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Full-Text Articles in Physical Sciences and Mathematics
Uniqueness Of Solutions Of Differential Equations, Gerald Head
Uniqueness Of Solutions Of Differential Equations, Gerald Head
Masters Theses & Specialist Projects
Uniqueness of solutions for ordinary differential equations is studied. The classical theorems which guarantee uniqueness are surveyed, including discussion and examples. Other results concerning uniqueness are considered in the final chapter, including the relationship between convergence of successive approximations and uniqueness, non-uniqueness and continuous dependence on initial conditions.
Gröbner Bases And Syzygy Modules, Yonggan Zhao
Gröbner Bases And Syzygy Modules, Yonggan Zhao
Masters Theses & Specialist Projects
The theory of Gröbner bases has become a useful tool in computational commutative algebra. In this paper, we outline some basic results, as they are found in [1], including the concepts of terms ordering, multivariable polynomial division, Gröbner bases, Buchberger's algorithm, and syzygy modules. Specially, we present several equivalent definitions for Gröbner bases and prove how to compute a Gröbner basis for an ideal I of A = k[x1, x2, • • • , xn] generated by {fl, f2, • • • , f8} through Buchberger's algorithm. As an application of Gröbner bases, we present a standard method (see [1]) …
An Object Oriented Implemtation Of Fractal Image Compression, Darrell Burkhead
An Object Oriented Implemtation Of Fractal Image Compression, Darrell Burkhead
Masters Theses & Specialist Projects
The technique of Fractal Image Compression, although new, has been described in several ways. Thus far, all descriptions of this compression algorithm read by the author have been in procedural form. The purpose of this paper is to present the Fractal Image Compression algorithm in an object-oriented form and to point out the advantages of this organization. The main advantages of taking an object-oriented approach to this problem are flexibility and maintainability. Different aspects of this algorithm are handled by different objects, thereby allowing for easy customization and testing of each part. Another advantage of this approach is that the …