More Like this

1. TEMPERED HOMOGENEOUS SPACES IV

   https://doi.org/10.1017/s1474748022000287  

   Benoist, Yves; Kobayashi, Toshiyuki (June 2022, Journal of the Institute of Mathematics of Jussieu)

   Let 𝐺 be a complex semisimple Lie group and 𝘏 a complex closed connected subgroup. Let g and h be their Lie algebras. We prove that the regular representation of 𝐺 in 𝐿²(𝐺/𝘏) is tempered if and only if the orthogonal of h in g contains regular elements by showing simultaneously the equivalence to other striking conditions, such as h has a solvable limit algebra. 

   more » « less
2. Synthesis and Characterization of Isostructural Th(IV) and U(IV) Pyridine Dipyrrolide Complexes

   https://doi.org/10.1021/acs.inorgchem.3c04391  

   Valerio, Leyla R; Hakey, Brett M; Leary, Dylan C; Stockdale, Erin; Brennessel, William W; Milsmann, Carsten; Matson, Ellen M (February 2024, Inorganic Chemistry)

   A series of pyridine dipyrrolide actinide(IV) complexes, (MesPDPPh)AnCl2(THF) and An(MesPDPPh)2 (An = U, Th, where (MesPDPPh) is the doubly deprotonated form of 2,6-bis(5-(2,4,6-trimethylphenyl)-3-phenyl-1H-pyrrol-2-yl)pyridine), have been prepared. Characterization of all four complexes has been performed through a combination of solid- and solution-state methods, including elemental analysis, single crystal X-ray diffraction, and electronic absorption and nuclear magnetic resonance spectroscopies. Collectively, these data confirm the formation of the mono- and bis-ligated species. Time-dependent density functional theory has been performed on all four An(IV) complexes, providing insight into the nature of electronic transitions that are observed in the electronic absorption spectra of these compounds. Room temperature, solution-state luminescence of the actinide complexes is presented. Both Th(IV) derivatives exhibit strong photoluminescence; in contrast, theU(IV) species are nonemissive. 

   more » « less
3. A High‐Valent Manganese(IV)–Oxo–Cerium(IV) Complex and Its Enhanced Oxidizing Reactivity

   https://doi.org/10.1002/anie.201910032  

   Karmalkar, Deepika G.; Sankaralingam, Muniyandi; Seo, Mi Sook; Ezhov, Roman; Lee, Yong‐Min; Pushkar, Yulia N.; Kim, Won‐Suk; Fukuzumi, Shunichi; Nam, Wonwoo (September 2019, Angewandte Chemie International Edition)

   Abstract A mononuclear nonheme manganese(IV)–oxo complex binding the Ce⁴⁺ion, [(dpaq)Mn^IV(O)]⁺–Ce⁴⁺(1‐Ce⁴⁺), was synthesized by reacting [(dpaq)Mn^III(OH)]⁺(2) with cerium ammonium nitrate (CAN).1‐Ce⁴⁺was characterized using various spectroscopic techniques, such as UV/Vis, EPR, CSI‐MS, resonance Raman, XANES, and EXAFS, showing an Mn−O bond distance of 1.69 Å with a resonance Raman band at 675 cm⁻¹. Electron‐transfer and oxygen atom transfer reactivities of1‐Ce⁴⁺were found to be greater than those of Mn^IV(O) intermediates binding redox‐inactive metal ions (1‐Mⁿ⁺). This study reports the first example of a redox‐active Ce⁴⁺ion‐bound Mn^IV‐oxo complex and its spectroscopic characterization and chemical properties. 

   more » « less
4. Non-Euclidean Virtual Reality IV: Sol

   Coulon, Rémi; Matsumoto, Elisabetta; Segerman, Henry; Trettel, Steve (January 2020, Proceedings of Bridges 2020: Mathematics, Art, Music, Architecture, Education, Culture)

   null (Ed.)

   This article presents virtual reality software designed to explore the Sol geometry. The simulation is available on 3-dimensional.space/sol.html 

   more » « less
5. Non-euclidean virtual reality IV: sol

   Coulon, Rémi; Matsumoto, Elisabetta; Segerman, Henry; Trettel, Steve (January 2020, Proceedings of Bridges 2020)

   null (Ed.)

   We describe a method of rendering real-time scenes in Nil geometry, and use this to give an expository account of some interesting geometric phenomena. You can play around with the simulation at 3-dimensional.space/nil.html. 

   more » « less