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131.
Let {ø n (dμ)} be a system of orthonormal polynomials on the unit circle with respect to a measuredμ. Szegö's theory is concerned with the asymptotic behavior ofø n (dμ) when logμ′∈L 1. In what follows we will discuss the asymptotic behavior of the ratioø n (dμ 2)/ø n (dμ 1) on the unit circle whendμ 1 anddμ 2 are close in a sense (e.g.,dμ 2=gdμ 1, where g≥0 is such thatQ(e it )g(t) andQ(e it )/g(t) are bounded for a suitable polynomialQ) and μ 1 ′ >0 almost everywhere or (a somewhat weaker requirement) lim n→∞Φ n (dμ 1,0)=0 for the monic polynomial Φ n . The asymptotic behavior of the same fraction outside the unit circle was discussed in an earlier paper. 相似文献
132.
E. Brüning 《Czechoslovak Journal of Physics》1987,37(4):492-502
A definition of local functions of generalized free fields is suggested. Their concrete form is determined in a fairly general setting by analysing realizations of locality. A huge class of new models of relativistic quantum fields results in this way.Presented at the International Conference Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 23–27, 1986. 相似文献
133.
134.
Summary In this note we use a new averaging method, which was introduced in [2], to explain the geometrical behaviour of systems governed by nonlinear boundary value problems of the formy+g(y)=K sin(t),y(0)=y(/)=0. We show by numerical computations that global features of the solutions (such as the number of solutions, their magnitude, bifurcation behaviour, etc.) agree in both the original and averaged model. As an example, the pendulum equation is discussed in detail.
Supported by the Deutsche Forschungsgemeinschaft under grant No. BA 735/3-1 相似文献
Zusammenfassung In dieser Arbeit benutzen wir eine neue, in [2] eingeführte Mittelwertmethode, um das geometrische Verhalten nichtlinearer Randwertprobleme der Formy+g(y)=K sin(t),y(0)=y(/)=0. zu erklären. Wir belegen durch numerische Untersuchungen, daß globale Eigenschaften der Lösungen (wie z. B. die Anzahl der Lösungen, ihre Größenordnung, das Verzweigungsverhalten usw.) in der originalen und genäherten Gleichung übereinstimmen. Als Beispiel wird die Pendelgleichung ausführlich diskutiert.
Supported by the Deutsche Forschungsgemeinschaft under grant No. BA 735/3-1 相似文献
135.
We have investigated the suitability of poly-(alkyl--cyanoacrylates) (p-(alkyl-CAc)) for two-photon four-level holographic recording. It is shown that these materials follow indeed a two-photon four-level mechanism with the second absorption step in the near infrared. Light induces the polymerization of residual monomer in the matrix. The reaction is associated with positive density changes. The sensitivity ofp-(alkyl-CAc) depends strongly on composition and age of the sample. Maximum sensitivities achieved are comparable to the so far best-known two-photon four-level ir-sensitive systems. 相似文献
136.
Paul I. Surjasasmita Ben S. Freiser 《Journal of the American Society for Mass Spectrometry》1993,4(2):135-144
In this paper we report an extension of our earlier study on the structure of Alfacetone)2 + Collision-induced dissociation (CID) on MfacetoneXacetone-d6)+ for M = Al, Fe, Co, and Cu yields primarily, if not exclusively, nearly equal amounts of acetone and acetone-d6. Likewise, infrared multiphoton dissociation (IRMPD) at 10.6 μm yields, exclusively, nearly equal losses of the labeled and unlabeled acetones. These results suggest that the two acetone ligands bind in an equivalent fashion. Sc+ was also studied, which proved to be the most interesting. Sc+ reacts with acetone to form primarily ScO+, which undergoes higher order reactions leading to several products including ScO(acetone)2 +. IRMPD on this ion produces ScO(acetone-d6)(CD2CO)+, while its perdeuterated analog also produces ScO(acetone-d6)+ in addition to ScO(acetone-d6(CD2CO)+. The IRMPD results are supplemented by studying the primary and higher order reactions of Sc+ with acetone, as well as the CID of ScO(acetone)2 +. Finally, a qualitative assessment of the infrared photodissociation cross sections is given. It is found that the relative photodissociation cross sections follow the orders Co(acetone-d6)2 + > Co(acetone)(acetone-d6) > Co(acetone)2 + and Co(acetone-d6)+ > Co(acetone)+. 相似文献
137.
