Results 1 - 10 of 1409
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[en] Differential algebra (DA) is a new method of automatic differentiation. DA can rapidly and efficiently calculate the values of derivatives of arbitrarily complicated functions, in arbitrarily many variables, to arbitrary order, via its definition of multiplication. I provide a brief introduction to DA, and enumerate some of its recent applications. (author). 6 refs
[en] We introduce the construction of a (D,A)∞-(co)module over a (D,A)∞-(co) algebra and study its main homotopy properties. We establish a connection between (D,A)∞-(co)modules over (D,A)∞-(co)algebras and spectral sequences, and thus obtain the structure of an A∞-comodule over the Milnor A∞-coalgebra on the homology of any spectrum directly from the differentials of the Adams spectral sequence of this spectrum
[en] The techniques of integration by parts and differential reduction differ in the counting of master integrals. This is illustrated using as an example the two-loop sunset diagram with on-shell kinematics. A new algebraic relation between the master integrals of the two-loop sunset diagram that does not follow from the standard integration-by-parts technique is found.
[en] The problem of numerically approximating a class of dynamical systems with discontinuous state variables by forward Euler method for differential inclusions, viewed as dynamical systems, is discussed in this paper. It is shown that such discontinuous initial value problems may be transformed into set-valued problems and then approximated by special numerical methods for differential inclusions which may be viewed as (ideally continuous) dynamical systems
[en] It is established that among all the differentiable homeomorphic changes of variable only the functions and for preserve convergence everywhere of the Fourier-Haar series. The same is true for absolute convergence everywhere. Bibliography: 8 titles. (paper)
[en] In this note we introduce a notion of quasilower subdifferentiability which is an extension of that of lower subdifferentiability due to Plastria F. by using the concept of ε-subdifferential in convex analysis. We obtain that at a given point a function is quasilower subdifferentiable if and only if the values of this function and its second quasiconvex conjugate coincide. It is proved that the second quasiconvex conjugate is a best approximation in the class of second hα-conjugate defined by Martinez-Legaz and Romano-Rodriguez S. An application of the notion of quasilower subdifferentiability for the facial programming problems is given. (author). 10 refs
[en] We construct planar polynomial differential systems of even (respectively odd) degree n > 3, of the form linear plus a nonlinear homogeneous part of degree n having a weak focus of order n2 -1 (respectively (n2-1)/2 ) at the origin. As far as we know this provides the highest order known until now for a weak focus of a polynomial differential system of arbitrary degree n. (author)
[en] In this paper, the (p, q)-derivative and the (p, q)-integration are investigated. Two suitable polynomial bases for the (p, q)-derivative are provided and various properties of these bases are given. As application, two (p, q)-Taylor formulas for polynomials are given, the fundamental theorem of (p, q)-calculus is included and the formula of (p, q)-integration by part is proved.