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The Euler--Maclaurin (EM) summation formula is used in many theoretical studies and numerical calculations. It approximates the sum $\sum_{k=0}^{n-1} f(k)$ of values of a function $f$ by a linear combination of a corresponding integral of…
The papers mentioned in the bibliography lead to this new hypothesis which constitutes a wide panorama of the physical reality. Its coherence and its simplicity are virtues that make interesant to gaze upon it.
The Euler characteristic transform (ECT) is a simple to define yet powerful representation of shape. The idea is to encode an embedded shape using sub-level sets of a a function defined based on a given direction, and then returning the…
Ellipsoids possess several beautiful properties associated with classical potential theory. Some of them are well known, and some have been forgotten. In this article we hope to bring a few of the "lost" pieces of classical mathematics back…
Quantum computing exposes the brilliance of quantum mechanics through computer science and, as such, gives oneself a marvelous and exhilarating journey to go through. This article leads along that journey with a historical and current…
A solution to the part and whole problem is presented in this paper by using a complex mathematical representation that permits to define the Holon concept as a unit that remains itself in spite of complex operations such as integration and…
In this paper a novel calculus system has been established based on the concept of 'werden'. The basis of logic self-contraction of the theories on current calculus was shown. Mistakes and defects in the structure and meaning of the…
The goal of this article is to invite the reader to get to know and to get involved into higher Teichm\"uller theory by describing some of its many facets.
The use of Cauchy's method to prove Euler's well-known formula is an object of many controversies. The purpose of this paper is to prove that Cauchy's method applies for convex polyhedra and not only for them, but also for surfaces such as…
We present an astonishingly simple and elegant proof of the celebrated Basel problem.
Recently the new q-Euler numbers are defined. In this paper we derive the the Kummer type congruence related to q-Euler numbers and we introduce some interesting formulae related to these q-Euler numbers.
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 introduce and prove several new formulas for the Euler-Mascheroni Constant. This is done through the introduction of the defined E-Harmonic function, whose properties, in this paper, lead to two novel formulas, alongside a family of…
Starting with the recursive extended Euclid's algorithm, we apply a systematic approach using matrix notation to transform it into an iterative algorithm. The partial correctness proof derived from the transformation turns out to be very…
The title says what is done here. Euler finds a news series for the arc of an ellipse. The paper is translated from the Latin original into German.
We present a new method for characterizing the interpretive possibilities generated by elliptical constructions in natural language. Unlike previous analyses, which postulate ambiguity of interpretation or derivation in the full clause…
Euler gives an asymptotic approximation for the function f(x) and recognizes that he is trying to interpolate the factorial function introduced in E19 "De progressionibus transcendentibus seu quarum termini generales algebraice dari…
This paper has been withdrawn by the author. In this article I review W\"ust's recent handbook on mathematical physics from a philosophical standpoint. It emerges a structural approach to mathematics which evidences the utility of logic in…
Formulaic expressions, such as 'in this paper we propose', are helpful for authors of scholarly papers because they convey communicative functions; in the above, it is showing the aim of this paper'. Thus, resources of formulaic…
We give an Euler Maclaurin formula with remainder for the sum of the values of a smooth function on the integral points in a simple integral polytope. This formula is proved by elementary methods.