For all types of quadratic forms,the cross-correlations between geometric sequences and the newly defined quadratic form sequences are determined to extend the results presented by Klapper in 1993 and 1997.The techniq...For all types of quadratic forms,the cross-correlations between geometric sequences and the newly defined quadratic form sequences are determined to extend the results presented by Klapper in 1993 and 1997.The technique for computing cross-correlations is based on counting the number of solutions for a system of equations that consists of a quadratic form and a linear function.展开更多
Geometric computing is an important tool in design and manufacturing and in arts. Conventionally, geometric computing is taken by algebraic computing. The vivid intuition of objects in visualization is lost in numeric...Geometric computing is an important tool in design and manufacturing and in arts. Conventionally, geometric computing is taken by algebraic computing. The vivid intuition of objects in visualization is lost in numeric functions, which is however very useful to human cognition as well as emotion. In this paper, we proposed a concept and theory of geometric basis （GB） as the solving cell for geometric computing. Each GB represents a basic geometric operation. GB works as both expressing and solving cell just like the concept of basis in linear algebra by which every element of the vector space can be expressed. For 3D problems, with a procedure of a projections reduction, the problem can be reduced to plane and the reduction function can be designed as a GB. A sequence of GB can construct a higher layer GB. Then, by the traversal of tree, a sequence of GB is got and this sequence is just the construction process and also the solution of this geometric problem.展开更多
Families of periodic sequences with high linear span and ideal correlation property are found important in code division multiple access communication systems and cryptography. Klapper et al constructed a family of Pe...Families of periodic sequences with high linear span and ideal correlation property are found important in code division multiple access communication systems and cryptography. Klapper et al constructed a family of Periodic sequences named quadratically related geometric sequences, computed their auto and cross-correlation functions. The to result of Klapper is proved and improved by a much simpler new approach in this article.展开更多
文摘For all types of quadratic forms,the cross-correlations between geometric sequences and the newly defined quadratic form sequences are determined to extend the results presented by Klapper in 1993 and 1997.The technique for computing cross-correlations is based on counting the number of solutions for a system of equations that consists of a quadratic form and a linear function.
文摘Geometric computing is an important tool in design and manufacturing and in arts. Conventionally, geometric computing is taken by algebraic computing. The vivid intuition of objects in visualization is lost in numeric functions, which is however very useful to human cognition as well as emotion. In this paper, we proposed a concept and theory of geometric basis （GB） as the solving cell for geometric computing. Each GB represents a basic geometric operation. GB works as both expressing and solving cell just like the concept of basis in linear algebra by which every element of the vector space can be expressed. For 3D problems, with a procedure of a projections reduction, the problem can be reduced to plane and the reduction function can be designed as a GB. A sequence of GB can construct a higher layer GB. Then, by the traversal of tree, a sequence of GB is got and this sequence is just the construction process and also the solution of this geometric problem.
文摘Families of periodic sequences with high linear span and ideal correlation property are found important in code division multiple access communication systems and cryptography. Klapper et al constructed a family of Periodic sequences named quadratically related geometric sequences, computed their auto and cross-correlation functions. The to result of Klapper is proved and improved by a much simpler new approach in this article.
