Two Questions on Products of Toeplitz Operators on the Bergman Space

The zero product problem and the commuting problem for Toeplitz operators on the Bergman space over the unit disk are some of the most interesting unsolved problems. For bounded harmonic symbols these are solved but for general bounded symbols it is still far from being complete. This paper shows that the zero product problem holds for a special case where one of the symbols has certain polar decomposition and the other is a general bounded symbol. We also prove that the commutant of T_z+[`(z)]T_z+\bar{z} is sum of powers of itself.     

Second moments of ESR signals from poly(p-phenylene) and the deuterated analog

The second moments of the ESR signals obtained from poly(p-phenylene) (PPP) and deuterated PPP were measured at 9.5 and 35 GHz. The theoretical and experimental contributions to the second moments were considered. It is shown that for deuterated PPP, deuteron hyperfine splitting makes a negligible contribution to the observed second moment. The proton hyperfine contributions to the second moments of the radical species in PPP and p-sexiphenyl were estimated and it was concluded that the unpaired electron was delocalized over only 2-4 phenylene units. A rationale is offered in terms of polarons present as defects in the PPP chains.     

Chemistry of dihydro-1,4-dioxin III a new method for the preparation of α,α′-dihydroxy ketones from ketones and aldehydes

Title compounds, 7, were prepared from ketones and aldehydes via the intermediate 3 by methanolic peracid epoxidation followed by NaBH₄ reduction and acidic hydrolysis. Application of this method to the preparation of the unnatural corticoid side chain was reported.     

Synthesis of the complete carbocyclic skeleton of vinigrol

[reaction: see text] An efficient entry to the fully elaborated skeleton of vinigrol is described. The installation of the desired stereochemistry at C(12) and the construction of the eight-membered ring were achieved in one operation by a remarkably facile anionic oxy-Cope rearrangement of Z-isopropenyl isomer 24.     

Quadratic kernel-free non-linear support vector machine

A new quadratic kernel-free non-linear support vector machine (which is called QSVM) is introduced. The SVM optimization problem can be stated as follows: Maximize the geometrical margin subject to all the training data with a functional margin greater than a constant. The functional margin is equal to W ^T X + b which is the equation of the hyper-plane used for linear separation. The geometrical margin is equal to . And the constant in this case is equal to one. To separate the data non-linearly, a dual optimization form and the Kernel trick must be used. In this paper, a quadratic decision function that is capable of separating non-linearly the data is used. The geometrical margin is proved to be equal to the inverse of the norm of the gradient of the decision function. The functional margin is the equation of the quadratic function. QSVM is proved to be put in a quadratic optimization setting. This setting does not require the use of a dual form or the use of the Kernel trick. Comparisons between the QSVM and the SVM using the Gaussian and the polynomial kernels on databases from the UCI repository are shown.     

Calix[4]azacrowns as novel molecular scaffolds for the generation of visible and near-infrared lanthanide luminescence

Two calix[4]azacrowns, capped with two aminopolyamide bridges, were used as ligands for the complexation of lanthanide ions [Eu(III), Tb(III), Nd(III), Er(III), La(III)]. The formation of 1:2 and 1:1 complexes was observed, and stability constants, determined by UV absorption and fluorescence spectroscopy, were found to be generally on the order of log beta(11) approximately 5-6 and log beta(12) approximately 10. The structural changes of the ligands upon La(III) complexation were probed by 1H NMR spectroscopy. The two ligands were observed to have opposite fluorescence behaviors, namely, fluorescence enhancement (via blocking of photoinduced electron transfer from amine groups) or quenching (via lanthanide-chromophore interactions) upon metal ion complexation. Long-lived lanthanide luminescence was sensitized by excitation in the pi,pi band of the aromatic moieties of the ligands. The direct involvement of the antenna triplet state was demonstrated via quenching of the ligand phosphorescence by Tb(III). Generally, Eu(III) luminescence was weak (Phi(lum) 相似文献   

MEH-PPV/Alq_3-based bulk heterojunction photodetector

In this paper, we present the effect of varied illumination levels on the electrical properties of the organic blend bulk heterojuction （BHJ） photodiode. To prepare the BHJ blend, poly（2-methoxy-5（2P-ethylhexyloxy） phenyleneviny- lene （MEH-PPV） and aluminum-tris-（8-hydroxyquinoline） （Alq3） are used as donor and acceptor materials, respectively. In order to fabricate the photodiode, a 40-nm thick film of poly（3, 4-ethylendioxytbiophene）：poly（styrensulfonate） （PE- DOT：PSS） is primarily deposited on a cleaned ITO coated glass substrate by spin coating technique. The organic photo- sensitive blend is later spun coated on the PEDOT：PSS layer, followed by the lithium fluoride （LiF） and aluminium （A1） thin films deposition by thermal evaporation. The optical properties of the MEH-PPV：Alq3 blend thin films are investigated using photoluminescence （PL） and UV-Vis spectroscopy. The photodiode shows good photo-current response as a function of variable illumination levels. The responsivity value - 8 mA/W at 3 V is found and the ratio of photo-current to dark current （lph/IDark） is found to be 1.24.     

Investigation of the radiative lifetime in core–shell CdSe/ZnS and CdSe/ZnSe quantum dots

Using the one band effective mass approximation model we computed the optical properties of the spherical shaped CdSe/ZnS and Cdse/ZnSe core–shell quantum dot (CSQD). For each structure we calculated the charge carrier energies and corresponding wave functions. We investigated the dependence of the carrier energies on various parameters of the CSQD, including its size. Then we calculated the radiative recombination lifetime for the two types of CSQDs nanocrystals. We found that as the size of the dot is increased the optical gap of CSQD is reduced, resulting in a reduction in electron energies and an increase in hole energies. We have shown that the radiative recombination lifetime in the CdSe/ZnS and CdSe/ZnSe CSQDs decreased by increasing the shell thickness around the core of the QD. We also showed that the radiative lifetime in the CdSe/ZnS is less than that in the CdSe/ZnSe CSQDs and is sensitive to the size and nature of shell of the semiconductor's material.     

Numerical Experience with Multiple Update Quasi-Newton Methods for Unconstrained Optimization

The authors have derived what they termed quasi-Newton multi step methods in [2]. These methods have demonstrated substantial numerical improvements over the standard single step Secant-based BFGS. Such methods use a variant of the Secant equation that the updated Hessian (or its inverse) satisfies at each iteration. In this paper, new methods will be explored for which the updated Hessians satisfy multiple relations of the Secant-type. A rational model is employed in developing the new methods. The model hosts a free parameter which is exploited in enforcing symmetry on the updated Hessian approximation matrix thus obtained. The numerical performance of such techniques is then investigated and compared to other methods. Our results are encouraging and the improvements incurred supercede those obtained from other existing methods at minimal extra storage and computational overhead.