Approximation of the dilogarithm function.
Approximation of the Stieltjes integral and applications in numerical integration
Some inequalities for the Stieltjes integral and applications in numerical integration are given. The Stieltjes integral is approximated by the product of the divided difference of the integrator and the Lebesgue integral of the integrand. Bounds on the approximation error are provided. Applications to the Fourier Sine and Cosine transforms on finite intervals are mentioned as well.
Approximation of Ultra-Differentiable Functions by Polynomials and Entire Functions.
Approximation of Univariate Set-Valued Functions - an Overview
2000 Mathematics Subject Classification: 26E25, 41A35, 41A36, 47H04, 54C65.The paper is an updated survey of our work on the approximation of univariate set-valued functions by samples-based linear approximation operators, beyond the results reported in our previous overview. Our approach is to adapt operators for real-valued functions to set-valued functions, by replacing operations between numbers by operations between sets. For set-valued functions with compact convex images we use Minkowski...
Approximation of by .
Approximations and error bounds for computing the inverse mapping
In this paper we propose a procedure to construct approximations of the inverse of a class of differentiable mappings. First of all we determine in terms of the data a neighbourhood where the inverse mapping is well defined. Then it is proved that the theoretical inverse can be expressed in terms of the solution of a differential equation depending on parameters. Finally, using one-step matrix methods we construct approximate inverse mappings of a prescribed accuracy.
Approximative Funktionalgleichungen und Mittelwertsätze für Dirichletreihen, die Spitzenformen assoziiert sind.
Archimedes was right.II.
Are most measurable functions one-to-one?
Are the coefficients of a polynomial well-conditioned functions of its roots?
Area functionals and Godbillon-Vey cocycles
We investigate the natural domain of definition of the Godbillon-Vey 2- dimensional cohomology class of the group of diffeomorphisms of the circle. We introduce the notion of area functionals on a space of functions on the circle, we give a sufficiently large space of functions with nontrivial area functional and we give a sufficiently large group of Lipschitz homeomorphisms of the circle where the Godbillon-Vey class is defined.
Argument estimates for certain analytic functions associated with the convolution structure.
Arhangel'skiĭ sheaf amalgamations in topological groups
We consider amalgamation properties of convergent sequences in topological groups and topological vector spaces. The main result of this paper is that, for arbitrary topological groups, Nyikos’s property is equivalent to Arhangel’skiĭ’s formally stronger property α₁. This result solves a problem of Shakhmatov (2002), and its proof uses a new perturbation argument. We also prove that there is a topological space X such that the space of continuous real-valued functions on X with the topology...
Around Bolzano's approach to real numbers
Arrow-Hahn economic models with weakened conditions of continuity
In this article we give descriptions of some economic models that are based on Arrow-Hahn economic model. Finally we consider a model with two major assumptions: first, there is discontinuous excess demand function and, second, if price goes to zero, then it is possible that excess demand may approach infinity. For this last new economic model the existence of quasi-equilibrium is proved.
Associative -dimensional copulas
The associativity of -dimensional copulas in the sense of Post is studied. These copulas are shown to be just -ary extensions of associative 2-dimensional copulas with special constraints, thus they solve an open problem of R. Mesiar posed during the International Conference FSTA 2010 in Liptovský Ján, Slovakia.
Asymmetric covariance estimates of Brascamp–Lieb type and related inequalities for log-concave measures
An inequality of Brascamp and Lieb provides a bound on the covariance of two functions with respect to log-concave measures. The bound estimates the covariance by the product of the norms of the gradients of the functions, where the magnitude of the gradient is computed using an inner product given by the inverse Hessian matrix of the potential of the log-concave measure. Menz and Otto [Uniform logarithmic Sobolev inequalities for conservative spin systems with super-quadratic single-site potential....
Asymmetry level as a fuzzy measure.
Asymptotic analysis of positive solutions of generalized Emden-Fowler differential equations in the framework of regular variation
Positive solutions of the nonlinear second-order differential equation are studied under the assumption that p, q are generalized regularly varying functions. An application of the theory of regular variation gives the possibility of obtaining necessary and sufficient conditions for existence of three possible types of intermediate solutions, together with the precise information about asymptotic behavior at infinity of all solutions belonging to each type of solution classes.
Asymptotic behavior for the best lower bound of Jensen's functional