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Contributions to the Chemistry of Transition Metal Alkyl Compounds. XLVI. Polarographic Properties of Dibenzyl and Diphenyl Titanium in Aprotic Solvents The polarographic properties of dibenzyl and diphenyl titanium were investigated using acetonitrile (AN), dimethylformamide (DMF), and dimethylsulfoxide (DMSO) as solvents. Both compounds are reduced irreversibly at very negative potentials in a two-electron step with formation of titanium. The half-wave potentials depend on the donor strength of the solvents. With increasing donor number the half-wave potentials are shifted to more negative values. The fact that the limiting currents turned out to be diffusion controlled suggests a monomeric structure of the titanium diorganyls in AN, DMF, and DMSO. 相似文献
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Xuan Thinh Duong Irina Holmes Ji Li Brett D. Wick Dongyong Yang 《Journal of Functional Analysis》2019,276(4):1007-1060
In this paper we establish the characterization of the weighted BMO via two weight commutators in the settings of the Neumann Laplacian on the upper half space and the reflection Neumann Laplacian on with respect to the weights associated to and respectively. This in turn yields a weak factorization for the corresponding weighted Hardy spaces, where in particular, the weighted class associated to is strictly larger than the Muckenhoupt weighted class and contains non-doubling weights. In our study, we also make contributions to the classical Muckenhoupt–Wheeden weighted Hardy space (BMO space respectively) by showing that it can be characterized via the area function (Carleson measure respectively) involving the semigroup generated by the Laplacian on and that the duality of these weighted Hardy and BMO spaces holds for Muckenhoupt weights with while the previously known related results cover only . We also point out that this two weight commutator theorem might not be true in the setting of general operators L, and in particular we show that it is not true when L is the Dirichlet Laplacian on . 相似文献
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Moscow University Chemistry Bulletin - Hydrodistillation (HD), steam distillation (SD) and microwave-assisted hydrodistillation (MAHD) extraction methods were assessed for their effects on yield,... 相似文献
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A simple method of measuring the wavelength γ1 and the spectral line spacing Δγ of a multi-mode dye laser light by using the correlated speckle patterns produced at the far-field of a diffuser is proposed. Examples of the obtained values of γ1 and Δγ are 6.0 × 103 Å and 3.0 × 101 Å, respectively. 相似文献
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Let be a space of homogeneous type, and be the generator of a semigroup with Gaussian kernel bounds on . We define the Hardy spaces of for a range of , by means of area integral function associated with the Poisson semigroup of , which is proved to coincide with the usual atomic Hardy spaces on spaces of homogeneous type.
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In an attempt to examine the random version of the spectral theorem, the notion of random spectral measures and generalized random spectral measures are introduced and investigated. It is shown that each generalized random spectral measure on $(\mathbb C ,\mathcal{B}(\mathbb C ))$ admits a modification which is a random spectral measure. 相似文献
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Let L be a Schrdinger operator of the form L =-? + V acting on L~2(R~n), n≥3, where the nonnegative potential V belongs to the reverse Hlder class B_q for some q≥n. Let BMO_L(R~n) denote the BMO space associated to the Schrdinger operator L on R~n. In this article, we show that for every f ∈ BMO_L(R~n) with compact support, then there exist g ∈ L~∞(R~n) and a finite Carleson measure μ such that f(x) = g(x) + S_(μ,P)(x) with ∥g∥∞ + |||μ|||c≤ C∥f∥BMO_L(R~n), where S_(μ,P)=∫(R_+~(n+1))Pt(x,y)dμ(y, t),and Pt(x, y) is the kernel of the Poisson semigroup {e-~(t(L)~(1/2))}t0 on L~2(R~n). Conversely, if μ is a Carleson measure, then S_(μ,P) belongs to the space BMO_L(R~n). This extends the result for the classical John-Nirenberg BMO space by Carleson(1976)(see also Garnett and Jones(1982), Uchiyama(1980) and Wilson(1988)) to the BMO setting associated to Schrdinger operators. 相似文献
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In this paper, we extend the well-known result “the predual of Hardy space \(H^1\) is VMO” to the product setting, associated with differential operators. Let \(L_i\), \(i = 1, 2\), be the infinitesimal generators of the analytic semigroups \(\{e^{-tL_i}\}\) on \(L^2({\mathbb {R}})\). Assume that the kernels of the semigroups \(\{e^{-tL_i}\}\) satisfy the Gaussian upper bounds. We introduce the VMO spaces VMO\(_{L_1, L_2}(\mathbb {R}\times \mathbb {R})\) associated with operators \(L_1\) and \(L_2\) on the product domain \(\mathbb {R}\times \mathbb {R}\), then show that the dual space of VMO\(_{L_1, L_2}(\mathbb {R}\times \mathbb {R})\) is the Hardy space \(H^1_{L_1^*, L_2^*}(\mathbb {R}\times \mathbb {R})\) associated with the adjoint operators \(L^*_1\) and \(L^*_2\). 相似文献
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