All posts under category "Mathematics / Math.GM"
We have calculated numerically geometrical means of the denominators of the continued fraction approximations to the Brun constant B2. We get values close to the Khinchin constant. Next we calculated the n-th square roots of the denominators of the n-th convergents of these continued fractions obtai
We study the asymptotic behavior of a bounded solution of an inhomogeneous delay linear difference equation in a Banach space by using the spectrum of bounded sequences. We get a significant extension of excellent results in [1]. A new simple proof is also found for the famous Gelfand spectral radiu
Make an exponential transformation in the integral formulation of Riemann's zeta-function zeta(s) for Re(s) > 0. Separately, in addition make the substitution s -> 1 - s and then transform back to s again using the functional equation. Using residue calculus, we can in this way get two alternative,
Starting with real line number system based on the theory of the Yang's fractional set, the generalized Young inequality is established. By using it some results on the generalized inequality in fractal space are investigated in detail.
A formula expressing a point of order 8 on an elliptic curve, in terms of the roots of the associated cubic polynomial, is given. Doubling such a point yields a point of order 4 distinct from the well-known points of order 4 given in standard references such as 'A course of Modern Analysis' by Whitt
A very simple but useful almost sure convergence theorem of probability is given.
During the last few years of his life, Ramanujan had adamantly tried to invert the modular invariant. Subsequent efforts failed until May 30, 2011 when an explicit closed formula for an inverse was presented at the CCRAS (Moscow, Russia). This very formula, along with some special values of the modu
We define the eigenderivatives of a linear operator on any real or complex Banach space, and give a sufficient condition for their existence.
In this paper, by using hardy inequality, we establish some new integral inequalities of Hardy-Hilbert type with general kernel. As applications, equivalent forms and some particular results are built; the corresponding to the double series inequalities are given.reverse forms are considered also.
In this paper we extend the Dirichlet integral formula of Lobachevsky. Let $f(x)$ be a continuous function and satisfy in the $pi$-periodic assumption $f(x+pi)=f(x)$, and $f(pi-x)=f(x)$, $0leq x<infty $. If the integral $int_0^infty frac{sin^4x}{x^4}f(x)dx$ defined in the sense of the improper Riema
Michael Kinyon's 2005 open problem, based on the universality of Osborn loops is solved. It is shown that not every Osborn loop is universal.
We have used the first 2600 nontrivial zeros gamma_l of the Riemann zeta function calculated with 1000 digits accuracy and developed them into the continued fractions. We calculated the geometrical means of the denominators of these continued fractions and for all cases we get values close to the Kh
I give simple elementary proofs for some well-known Hankel determinants and their q-analogues.
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