Related papers: Gauss and the Eccentric Halsted
This is the paper "Niels Henrik Abel and the birth of fractional calculus", Podlubny, I., Magin, R. L., Trymorush I., Fractional Calculus and Applied Analysis, vol.20, no.5, pp.1068-1075, 2017 (https://doi.org/10.1515/fca-2017-0057) with…
We give lower bounds for the numbers of real solutions in problems appearing in Schubert calculus in the Grassmannian Gr(n,d) related to osculating flags. It is known that such solutions are related to Bethe vectors in the Gaudin model…
Mathematical aspects of contemporary classical and quantum gauge theory are sketched.
Academic biography of Karl Weierstrass, his basic works, influence of his doctrine on the development of mathematics.
In this note, we give explicit expressions of Gauss sums for general (resp. special) linear groups over finite fields, which involves Gauss sums (resp. Kloosterman sums). The key ingredient is averaging such sums over Borel subgroups. As…
We show that there exists a Galois correspondence between subalgebras of an H-comodule algebra A over a base ring R and generalised quotients of a Hopf algebra H. We also show that Q-Galois subextensions are closed elements of the…
We comment on the recent attempt by M. Franz et al [1] to further justify their earlier calculation of the gauge-invariant electron propagator in the context of the QED_3 theory of the pseudogap phase in cuprates [2]. First, we use the…
The hitherto unknown author of a citation by Goethe in his History of Colours is identified as J. E. Montucla and the context of Montucla's quotation is discussed.
In his paper, "On a Partition Function of Richard Stanley," George Andrews proves a certain partition identity analytically and asks for a combinatorial proof. This paper provides the requested combinatorial proof.
We review several inequalities concerning Gaussian measures - isoperimetric inequality, Ehrhard's inequality, Bobkov's inequality, S-inequality and correlation conjecture.
This note is a discussion commenting on the paper by Ly et al. on "Harold Jeffreys's Default Bayes Factor Hypothesis Tests: Explanation, Extension, and Application in Psychology" and on the perceived shortcomings of the classical Bayesian…
This paper has been withdrawn by the authors due to the fact that the conjecture has indeed already long been established.
Speculations and theories about the existence of other worlds have a long history. In recent times, the arguments have shifted away from their typical philosophical and theological character to supposedly become more objective thanks to…
In the historical literature there has been an extended discussion on the question, whether the report of Sartorius von Waltershausen about C. F. Gauss checking the largest triangle of the geodetical measurement campaign in the kingdom of…
In this paper the transcendental Galois extensions of a field will be introduced as counterparts to algebraic Galois ones. There exist several types of transcendental Galois extensions of a given field, from the weakest one to the strongest…
Under a weakened version of Hardy-Littlewood Conjecture on the number of representations in Goldbach problem, J. H. Fei proved bounds for the Siegel zeros. Recently G. Bhowmik and K. Halupczok generalized Fei's result under a weaker…
The contributions of Lucio Russo to the mathematics of percolation and disordered systems are outlined. The context of his work is explained, and its ongoing impact on current work is described and amplified.
In this written version of a pre-dinner-speech at the workshop "The Nature of Gravity" at ISSI I illustrate Pauli's science primarily with material that has not formally been published by him, but was communicated in detailed letters to…
A family of congruences interpolating between those of Wilson and Giuga is constructed. Several elementary results are established, in order to present a possible approach to establishing Giuga's conjecture.
The main purpose of this article is to study higher power mean values of generalized quadratic Gauss sums using estimates for character sums, analytic method and algebraic geometric methods. In this article, we prove two conjectures which…