Comparison of Twisted P-Form Spectra for Flat Manifolds with Diagonal Holonomy

We give an explicit formula for the multiplicities of the eigenvalues ofthe Laplacian acting on sections of natural vector bundles over acompact flat Riemannian manifold M = \ ⁿ , a Bieberbach group. In the case of the Laplacian acting onp-forms, twisted by a unitary character of , when hasdiagonal holonomy group F ₂ ^k , these multiplicities have acombinatorial expression in terms of integral values of Krawtchoukpolynomials and the so called Sunada numbers. If the Krawtchoukpolynomial K _p ⁿ (x)does not have an integral root, this expressioncan be inverted and conversely, the presence of such roots allows toproduce many examples of p-isospectral manifolds that are notisospectral on functions. We compare the notions of twistedp-isospectrality, twisted Sunada isospectrality and twisted finitep-isospectrality, a condition having to do with a finite part of thespectrum, proving several implications among them and getting a converseto Sunada's theorem in our context, for n 8. Furthermore, a finitepart of the spectrum determines the full spectrum. We give new pairs ofnonhomeomorphic flat manifolds satisfying some kind of isospectralityand not another. For instance: (a) manifolds which are isospectral onp-forms for only a few values of p 0, (b) manifolds which aretwisted isospectral for every , a nontrivial character of F, and(c) large twisted isospectral sets.     

Spectral Theory of the Atiyah–Patodi–Singer Operator on Compact Flat Manifolds

We study the spectral theory of the Dirac-type boundary operator \(\mathcal{D}\) defined by Atiyah, Patodi, and Singer, acting on smooth even forms of a compact flat Riemannian manifold M. We give an explicit formula for the multiplicities of the eigenvalues of \(\mathcal{D}\) in terms of values of characters of exterior representations of SO(n), where n=dim?M. As a consequence, we give large families of \(\mathcal{D}\)-isospectral flat manifolds that are non-homeomorphic to each other. Furthermore, we derive expressions for the eta series in terms of special values of Hurwitz zeta functions and, as a result, we obtain a simple explicit expression of the eta invariant.     

Study of structural and electronic transport properties of Ce-doped LaMnO3

The structural and electronic transport properties of La_1−x Ce _x MnO₃ (x=0.0–1.0) have been studied. All the samples exhibit orthorhombic crystal symmetry and the unit cell volume decreases with Ce doping. They also make a metal-insulator transition (MIT) and transition temperature increases with increase in Ce concentration up to 50% doping. The system La_0.5Ce_0.5MnO₃ also exhibits MIT instead of charge-ordered state as observed in the hole doped systems of the same composition.     

Internal kink instability during off-axis electron cyclotron current drive in the DIII-D tokamak

Experimental evidence is reported of an internal kink instability driven by a new mechanism: barely trapped suprathermal electrons produced by off-axis electron cyclotron heating on the DIII-D tokamak. It occurs in plasmas with an evolving safety factor profile q(r) when q(min) approaches 1. This instability is most active when ECCD is applied on the high field side of the flux surface. It has a bursting behavior with poloidal/toroidal mode number = m/n = 1/1. In positive magnetic shear plasmas, this mode becomes the fishbone instability. This observation can be qualitatively explained by the drift reversal of the barely trapped suprathermal electrons.     

Fourier Transform Spectroscopy of the A'(1)Pi-X(1)Sigma(+) System of CaO

The A'(1)Pi-X(1)Sigma(+) near-infrared system of CaO was observed for the first time at high resolution using a Fourier transform spectrometer. The A'(1)Pi-X(1)Sigma(+) chemiluminescence was excited in a Ca + N(2)O flame produced in a Broida-type oven. More than 3000 rotational lines, classified into 19 bands involving the A'(1)Pi 0 /= 2) levels with the nearby b(3)Sigma(+) (v-2) levels has been detected. An extended set of A'(1)Pi (v = 0-3) data has been obtained which is suitable for use in a future multistate deperturbation analysis of the a(3)Pi approximately A'(1)Pi approximately b(3)Sigma(+) approximately A(1)Sigma(+) complex of excited states. The new near-infrared spectra of the A'(1)Pi-X(1)Sigma(+) transition of CaO also permits the first direct high-resolution linkage between the orange and green systems and the near-infrared bands. Copyright 2000 Academic Press.     

Improved Parameterization for Combined Isotopomer Analysis of Diatomic Spectra and Its Application to HF and DF

A new way of representing vibration-rotation term values for multiple isotopomers of a given electronic state of a diatomic molecule is presented which resolves problems associated with the way the conventional combined isotopomer expansion represents the atomic mass-dependent JWKB and Born-Oppenheimer breakdown correction terms. Its application to infrared and microwave data for HF and DF yields new Dunham expansion coefficients and Born-Oppenheimer breakdown correction terms for this species. This procedure is implemented in a generally available computer program for fitting to various types of data involving one or several electronic states of multiple isotopomers of a diatomic molecule. Copyright 1999 Academic Press.