Zojer E Beljonne D Pacher P Brédas JL 《Chemistry (Weinheim an der Bergstrasse, Germany)》2004,10(11):2668-2680
Quadrupolar-type substitution of pi-conjugated chromophores with donor and acceptor groups has been shown to increase their two-photon absorption (TPA) response by up to two orders of magnitude. Here, we apply highly correlated quantum-chemical calculations to evaluate the impact of the nature of conjugated bridge and the charge-transfer distance on that enhancement. We compare chromophores with phenylenevinylene-, thienylenevinylene-, polyene-, and indenofluorene-type backbones substituted by dimethylamino and cyano groups. In all compounds, we find a strongly TPA-active A(g) state (either 2A(g) or 3A(g)) in the low-energy region, as well as a higher lying TPA-active state (mA(g)) at close to twice the energy of the lowest lying one-photon allowed state; the smaller energy detuning in the mA(g) states results in very large TPA cross sections delta. We also investigate the influence of the degree of ground-state polarization on TPA. Independent of the nature of the backbone and the donor-acceptor separation, delta displays the same qualitative evolution with a maximum before the cyanine-like limit; the highest TPA cross sections are calculated for distirylbenzene- and polyene-based systems. 相似文献
138.
Svilen Bobev Paul H. Tobash Joe D. Thompson John L. Sarrao 《Journal of solid state chemistry》2005,178(6):2091-2103
A number of rare-earth alumo-silicides (R-Al-Si) have been synthesized from the corresponding elements by high-temperature reactions, carried out in excess of aluminum to serve as a flux. Under these experimental conditions, large single crystals of all R-Al-Si ternary phases were readily produced. The crystal structures these ternaries adopt were studied by means of powder and single-crystal X-ray diffraction and were classified as follows: (1) the early rare-earths (R=La, Ce, Pr, Nd, Sm, Gd) yield RAlxSi2−x, x∼1, non-stoichiometric ternary derivatives of the body-centered α-ThSi2-type; (2) the late rare-earths (R=Tb, Dy, Ho, Er, Tm) form stoichiometric R2Al3Si2 compounds that crystallize in the C-centered monoclinic Y2Al3Si2-type; (3) the divalent Eu and Yb produce EuAl2Si2 and YbAl2Si2 with the trigonal CaAl2Si2-type, whereas the last lanthanide element, Lu, forms LuAlSi with C-centered orthorhombic YAlGe-type. These structural trends are reviewed, and the evolution of the basic physical properties such as magnetism, heat capacity and electrical resistivity when moving across the series is described in detail. 相似文献
139.
Roy Edward Bruns Paul Martin Kuznesof James Elton Moore 《Journal of Molecular Structure》1975,29(2):211-223
CNDO molecular orbital calculations have been performed to analyze donor—acceptor interactions between molecular chlorine and benzene, toluene, mesitylene and hexamethylbenzene and the, as yet, unreported chlorine—hexafluorobenzene and carbon disulfide—benzene pairs. The stabilization energy and the dipole moment and its derivative (?p/?RCICI) calculated for the benzene—chlorine complex are in good agreement with the estimated experimental values. The trends in the experimental stabilization energies and the Cl-Cl vibrational frequencies with increasing methyl substitution appear to be well reproduced by the calculations. The charge transferred from the benzene donor is polarized toward the outer chlorine atom or sulfur atom. For hexafluorobenzene-chlorine the direction of electronic charge polarization is reversed from that of the benzene and methylbenzene complexes. The calculated results are discussed within the framework of Muliiken's simplified resonance theory for complexes. 相似文献
140.
The diamagnetic square planar d(8) complexes [meso-arylcorrolato]copper(III) become paramagnetic upon warming, indicative of the equilibrium between the [corrolato]copper(III) and the [corrolato](+)* copper(II) forms of the complex. [meso-Triphenylcorrolato]copper(III) was structurally characterized and found to be saddled. 相似文献