Proof of a conjecture of Z-W Sun on ratio monotonicity

Sun, Brian Y.; Hu, Yingying; Wu, Baoyindureng

doi:10.1186/s13660-016-1221-y

Cited by 23 publications

(42 citation statements)

References 11 publications

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“…2B, built for the 2A → B; 2B → C reaction, shows its strong convexity property that leads to decrease of convergence frequency. In contrast, for nonconvex [15] functions we can achieve a significant improvement, as the A → B; 2B → C reaction demonstrates. Such a pattern is consistent with the optimization theory saying that the Armijo secondorder line search should be computed and applied only if the Hessian-approximation matrix is negative definite [28,34].…”

Section: Resultsmentioning

confidence: 99%

“…The literature indicates that many least-squares model-fitting problems in kinetics are nonlinear, nonconvex, and have multiple solutions [15]. There are two ways to overcome these difficulties: either by applying global optimization procedures, such as genetic algorithms [16,17] or simulated annealing, or by modifying gradient-based methods.…”

Section: Optimizationmentioning

confidence: 99%

“…The line search rules are known to enhance global convergence [15,[21][22][23] of gradient-based methods:…”

Section: Optimizationmentioning

confidence: 99%

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Equivalency of Kinetic Schemes: Causes and an Analysis of Some Model Fitting Algorithms

Петров

Dergachev

2017

Int. J. Chem. Kinet.

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The same experimental data can often be equally well described by multiple mathematically equivalent kinetic schemes. In the present work, we investigate several model‐fitting algorithms and their ability to distinguish between mechanisms and derive the correct kinetic parameters for several different reaction classes involving consecutive reactions. We have conducted numerical experiments using synthetic experimental data for six classes of consecutive reactions involving different combinations of first‐ and second‐order processes. The synthetic data mimic time‐dependent absorption data as would be obtained from spectroscopic investigations of chemical kinetic processes. The connections between mathematically equivalent solutions are investigated, and analytical expressions describing these connections are derived. Ten optimization algorithms based on nonlinear least squares methods are compared in terms of their computational cost and frequency of convergence to global solutions. Performance is discussed, and a preferred method is recommended. A response surface visualization technique of projecting five‐dimensional data onto the three‐dimensional search space of the minimal function values is developed.

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Section: Resultsmentioning

confidence: 99%

Section: Optimizationmentioning

confidence: 99%

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Equivalency of Kinetic Schemes: Causes and an Analysis of Some Model Fitting Algorithms

Петров

Dergachev

2017

Int. J. Chem. Kinet.

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“…[19] Magnetic goethite (based on nano-Fe 3 O 4 ), which has the combined advantages of a magnetic material and nanoparticles, can suitably meet most of the requirements of an ideal adsorbent. [20] Such materials not only inherit the advantages of nanomaterial adsorbents but can also compensate for disadvantages such as chemical instability and difficulty in separation and recovery of some adsorbents, to improve adsorption efficiency. Moreover, compared to other adsorbents, considering the extremely low cost and huge reserves of goethite and Fe 3 O 4 , magnetic goethite is worth considering in practical applications.…”

Section: Introductionmentioning

confidence: 99%

Removal of Cr(VI) from Wastewater by a Novel Adsorbent of Magnetic Goethite: Adsorption Performance and Adsorbent Characterisation

Liu

Chen

et al. 2019

ChemistrySelect

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A novel adsorbent of magnetic goethite was prepared by neutralisation hydrolysis and employed for Cr(VI) adsorption from aqueous solution. The magnetic goethite adsorbent was characterised by using scanning electron microscopy (SEM), X‐ray diffractometer (XRD), vibrating sample magnetometer (VSM), fourier transform infrared (FTIR), brunauer‐Emmett‐Teller (BET) and X‐ray photoelectron spectroscopy (XPS) method. VSM showed that the prepared adsorbents are super‐paramagnetic iron hydroxide. FTIR spectra revealed that magnetic goethite have ‐OH and other functional groups. The effects of various factors, including pH, adsorbent dosage, initial concentration, and ion concentration, were evaluated. Under the conditions of pH 3, 4 g/L magnetic goethite, 20 mg/L Cr(VI) concentration, and 0.01 mol/L NaNO3, the removal efficiency of Cr (VI) reached 88.2% and the adsorption capacity of the adsorbent reached 4.32 mg/g. The adsorption kinetic tests showed that the adsorption of Cr(VI) on the adsorbent matched well with pseudo‐second‐order kinetics, indicating the occurrence of chemisorption. The fitting of the Langmuir isotherm model showed that the adsorption of Cr(VI) on magnetic goethite was monolayer adsorption. On the other hand, thermodynamic studies conjectured that the adsorption processes of magnetic goethite for Cr(VI) was endothermic and spontaneous. These results suggest that magnetic goethite has great potential for the removal of heavy metals from wastewater.

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“…Moreover, a promising solution to this problem is the application of reusable heterogeneous catalysts with high catalytic efficiency under mild conditions. These catalysts include: (1) supported noble metals such as 0.05 g/g (5 %) Ru/Al 2 O 3 , [5] and (2) transition metals such as CoAPO-5, [6] CrAlPO-5, [7] Cu-BIM-PMO, [8] metal-containing ZSM-5 (MZSM-5) (M ¼ Cu, Co, Mn, Ni, Fe), [9] and silicasupported (SiO) 3 MOR (M ¼ Ti, Zr; R¼H, t Bu) [10] organometallic complexes with transition metals as active components. During their use, noble-metal-containing catalysts display high activity but are too expensive to be applied on a large scale in the industry.…”

Section: Introductionmentioning

confidence: 99%

Decomposition of cyclohexyl hydroperoxide over bimetallic mesoporous materials containing cobalt and chromium

Guo

et al. 2016

Can J Chem Eng

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Bimetallic mesoporous Co‐Cr‐TUD‐1 and its counterparts Co‐TUD‐1 and Cr‐TUD‐1 were synthesized by a direct hydrothermal treatment (DHT) method with triethanolamine as a template. The products were characterized by many techniques. Results show that Co and Cr are incorporated into the framework of TUD‐1. The catalytic behaviours of the samples were tested in decomposition of cyclohexyl hydroperoxide (CHHP). Co‐Cr‐TUD‐1 (Si/(Co + Cr) = 25) shows the highest catalytic efficiency with a CHHP conversion of 96.9 % and total selectivity of cyclohexanone and cyclohexanol of 95.9 %, which outperforms Co‐TUD‐1 and Cr‐TUD‐1 and indicates a synergistic effect between Co and Cr in Co‐Cr‐TUD‐1. The catalysts are mainly heterogeneous as shown in various experiments, while the catalytic performances of recovered catalysts declined modestly, indicating non‐negligible amounts of Co and Cr are leached after some cycles.

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Proof of a conjecture of Z-W Sun on ratio monotonicity

Cited by 23 publications

References 11 publications

Equivalency of Kinetic Schemes: Causes and an Analysis of Some Model Fitting Algorithms

Equivalency of Kinetic Schemes: Causes and an Analysis of Some Model Fitting Algorithms

Removal of Cr(VI) from Wastewater by a Novel Adsorbent of Magnetic Goethite: Adsorption Performance and Adsorbent Characterisation

Decomposition of cyclohexyl hydroperoxide over bimetallic mesoporous materials containing cobalt and chromium

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