The Euler-Jacobi formula provides an algebraic relation between the singular points of a polynomial vector field and their topological indices. Using this formula we obtain the configuration of the singular points together with their topological indices for the planar quadratic-quartic polynomial ...
In the 1950's Hasse gave a formula that relates the class number of a biquadratic dicyclic number field to the class numbers of its, three quadratic subfields. Similar formulas are derived here for biquadratic dicyclic extensions of more general base fields, in cases where the base fields reta...
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We establish the first polynomial-strength time-space lower bounds for problems in the linear-time hierarchy on randomized machines with bounded two-sided error. We show that for any integer l > 1 and constant c < l, there exists a posit... S Diehl,D Melkebeek - Springer, Berlin, Heidel...
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In today’s modern days, the Internet has an ocean of platforms for education and learning. To streamline and organize your learning, you need to focus on the right one which, in turn, should provide you with enough support. When it comes to student support and quality of study material,...
E.g., a quadratically convergent algorithm will require fewer function calls and parameter updates than a linearly convergent algorithm, and usually be much faster as well. However, the actual speed advantage can be undermined if the former requires very costly hessian computations (say). For the...
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In this article, our purpose is to construct an FVE scheme for the nonlinear time fractional mobile/immobile transport equations on triangular girds by using the WSGD formula. In spatial discretization, we construct the primal and dual partitions, select the piecewise linear polynomial space and th...
but since[Math Processing Error]for allkand[Math Processing Error], we also have [Math Processing Error] (8) Together with Eq. (7), this yields: [Math Processing Error] (9) This last expression is known asSchönberg’s quadratic form[4]. It is well known that it is non-negative ...