In the vector space of real vectors, comparison was executed of the multilinear forms, covariant derivatives, the total differentials and derivatives in the direction which are calculated with different metrics—with ...In the vector space of real vectors, comparison was executed of the multilinear forms, covariant derivatives, the total differentials and derivatives in the direction which are calculated with different metrics—with Euclidean metric and with pseudoeuclidean metric of a zero index. Comparison was executed of the Taylor’s formulas to different metrics. What is established by us is that multilinear forms of different metrics have different values;covariant derivatives have identical values;the total differentials and derivatives in the direction have different values. In Euclidean space, Taylor’s formula with any order of accuracy assigned in advance is equal, but in pseudoeuclidean space Taylor’s formula is not equal with any order of accuracy. It is concluded that in space with a pseudoeuclidean metric, the computing sense of the differential and integral calculus created in Euclidean space is lost and the possibility of mathematical model operation of real physical processes in vector space with pseudoeuclidean metric is called into question.展开更多
文摘In the vector space of real vectors, comparison was executed of the multilinear forms, covariant derivatives, the total differentials and derivatives in the direction which are calculated with different metrics—with Euclidean metric and with pseudoeuclidean metric of a zero index. Comparison was executed of the Taylor’s formulas to different metrics. What is established by us is that multilinear forms of different metrics have different values;covariant derivatives have identical values;the total differentials and derivatives in the direction have different values. In Euclidean space, Taylor’s formula with any order of accuracy assigned in advance is equal, but in pseudoeuclidean space Taylor’s formula is not equal with any order of accuracy. It is concluded that in space with a pseudoeuclidean metric, the computing sense of the differential and integral calculus created in Euclidean space is lost and the possibility of mathematical model operation of real physical processes in vector space with pseudoeuclidean metric is called into question.
