相关论文: Approximations for the natural logarithm from sole…
When the sequence of regular polygons with consecutively increasing numbers of sides is joined edge-to-edge in a single direction while minimizing bending, the resulting structure assumes the shape of a logarithmic spiral. This paper proves…
The natural logarithm can be represented by an infinite series that converges for all positive real values of the variable, and which makes concavity patently obvious. Concavity of the natural logarithm is known to imply, among other…
In this note we formulate some questions in the study of approximations of reals by rationals of the form a/b^2 arising in theory of Shr"odinger equations. We hope to attract attention of specialists to this natural subject of number…
The Euclidean algorithm makes possible a simple but powerful generalization of Taylor's theorem. Instead of expanding a function in a series around a single point, one spreads out the spectrum to include any number of points with given…
We determine the Lagrange function in Taylor polynomial approximation by solving an appropriate initial-value problem. Hence, we determine the remainder term which we then approximate by means of a natural cubic spline. This results in a…
``Quasi-elliptic'' functions can be given a ring structure in two different ways, using either ordinary multiplication, or convolution. The map between the corresponding standard bases is calculated. A related structure has appeared…
A bimatroid is a matroid-like generalization of the collection of regular minors of a matrix. In this article, we use the theory of Lorentzian polynomials to study the logarithmic concavity of natural sequences associated to bimatroids.…
We study how well a real number can be approximated by sums of two or more rational numbers with denominators up to a certain size.
Given a list of N numbers, the maximum can be computed in N iterations. During these N iterations, the maximum gets updated on average as many times as the Nth harmonic number. We first use this fact to approximate the Nth harmonic number…
An $(n+1)$-toroid is a quotient of a tessellation of the $n$-dimensional Euclidean space with a lattice group. Toroids are generalizations of maps in the torus on higher dimensions and also provide examples of abstract polytopes. Equivelar…
The satisfactory development of Quaternionic Analysis has indicated new solutions for physical and mathematical problems. It is worth mentioning the fact that quaternions possess four dimensions, and in this way they may be considered as…
The optimal one-sided parametric polynomial approximants of a circular arc are considered. More precisely, the approximant must be entirely in or out of the underlying circle of an arc. The natural restriction to an arc's approximants…
Probably we have observed a new simple phenomena dealing with approximations to two real numbers.
In this paper the double-sided Talor's approximations are used to obtain generalisations and improvements of some trigonometric inequalities.
We describe an approximate rational arithmetic with round-off errors (both absolute and relative) controlled by the user. The rounding procedure is based on the continued fraction expansion of real numbers. Results of computer experiments…
The papers shows an algorithm to search for approximations of reals to rationals of the form a/b^2 that runs on \sqrt(b) polynomial time steps.
The theory of Touchard polynomials is generalized using a method based on the definition of exponential operators, which extend the notion of the shift operator. The proposed technique, along with the use of the relevant operational…
We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.
For every natural number $T,$ we write $\Ln T$ as a series, generalizing the known series for $\Ln 2.$
We relate a previous result of ours on families of Diophantine equations having only trivial solutions with a result on the approximation of an algebraic number by products of rational numbers and units. We compare this approximation with a…