Search results for " Mathematica"

On irreducible products of characters

2021

Abstract We study the problem when the product of two non-linear Galois conjugate characters of a finite group is irreducible. We also prove new results on irreducible tensor products of cross-characteristic Brauer characters of quasisimple groups of Lie type.

Powers of conjugacy classes in a finite groups

2020

[EN] The aim of this paper is to show how the number of conjugacy classes appearing in the product of classes affect the structure of a finite group. The aim of this paper was to show several results about solvability concerning the case in which the power of a conjugacy class is a union of one or two conjugacy classes. Moreover, we show that the above conditions can be determined through the character table of the group.

Regulāru valodu pazīšana ar galīgu kvantu automātu

2007

Inhomogeneous free-electron distribution in InN nanowires: Photoluminescence excitation experiments

2010

Photoluminescence excitation (PLE) spectra have been measured for a set of self-assembled InN nanowires (NWs) and a high-crystalline quality InN layer grown by molecular-beam epitaxy. The PLE experimental lineshapes have been reproduced by a self-consistent calculation of the absorption in a cylindrical InN NW. The differences in the PLE spectra can be accounted for the inhomogeneous electron distribution within the NWs caused by a bulk donor concentration $({N}_{D}^{+})$ and a two-dimensional density of ionized surface states $({N}_{ss}^{+})$. For NW radii larger than 30 nm, ${N}_{D}^{+}$ and ${N}_{ss}^{+}$ modify the absorption edge and the lineshape, respectively, and can be determined f…

Albanese Maps and Fundamental Groups of Varieties With Many Rational Points Over Function Fields

2020

We investigate properties of the Albanese map and the fundamental group of a complex projective variety with many rational points over some function field, and prove that every linear quotient of the fundamental group of such a variety is virtually abelian, as well as that its Albanese map is surjective, has connected fibres, and has no multiple fibres in codimension one.

A new plant wide modelling approach for the reduction of greenhouse Gas emission from wastewater treatment plants

2017

Recent studies about greenhouse gas (GHG) emissions show that sewer collection systems and wastewater treatment plants (WWTPs) are anthropogenic GHG potential sources. Therefore, they contribute to the climate change and air pollution. This increasing interest towards climate change has led to the development of new tools for WWTP design and management. This paper presents the first results of a research project aiming at setting-up an innovative mathematical model platform for the design and management of WWTPs. More specifically, the study presents the project’s strategy aimed at setting-up a plant-wide mathematical model which can be used as a tool for reducing/controlling GHG from WWTP.…

Inverse Problems Light: Numerical Differentiation

2001

(2001). Inverse Problems Light: Numerical Differentiation. The American Mathematical Monthly: Vol. 108, No. 6, pp. 512-521.

F-signature of pairs: Continuity, p-fractals and minimal log discrepancies

2011

This paper contains a number of observations on the {$F$-signature} of triples $(R,\Delta,\ba^t)$ introduced in our previous joint work. We first show that the $F$-signature $s(R,\Delta,\ba^t)$ is continuous as a function of $t$, and for principal ideals $\ba$ even convex. We then further deduce, for fixed $t$, that the $F$-signature is lower semi-continuous as a function on $\Spec R$ when $R$ is regular and $\ba$ is principal. We also point out the close relationship of the signature function in this setting to the works of Monsky and Teixeira on Hilbert-Kunz multiplicity and $p$-fractals. Finally, we conclude by showing that the minimal log discrepancy of an arbitrary triple $(R,\Delta,\b…

PT-symmetry and Schrödinger operators. The double well case

2015

We study a class of $PT$-symmetric semiclassical Schrodinger operators, which are perturbations of a selfadjoint one. Here, we treat the case where the unperturbed operator has a double-well potential. In the simple well case, two of the authors have proved in [6] that, when the potential is analytic, the eigenvalues stay real for a perturbation of size $O(1)$. We show here, in the double-well case, that the eigenvalues stay real only for exponentially small perturbations, then bifurcate into the complex domain when the perturbation increases and we get precise asymptotic expansions. The proof uses complex WKB-analysis, leading to a fairly explicit quantization condition.

F-singularities via alterations

2011

For a normal F-finite variety $X$ and a boundary divisor $\Delta$ we give a uniform description of an ideal which in characteristic zero yields the multiplier ideal, and in positive characteristic the test ideal of the pair $(X,\Delta)$. Our description is in terms of regular alterations over $X$, and one consequence of it is a common characterization of rational singularities (in characteristic zero) and F-rational singularities (in characteristic $p$) by the surjectivity of the trace map $\pi_* \omega_Y \to \omega_X$ for every such alteration $\pi \: Y \to X$. Furthermore, building on work of B. Bhatt, we establish up-to-finite-map versions of Grauert-Riemenscheneider and Nadel/Kawamata-V…