منابع مشابه
Quadrature formulae of non-standard type
We discuss quadrature formulae of highest algebraic degree of precision for integration of functions of one or many variables which are based on non-standard data, i.e., in which the information used is different from the standard sampling of function values. Among the examples given in this survey is a quadrature formula for integration over the disk, based on linear integrals on n chords, whi...
متن کاملCauchy-green Type Formulae in Clifford Analysis
A Cauchy integral formula is constructed for solutions to the polynomial Dirac equation (Dk+Yfcrn~JQ bmDm)f = 0 , where each bm is a complex number, D is the Dirac operator in R" , and f is defined on a domain in R" and takes values in a complex Clifford algebra. Some basic properties for the solutions to this equation, arising from the integral formula, are described, including an approximatio...
متن کاملNew Whitney-Type Formulae for Plane Curves
The classical Whitney formula relates the algebraic number of self-intersections of a generic plane curve to its winding number. We generalize it to an innnite family of identities, expressing the winding number in terms of the internal geometry of a plane curve. This enables us to split the Whit-ney formula by some characteristic of double points. It turns out, that only crossings of a very sp...
متن کاملQuadrature Formulae and Functions of Exponential Type
In this paper we obtain certain generalizations of the trapezoidal rule and the Euler-Maclaurin formula that involve derivatives. In the case of quadrature of functions of exponential type over infinite intervals we find conditions under which existence of the (improper) integral and convergence of the approximating series become equivalent. In the process, we also establish a best possible ver...
متن کاملWillard Thompson
Complexity theory has a profound influence on the field of cryptology. The time complexity of breaking a cipher system must be significant enough to thwart any adversary from succeeding. However, with the emergence of quantum computers an adversary may have no difficulty in breaking known cipher systems. If quantum computers would exist today new mechanisms for security would need to be built. ...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2012
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2011.11.011