Lagrangian-Dual Functions and Moreau–Yosida Regularization

2008 ◽  
Vol 19 (1) ◽  
pp. 39-61 ◽  
Author(s):  
Fanwen Meng ◽  
Gongyun Zhao ◽  
Mark Goh ◽  
Robert De Souza
Keyword(s):  
Lagrangian Dual ◽  
Yosida Regularization ◽  
Dual Functions

scholarly journals Offretite Zeolite Single Crystals Synthesized by Amphiphile-Templating Approach

Molecules ◽  
2021 ◽  
Vol 26 (8) ◽  
pp. 2238
Author(s):  
Eng-Poh Ng ◽  
Nur Hidayahni Ahmad ◽  
Fitri Khoerunnisa ◽  
Svetlana Mintova ◽  
Tau Chuan Ling ◽  
...  
Keyword(s):  
Cetyltrimethylammonium Bromide ◽  
Cost Effective ◽  
Acid Sites ◽  
Biofuel Production ◽  
Structure Directing Agent ◽  
High Crystallinity ◽  
Organic Templates ◽  
Synthesis Approach ◽  
Conventional Counterpart ◽  
Dual Functions

Offretite zeolite synthesis in the presence of cetyltrimethylammonium bromide (CTABr) is reported. The offretite crystals were synthesized with a high crystallinity and hexagonal prismatic shape after only 72 h of hydrothermal treatment at 180 °C. The CTABr has dual-functions during the crystallization of offretite, viz. as structure-directing agent and as mesoporogen. The resulting offretite crystals, with a Si/Al ratio of 4.1, possess more acid sites than the conventional offretite due to their high crystallinity and hierarchical structure. The synthesized offretite is also more reactive than its conventional counterpart in the acylation of 2-methylfuran for biofuel production under non-microwave instant heating condition, giving 83.5% conversion with 100% selectivity to the desired product 2-acetyl-5-methylfuran. Hence, this amphiphile synthesis approach offers another cost-effective and alternative route for crystallizing zeolite materials that require expensive organic templates.

scholarly journals A Dy(III) Fluorescent Single-Molecule Magnet Based on a Rhodamine 6G Ligand

Inorganics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 51
Author(s):  
Lin Miao ◽  
Mei-Jiao Liu ◽  
Man-Man Ding ◽  
Yi-Quan Zhang ◽  
Hui-Zhong Kou
Keyword(s):  
Magnetic Properties ◽  
Single Molecule ◽  
Magnetic Relaxation ◽  
Rhodamine 6G ◽  
Bond Angle ◽  
Magnetic Measurements ◽  
Single Molecule Magnet ◽  
Lanthanide Metals ◽  
Process Studies ◽  
Dual Functions

The complexes of lanthanide metals, especially dysprosium, can generally exhibit excellent magnetic properties. By means of modifying ligands, dual functions or even multi-functions can be achieved. Here, we synthesized an eight-coordinate Dy(III) complex 1, [Dy(HL-o)2(MeOH)2](ClO4)3·4.5MeOH, which is single-molecule magnet (SMM), and the introduction of the rhodamine 6G chromophore in the ring-opened ligand HL-o realizes ligand-centered fluorescence in addition to SMM. Magnetic measurements and ab initio calculations indicate that the magnetic relaxation for complex 1 should be due to the Raman relaxation process. Studies on magneto-structural correlationship of the rhodamine salicylaldehyde hydrazone Dy(III) complexes show that the calculated energy of the first Kramers Doublet (EKD1) is basically related to the Ophenoxy-Dy-Ophenoxy bond angle, i.e., the larger Ophenoxy-Dy-Ophenoxy bond angle corresponds to a larger EKD1.

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