6,337 research outputs found
Signatures of hermitian forms and the Knebusch Trace Formula
Signatures of quadratic forms have been generalized to hermitian forms over
algebras with involution. In the literature this is done via Morita theory,
which causes sign ambiguities in certain cases. In this paper, a hermitian
version of the Knebusch Trace Formula is established and used as a main tool to
resolve these ambiguities.
The last page is an erratum for the published version. We inadvertently (I)
gave an incorrect definition of adjoint involutions; (II) omitted dealing with
the case . As , the
omission does not affect our reasoning or our results. For the sake of
completeness we point out where some small changes should be made in the
published version.Comment: This is the final version before publication. The last page is an
updated erratum for the published versio
MMP for moduli of sheaves on K3s via wall-crossing: nef and movable cones, Lagrangian fibrations
Longitudinal and transversal spin dynamics of donor-bound electrons in fluorine-doped ZnSe: spin inertia versus Hanle effect
The spin dynamics of the strongly localized, donor-bound electrons in
fluorine-doped ZnSe epilayers is studied by pump-probe Kerr rotation
techniques. A method exploiting the spin inertia is developed and used to
measure the longitudinal spin relaxation time, , in a wide range of
magnetic fields, temperatures, and pump densities. The time of the
donor-bound electron spin of about 1.6 s remains nearly constant for
external magnetic fields varied from zero up to 2.5 T (Faraday geometry) and in
a temperature range K. The inhomogeneous spin dephasing time,
ns, is measured using the resonant spin amplification and Hanle
effects under pulsed and steady-state pumping, respectively. These findings
impose severe restrictions on possible spin relaxation mechanisms.Comment: 10 pages, 7 figure
Division, adjoints, and dualities of bilinear maps
The distributive property can be studied through bilinear maps and various
morphisms between these maps. The adjoint-morphisms between bilinear maps
establish a complete abelian category with projectives and admits a duality.
Thus the adjoint category is not a module category but nevertheless it is
suitably familiar. The universal properties have geometric perspectives. For
example, products are orthogonal sums. The bilinear division maps are the
simple bimaps with respect to nondegenerate adjoint-morphisms. That formalizes
the understanding that the atoms of linear geometries are algebraic objects
with no zero-divisors. Adjoint-isomorphism coincides with principal isotopism;
hence, nonassociative division rings can be studied within this framework.
This also corrects an error in an earlier pre-print; see Remark 2.11
Inhomogeneous nuclear spin polarization induced by helicity-modulated optical excitation of fluorine-bound electron spins in ZnSe
Optically-induced nuclear spin polarization in a fluorine-doped ZnSe epilayer
is studied by time-resolved Kerr rotation using resonant excitation of
donor-bound excitons. Excitation with helicity-modulated laser pulses results
in a transverse nuclear spin polarization, which is detected as a change of the
Larmor precession frequency of the donor-bound electron spins. The frequency
shift in dependence on the transverse magnetic field exhibits a pronounced
dispersion-like shape with resonances at the fields of nuclear magnetic
resonance of the constituent zinc and selenium isotopes. It is studied as a
function of external parameters, particularly of constant and radio frequency
external magnetic fields. The width of the resonance and its shape indicate a
strong spatial inhomogeneity of the nuclear spin polarization in the vicinity
of a fluorine donor. A mechanism of optically-induced nuclear spin polarization
is suggested based on the concept of resonant nuclear spin cooling driven by
the inhomogeneous Knight field of the donor-bound electron.Comment: 12 pages, 11 figure
The factorization of simple knots
For high-dimensional simple knots we give two theorems concerning unique factorization into irreducible knots, and provide examples to show that the hypotheses are necessary in each cas
How You Can Work To Increase The Presence And Improve The Experience Of Black, Latinx, And Native American People In The Economics Profession
Recently in economics there has been discussion of how to increase diversity in the profession and how to improve the work life of diverse peoples. We conducted surveys and interviews with Black, Latinx and Native American people. These groups have long been underrepresented in the economics profession. Participants were at various stages along the economics career trajectory, or on the trajectory no longer, and used their lived experience to reflect on what helps and hurts underrepresented minorities in economics. We heard a few consistent themes: bias, hostile climate, and the lack of information and good mentoring among them. Respondents\u27 insights and experience point toward action steps that you can take today to increase the presence and improve the work life of underrepresented minorities in the economics profession
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