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Low-lying triplet electronic states have been detected in furan, thiophene, and pyrrole by the method of variable-angle, electron-impact spectroscopy. Singlet → triplet transitions occur with maximum intensity at 3.99 eV and 5.22 eV in furan, 3.75 eV and 4.62 eV in thiophene, and 4.21 eV in pyrrole. A weak transition at 5.22 eV in pyrrole is assigned as the lowest observed singlet → singlet excitation in that molecule. 相似文献
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Yuval Z. Flicker 《Journal d'Analyse Mathématique》1987,49(1):135-202
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We present evidence for a nonsingular origin of the Universe with intial conditions determined by quantum physics and relativistic
gravity. In particular, we establish that the present temperature of the microwave background and the present density of the
Universe agree well with our predictions from these intial conditions, after evolution to the present age using the Einstein-Friedmann
equation. Remarkably, the quantum origin for the Universe naturally allows its evolution at exactly the critical density.
We also discuss the consequences of these results to some fundamental aspects of quantum physics in the early Universe. 相似文献
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Yuval Z. Flicker 《Mathematische Annalen》1987,279(2):173-191
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Yuval Z. Flicker 《Japanese Journal of Mathematics》2014,9(2):171-216
These are purely expository notes of Opdam’s analysis [O1] of the trace form τ(f) = f(e) on the Hecke algebra H = C c (I\G/I) of compactly supported functions f on a connected reductive split p-adic group G which are biinvariant under an Iwahori subgroup I, extending Macdonald’s work. We attempt to give details of the proofs, and choose notations which seem to us more standard. Many objects of harmonic analysis are met: principal series, Macdonald’s spherical forms, trace forms, Bernstein forms. The latter were introduced by Opdam under the name Eisenstein series for H. The idea of the proof is that the last two linear forms are proportional, and the proportionality constant is computed by projection to Macdonald’s spherical forms. Crucial use is made of Bernstein’s presentation of the Iwahori–Hecke algebra by means of generators and relations, as an extension of a finite dimensional algebra by a large commutative subalgebra. We give a complete proof of this using the universal unramified principal series right H-module M = C c (A(O)N\G/I) to develop a theory of intertwining operators algebraically. 相似文献
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The Selberg trace formula is of unquestionable value for the study of automorphic forms and related objects. In principal
it is a simple and natural formula, generalizing the Poisson summation formula, relating traces of convolution operators with
orbital integrals. This paper is motivated by the belief that such a fundamental and natural relation should admit asimple and short proof. This is accomplished here for test functions with a single supercusp-component, and another component which is spherical
and “sufficiently-admissible” with respect to the other components. The resulting trace formula is then use to sharpen and
extend the metaplectic correspondence, and the simple algebras correspondence, of automorphic representations, to the context
of automorphic forms with asingle supercuspidal component, over any global field. It will be interesting to extend these theorems to the context of all automorphic
forms by means of a simple proof. Previously a simple form of the trace formula was known for test functions with two supercusp
components; this was used to establish these correspondences for automorphic forms with two supercuspidal components. The
notion of “sufficiently-admissible” spherical functions has its origins in Drinfeld's study of the reciprocity law for GL(2)
over a function field, and our form of the trace formula is analogous to Deligne's conjecture on the fixed point formula in
étale cohomology, for a correspondence which is multiplied by by a sufficiently high power of the Frobenius, on a separated
scheme of finite type over a finite field. Our trace formula can be used (see [FK′]) to prove the Ramanujan conjecture for
automorphic forms with a supercuspidal component on GL(n) over a function field, and to reduce the reciprocity law for such forms to Deligne's conjecture. Similar techniques are
used in ['t'F] to establish base change for GL (n) in the context of automorphic forms with a single supercuspidal component. They can be used to give short and simple proofs
of rank one lifting theorems forarbitrary automorphic forms; see [″F] for base change for GL(2), [F′] for base change forU(3), and [′F′] for the symmetric square lifting from SL(2) to PGL(3).
Partially supported by NSF grants. 相似文献