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41.
We give a concise review and extension of S-procedure that is an instrumental tool in control theory and robust optimization analysis. We also discuss the approximate S-Lemma as well as its applications in robust optimization.The many suggestions and detailed corrections of an anonymous referee are gratefully acknowledged. 相似文献
42.
The spectral structure of two parameter unbounded operator pencils of waveguide type is studied. Theorems on discreteness
of the spectrum for a fixed parameter are proved. Variational principles for real eigenvalues in some parts of the root zones
are established. In the case of n = 1 (quadratic pencils) domains containing the spectrum are described (see Fig. 1–3). Conditions in the definition of the
pencils of waveguide type arise naturally from physical problems and each of them has a physical meaning. In particular a
connection between the energetic stability condition and a perturbation problem for the coefficients is given. 相似文献
43.
Felix Ali Mehmeti 《Mathematical Methods in the Applied Sciences》1994,17(9):697-752
Consider two copies N1, N2 of the interval [0, ∞]. Consider Klein-Gordon equations with (different) constant coefficients on ? × Nj ( = time × space). Assume the coincidence of the values of the solution at the boundary points of the Nj for all times and a transmission condition relating its first (one-sided) space derivatives at these points. Under a symmetry condition, we extend the spatial part of the equation and the transmission conditions to a self-adjoint operator (by Friedrichs extension) and reformulate our problem in terms of an abstract wave equation in a suitable Hilbert space. We derive an expansion of the solution in generalized eigenfunctions of this self-adjoint extension and show, that the L∞-norms (in space) of the solution and its first k space derivatives at the time t decay for t → ∞ at least as const. t¼, if the initial conditions satisfy a compatibility condition of order k derived in this paper. The loss of decay rate in comparison with the full line case (const. t?½, cf. [28]) is caused by the tunnel effect. Further we show that an abstract wave equation in a Hilbert space with a Friedrichs extension as spatial part can always be derived from a stationarity principle for an associated action-type functional. This yields a physical legitimation of our model by the principle of stationary action and moreover a criterion for the physical interpretability of all models created by the linear interaction concept [4, 6, 8, 10], in particular for the coupling of media of different dimension (alternative to [13, 16] for similar models). 相似文献
44.
Joel M. Kauffman Ali Khalaj Peter T. Litak John A. Novinski Gurdip S. Bajwa 《Journal of heterocyclic chemistry》1994,31(4):957-965
To improve the solubility, photostability and fluorescence quantum yield (Φ) of 2-arylbenzimidazolium ions the N-1 hydrogen was replaced by an alkyl group before N-3 was quatemized; this substitution did not reduce Φ, proving the absence of steric inhibition to attainment of coplanarity in the excited state. A related symmetrical 2,2′-arylenebis(1,3-dimethyldibenzimidazolium ion) had Φ = 0.86. The related 2,5-bis(1-methyl-2-benzimidazolyl)phenol had Φ = 0.38 at 22° as well as a very large Stokes' shift due to proton-transfer. These findings supported a new insight into the electron distribution of the first excited singlet state of oligophenylenes. The compounds are of interest as laser dyes and scintillation fluors. 相似文献
45.
46.
47.
Herein we describe the synthesis and characterization of compounds having the formulae R2SnL2 and R3SnL, where R = Me, n-Bu, Ph and n-Oct and L = 2-[N-(2,4,6-tribromophenylamido]propanoic acid. All the complexes have been characterized by various spectroscopic methods (IR and 1H, 13C, 119Sn NMR), elemental analysis, mass spectrometry and physical data. These compounds were also screened for their biological activity and found some encouraging results. 相似文献
48.
Trichloroisocyanuric acid is used as an effective oxidizing agent for the oxidation of 1,3,5-trisubstituted pyrazolines to their corresponding pyrazoles under both heterogeneous and also solvent free conditions with good yields at room temperature. 相似文献
49.
The reactions of bis(trimethylstannyl)ethyne, Me3Sn–C?C–SnMe3 ( 4 ), with trimethylsilyl‐ or dimethylsilyl‐dialkylboryl‐substituted alkenes 1 – 3 afford organometallic‐substituted allenes 5 , 6 and 8 , 9 in high yield. In the case of (E)‐2‐trimethylsilyl‐3‐diethylboryl‐2‐pentene ( 1) , a butadiene derivative 7 could be detected as an intermediate prior to rearrangement into the allene. All reactions were monitored by 29Si and 119Sn NMR, and the products were characterized by an extensive NMR data set (1H, 11B, 13C, 29Si, 119Sn NMR). Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
50.
István E. MarkóJean-Christophe Vanherck Ali AtesBernard Tinant Jean-Paul Declercq 《Tetrahedron letters》2003,44(16):3333-3336
Upon treatment with tBuOK/H2O, a variety of ω-halo-β-keto-ketals undergo smooth cyclisation, affording in excellent yields mono-protected [n,m] spiro bicyclic diketones. This transformation is highly stereoselective producing, in all cases, the diastereoisomerically pure spiro derivatives. 相似文献