Search results for "102"
showing 10 items of 2892 documents
A tribute to Massimo Lanza de Cristoforis
2020
It is with great pleasure that we dedicate the special issue Functional Analytic Methods in Partial Differential Equations of Complex Variables and Elliptic Equations to the 60th birthday of Massim...
On the arithmetic and geometry of binary Hamiltonian forms
2011
Given an indefinite binary quaternionic Hermitian form $f$ with coefficients in a maximal order of a definite quaternion algebra over $\mathbb Q$, we give a precise asymptotic equivalent to the number of nonequivalent representations, satisfying some congruence properties, of the rational integers with absolute value at most $s$ by $f$, as $s$ tends to $+\infty$. We compute the volumes of hyperbolic 5-manifolds constructed by quaternions using Eisenstein series. In the Appendix, V. Emery computes these volumes using Prasad's general formula. We use hyperbolic geometry in dimension 5 to describe the reduction theory of both definite and indefinite binary quaternionic Hermitian forms.
Abel transforms with low regularity with applications to X-ray tomography on spherically symmetric manifolds
2017
We study ray transforms on spherically symmetric manifolds with a piecewise $C^{1,1}$ metric. Assuming the Herglotz condition, the X-ray transform is injective on the space of $L^2$ functions on such manifolds. We also prove injectivity results for broken ray transforms (with and without periodicity) on such manifolds with a $C^{1,1}$ metric. To make these problems tractable in low regularity, we introduce and study a class of generalized Abel transforms and study their properties. This low regularity setting is relevant for geophysical applications.
Indefinite integrals involving the incomplete elliptic integrals of the first and second kinds
2016
ABSTRACTA substantial number of indefinite integrals are presented for the incomplete elliptic integrals of the first and second kinds. The number of new results presented is about three times the total number to be found in the current literature. These integrals were obtained with a Lagrangian method based on the differential equations which these functions obey. All results have been checked numerically with Mathematica. Similar results for the incomplete elliptic integral of the third kind will be presented separately.
Indefinite integrals involving the incomplete elliptic integral of the third kind
2016
ABSTRACTA substantial number of new indefinite integrals involving the incomplete elliptic integral of the third kind are presented, together with a few integrals for the other two kinds of incomplete elliptic integral. These have been derived using a Lagrangian method which is based on the differential equations which these functions satisfy. Techniques for obtaining new integrals are discussed, together with transformations of the governing differential equations. Integrals involving products combining elliptic integrals of different kinds are also presented.
Non-archimedean hyperbolicity and applications
2018
Inspired by the work of Cherry, we introduce and study a new notion of Brody hyperbolicity for rigid analytic varieties over a non-archimedean field $K$ of characteristic zero. We use this notion of hyperbolicity to show the following algebraic statement: if a projective variety admits a non-constant morphism from an abelian variety, then so does any specialization of it. As an application of this result, we show that the moduli space of abelian varieties is $K$-analytically Brody hyperbolic in equal characteristic zero. These two results are predicted by the Green-Griffiths-Lang conjecture on hyperbolic varieties and its natural analogues for non-archimedean hyperbolicity. Finally, we use …
From Graz to Göttingen: Neugebauer’s Early Intellectual Journey
2016
Otto Neugebauer’s early academic career was marked by a series of transitions. His interests shifted from physics to mathematics, and finally to the history of ancient mathematics and exact sciences. Yet even from his early years in Graz, Neugebauer was strongly attracted to the mathematical culture of Gottingen. When he arrived there in 1922, he quickly established a strong personal friendship with Richard Courant, the newly appointed Director of the Mathematics Institute. Neugebauer and Courant worked together closely up until 1933, when the Nazi government decimated the Gottingen scientific community. In this essay, Neugebauer’s historical work and his vision for a new approach to the st…
Dianthus superbus as a critically endangered species in Latvia: evaluation of its growth conditions and conservation possibilities
2021
Abstract Dianthus superbus is one of the most endangered species in Latvia and is on the verge of local extinction. Therefore, the aim of this study was to inventory previously identified populations of D. superbus in Latvia and to develop activities to conserve this species in accordance with the results obtained in situ. Expeditions on 18 previously documented locations, according to the data of Nature Conservation Agency, revealed only three existing D. superbus localities in Latvia with a significant number of specimens located in the Latgale region near Silenieki. In 2020, for the first time, two more new D. superbus localities were found in the vicinity of these three approved locatio…
Pulsating in Unison at Optical and X-Ray Energies: Simultaneous High Time Resolution Observations of the Transitional Millisecond Pulsar PSR J1023+00…
2019
PSR J1023+0038 is the first millisecond pulsar discovered to pulsate in the visible band; such a detection took place when the pulsar was surrounded by an accretion disk and also showed X-ray pulsations. We report on the first high time resolution observational campaign of this transitional pulsar in the disk state, using simultaneous observations in the optical (TNG, NOT, TJO), X-ray (XMM-Newton, NuSTAR, NICER), infrared (GTC) and UV (Swift) bands. Optical and X-ray pulsations were detected simultaneously in the X-ray high intensity mode in which the source spends $\sim$ 70% of the time, and both disappeared in the low mode, indicating a common underlying physical mechanism. In addition, o…
Nano-magnetic potassium impregnated ceria as catalyst for the biodiesel production
2019
Abstract The main objective of this work comprises the investigation of biodiesel production from rapeseed oil using potassium impregnated Fe3O4-CeO2 nanocatalyst. The various concentration of potassium impregnated Fe3O4-CeO2 was screened for catalytic conversion of rapeseed oil to triglyceride methyl ester. The 25 wt % potassium impregnated Fe3O4-CeO2 nanocatalyst showed best biodiesel production. Nanocatalyst was characterized by FTIR, XRD, SEM, TEM, BET and Hammett indicator for basicity test. The characterization of biodiesel was performed with GC-MS, 1H and 13C NMR. Moreover, the optimum reaction parameters such as catalyst amount (wt %), oil to methanol ratio, reaction time and reacti…