step involves only atridiagonal linear system and the good initial estimates for ri's are made. The tangent vectors are refined to avoid the unwanted inflections when the large variations in slope between neighboring points occur, and an example to show the refinement by local interpolation methods is given.The resulting curve will be a chain of bi-arcs, the common tangent points of which are chosen on the spline to ensure a better approximation. | 对于离散的型值点,本文采用转轴三次样条曲线拟合,再用公切点取在样条曲线上的双圆弧逼近,既保证了线型的光顺性,又便于图形的贮存、传送和再加工。经实践证明,用上法绘出的图形光顺性好、精度高,完全符合生产要求。 | | | | << 更多相关文摘 |
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