In account of the famous Cebysev inequality, a rich theory has appeared in the literature. We establish some new weighted Cebysev type integral inequalities. Our proofs are of independent interest and provide new estimates on these types of inequalities. 相似文献
A library of π‐expanded α,β‐unsaturated ketones was designed and synthesized. They were prepared by a combination of Wittig reaction, Sonogashira reaction, and aldol condensation. It was further demonstrated that the double aldol condensation can be performed effectively for highly polarized styrene‐ and diphenylacetylene‐derived aldehydes. The strategic placement of two dialkylamino groups at the periphery of D ‐π‐A‐π‐D molecules resulted in dyes with excellent solubility. These ketones absorb light in the region 400–550 nm. Many of them display strong solvatochromism so that the emission ranges from 530–580 nm in toluene to the near‐IR region in benzonitrile. Ketones based on cyclobutanone as central moieties display very high fluorescence quantum yields in nonpolar solvents, which decrease drastically in polar media. Photophysical studies of these new functional dyes revealed that they possess an enhanced two‐photon absorption cross section when compared with simpler ketone derivatives. Due to strong polarization of the resulting dyes, values of two‐photon absorption cross sections on the level of 200–300 GM at 800 nm were achieved, and thanks to that as well as the presence of the keto group, these new two‐photon initiators display excellent performance so that the operating region is 5–75 mW in some cases. 相似文献
We study the convergence of the Pre?i? type k‐step iterative method for a class of operators satisfying Pre?i? type contractive conditions on the setting of partial metric spaces. Some examples are presented to illustrate our obtained results. As applications of the presented convergence theorems, we derive global attractivity results for a class of matrix difference equations. Numerical experiments are also presented to illustrate the theoretical findings. 相似文献
Thermogravimetric (TG) investigations of organotin(IV) carboxylates with the general formula RmSnL4−m (where R=CH3, C2H5, n‐C4H9, C6H5, cyclo‐C6H11, n‐C8H17, m=2, 3, and L=para‐nitrophenylethanoate anion) have been performed. Derivative thermogravimetry (DTG) and differential thermal analysis (DTA) techniques, Horowitz‐Metzger method and the fundamental thermodynamic relations are used to evaluate the thermokinetic parameters of each thermal degradation pattern. Results reveal that the thermal stability is functional to Sn C and Sn O bonds. In the case of R2SnL2, activation energy, reaction order and pre‐exponential factor associated with the bulk degradation processes increase as the alkane chain length increases. Hence, Oct2SnL2 is thermally more stable than Bu2SnL2, which in turn is more resistant to thermal dissociation than Et2SnL2. The same phenomenon is not observed for R3SnL compounds because their degradation is highly irregular. Furthermore, R2SnL2 has larger values of kinetic parameters than those of corresponding triorganotin(IV) para‐nitrophenylethanotes. Thermodynamic parameters of these compounds also reinforce the above facts. 相似文献
Journal of Algebraic Combinatorics - We show that the $$\gamma $$ -vector of the interval subdivision of a simplicial complex with a nonnegative and symmetric h-vector is nonnegative. In... 相似文献
Journal of Thermal Analysis and Calorimetry - The aim of this work is the energy analysis of a novel semicircle-shaped parabolic trough solar collector filled with the water–boehmite alumina... 相似文献
The present study reports the green synthesis of starch–maleate (SM) at ambient temperature in solvent-free system using Rhizopus arrhizus lipase as a biocatalyst and maleic acid (MA) as an esterification agent. The synthetic scheme was found to be efficient, economical, and ecofriendly. The newly synthesized SM samples were characterized using Fourier transform infrared (FTIR) and proton nuclear magnetic resonance (1H NMR) spectroscopic techniques. The degree of substitution (DS) was found in the range of 0.53–0.62. Moreover, DS was found to be temperature and time-dependent. X-ray diffraction (XRD) exhibited that maleation did not change the crystalline nature of native starch. Scanning electron microscopy (SEM) revealed that size of SM granules was in the range of 4–18 µm. The activation energy (Ea) of SM formation was calculated to be 42.94 kcal mol?1 which clearly indicated the effective and rapid interaction of functional groups. Hence, the solvent-free solid-state synthetic methodology proved to be excellent for the synthesis of novel biomaterials with appreciable high DS for drug delivery and sorption of heavy metal ions from water. 相似文献