The higher derivatives of the inverse tangent function and rapidly convergent BBP-type formulas for pi.
The high-precision summation of series whose terms are rational numbers
The hyperbolic geometry of continued fractions .
The -translativity of Abel-type matrix.
The Lebesgue Constants for Borel Summation of Laplace Series.
The limiting behavior of sequences of Möbius transformations.
The Many Limits of Mixed Means. II. The Carlson Sequences.
The matrix transformations of double sequence space of .
The maximal solution of a restricted subadditive inequality in numerical analysis.
The measure of noncompactness of matrix transformations on the spaces and ().
The moments of infinite series.
The multipliers of a space of almost convergent continuous functions
The Nikodym property for ideals of sets defined by matrix summability methods.
The Pfaffian transform.
The prime number theorem for Beurling's generalized numbers. New cases
The QD-Algorithm and Multivariate Padé-Approximants.
The Rate of Convergence of Newtons' Process.
The reaping and splitting numbers of nice ideals
We examine the splitting number (B) and the reaping number (B) of quotient Boolean algebras B = (ω)/ℐ where ℐ is an ideal or an analytic P-ideal. For instance we prove that under Martin’s Axiom ((ω)/ℐ) = for all ideals ℐ and for all analytic P-ideals ℐ with the BW property (and one cannot drop the BW assumption). On the other hand under Martin’s Axiom ((ω)/ℐ) = for all ideals and all analytic P-ideals ℐ (in this case we do not need the BW property). We also provide applications of these characteristics...
The Relationship of Matrix Norms to Matrix Singularities.
The Riemann theorem and divergent permutations
In this paper the fundamental algebraic propeties of convergent and divergent permutations of ℕ are presented. A permutation p of ℕ is said to be divergent if at least one conditionally convergent series of real terms is rearranged by p to a divergent series . All other permutations of ℕ are called convergent. Some generalizations of the Riemann theorem about the set of limit points of the partial sums of rearrangements of a given conditionally convergent series are also studied.