Search results for "Calculus"
showing 10 items of 617 documents
A note on the exterior capillarity problem
1975
Elementare Berechnung der Multiplizitätenn-dimensionaler Spitzen
1977
Selbstadjungierte Operatoren als ?dual rein atomare? Skalaroperatoren
1978
Reforming the Teaching and Learning of Foundational Mathematics Courses: An Investigation into the Status Quo of Teaching, Feedback Delivery, and Ass…
2022
Several universities are witnessing an increase in students’ enrolment in mathematics-intensive programmes over the last decades. This increase has come with the price of high failure rates in foundational mathematics courses, which poses challenges to mathematics teaching and learning in higher education. It is therefore inevitable, for some universities, to transform the teaching and learning of mathematics to more student-centred approaches that engage the students mathematically and enhance their success rates. We approach this transformative effort by investigating students’ perception of teaching, feedback, and assessment as a first step in reforming the teaching of a firs…
Stability analysis of Beck's column over a fractional-order hereditary foundation
2018
This paper considers the case of Beck's column resting on a hereditary bed of independent springpots. The springpot possesses an intermediate rheological behaviour among linear spring and linear dashpot. It is defined by means of couple ( C β , β ) that characterize the material of the element and is ruled by a Caputo's fractional derivative. In this paper, we investigate the critical load of the column under the action of a follower load by means of a novel complex transform that allows to use the Routh–Hurwitz theorem in the complex half-plane for the stability analysis.
On the fractional probabilistic Taylor's and mean value theorems
2016
In order to develop certain fractional probabilistic analogues of Taylor's theorem and mean value theorem, we introduce the nth-order fractional equilibrium distribution in terms of the Weyl fractional integral and investigate its main properties. Specifically, we show a characterization result by which the nth-order fractional equilibrium distribution is identical to the starting distribution if and only if it is exponential. The nth-order fractional equilibrium density is then used to prove a fractional probabilistic Taylor's theorem based on derivatives of Riemann-Liouville type. A fractional analogue of the probabilistic mean value theorem is thus developed for pairs of nonnegative rand…
Bartlett formalism generating functions and Z-transforms in fluctuation and noise theory
1983
Abstract “La theorie des fonctions generatrices s'adapte elle meme et avec la plus grande generalite aux questions des probabilite les plus difficiles.” (Laplace, 1812) “An important part of probability theory consists of the derivation of the probability distribution of the sum of n random variables, each of which obeys a given probability law, and the development of asymptotic forms of these distributions valid for increasing n. Probability generating functions owe their dominant position to the simplification they permit to both problems. Their employment to obtain the successive moments of a probability distribution and to solve the difference equations of probability theory is ancillar…
Why Magnus expansion
2021
A short story about the origins of Magnus Expansion, why we got involved and how it led us to meet Geometric Integration. We present a biographical draft of Wilhelm Magnus, a sketchy discussion of ...
Weierstraß’s Approximation Theorem (1885) and his 1886 lecture course revisited
2015
The paper provides new insight into the origins of Weierstras’s 1886 lecture course on the foundations of function theory and of the mimeographed lecture notes connected to this course which were published by the author in German in 1988. A short overview of the content of the lecture course is given; the central role that Weierstras’s famous approximation theorem of 1885 played in it is emphasized. The paper uses archival material recently discovered at the Institut Mittag-Leffler in Djursholm.
Max von laue’s role in the relativity revolution
2008
Whereas countless studies have been devoted to Einstein’s work on relativity, the contributions of several other major protagonists have received comparatively little attention. Within the immediate German context, no single figure played a more important role in developing the consequences of the special theory of relativity (SR) than Max von Laue (1879–1960). Although remembered today mainly for his discovery of x-ray diffraction in 1912 – an achievement for which he was awarded the Nobel Prize – Laue’s accomplishments in promoting the theory of relativity were of crucial importance. They began early, well before most physicists even knew anything about a mysterious Swiss theoretician nam…