We prove a version for motivic cohomology of Thomason’s theorem on Bott-periodic K-theory, namely, that for a field k containing the nth roots of unity, the mod n motivic cohomology of a smooth k-scheme agrees with mod n étale cohomology, after inverting the element in H(k, Z/n(1)) corresponding to a primitive nth root of unity.

A tiie-differencing scheme consisting of an initializing step and N repetitions of a set of steps is proposed. For linear equations, the scheme is of Nth order. It is easily programmed and uses a minimal amount of storage space. The order may be changed by changing one parameter. An improved scheme is of Nth order even for nonlinear equations , for N 54.

Cooperative diversity networks have recently been proposed as a promising technology to improve performance over fading channels. In this paper, we consider incremental amplify-and-forward (AF) cooperative diversity networks which employ the Nth best relay when the best relay is unavailable due to issues such as scheduling or load balancing. The end-to-end performance is analyzed over independe...

We use the ultraproduct technique to study local properties of basic quantities of information-based complexity theory – the n-th minimal errors. We consider linear and nonlinear operators in normed spaces, information consists of continuous linear functionals and is assumed to be adaptive. We establish ultrastability and disprove regularity of n-th minimal errors. As a consequence, we answer a...

Based on the generalized continued-fraction method for finding the nth roots of real numbers, this paper presents a fast computation method for finding the principal nth roots of complex matrices. Computation algorithms with high convergence rates are developed, and their global convergence properties are investigated from the viewpoint of systems theory.

In this letter we present a technique for the implementation of Nth-order ultrafast temporal differentiators. This technique is based on two oppositely chirped fiber Bragg gratings in which the grating profile maps the spectral response of the Nth-order differentiator. Examples of 1(st), 2(nd), and 4(th) order differentiators are designed and numerically simulated.

This paper focuses on the fuzzy Volterra integro-differential equation of nth order of the second-kind with nonlinear fuzzy kernel and initial values. The derived integral equations are solvable, the solutions of which are unique under certain conditions. The existence and uniqueness of the solutions are investigated in a theorem and an upper boundary is found for solutions. Comparison of the e...