On the Korteweg-de Vries equation

Existence, uniqueness, and continuous dependence on the initial data are proved for the local (in time) solution of the (generalized) Korteweg-de Vries equation on the real line, with the initial function in the Sobolev space of order s>3/2 and the solution u(t) staying in the same space, s= being included For the proper KdV equation, existence of global solutions follows if s2. The proof is based on the theory of abstract quasilinear evolution equations developed elsewhere.Dedicated to Hans Lewy and Charles B. Morrey Jr.Partially supported by NSF Grant MCS76-04655.     

Ruthenium‐Catalyzed Cycloisomerization of 2,2′‐Diethynyl‐ biphenyls Involving Cleavage of a Carbon–Carbon Triple Bond

A ruthenium complex catalyzes a new cycloisomerization reaction of 2,2′‐diethynylbiphenyls to form 9‐ethynylphenanthrenes, thereby cleaving the carbon–carbon triple bond of the original ethynyl group. A metal–vinylidene complex is generated from one of the two ethynyl groups, and its carbon–carbon double bond undergoes a [2+2] cycloaddition with the other ethynyl group to form a cyclobutene. The phenanthrene skeleton is constructed by the subsequent electrocyclic ring opening of the cyclobutene moiety.     

Room-Temperature Phosphorescence from a Series of 3-Pyridylcarbazole Derivatives

Exploration of pure metal-free organic molecules that exhibit strong room-temperature phosphorescence (RTP) is an emerging research topic. In this regard, unveiling the design principles for an efficient RTP molecule is an essential, but challenging, task. A small molecule is an ideal platform to precisely understand the fundamental role of each functional component because the parent molecule can be easily derivatized. Here, the RTP behaviors of a series of 3-pyridylcarbazole derivatives are presented. Experimental studies in combination with theoretical calculations reveal the crucial role of the n orbital on the central pyridine ring in the dramatic enhancement of the intersystem crossing between the charge-transfer-excited singlet state and the locally excited triplet states. Single-crystal X-ray crystallographic studies apparently indicate that both the pyridine ring and fluorine atom contribute to the enhancement of the RTP because of the restricted motion owing to weak C−H⋅⋅⋅N and H⋅⋅⋅F hydrogen-bonding interactions. The single crystal of the fluorine-substituted derivative shows an ultra-long phosphorescent lifetime (τ_P) of 1.1 s and a phosphorescence quantum yield (Φ_P) of 1.2 %, whereas the bromine-substituted derivative exhibits τ_P of 0.15 s with a Φ_P of 7.9 %. We believe that this work provides a fundamental and universal guideline for the generation of pure organic molecules exhibiting strong RTP.     

Design,Synthesis, and Biochemical Evaluation of Alpha-Amanitin Derivatives Containing Analogs of the trans-Hydroxyproline Residue for Potential Use in Antibody-Drug Conjugates

Alpha-amanitin, an extremely toxic bicyclic octapeptide extracted from the death-cap mushroom, Amanita phalloides, is a highly selective allosteric inhibitor of RNA polymerase II. Following on growing interest in using this toxin as a payload in antibody-drug conjugates, herein we report the synthesis and biochemical evaluation of several new derivatives of this toxin to probe the role of the trans-hydroxyproline (Hyp), which is known to be critical for toxicity. This structure activity relationship (SAR) study represents the first of its kind to use various Hyp-analogs to alter the conformational and H-bonding properties of Hyp in amanitin.     

Enhancement of Photocatalytic Activity for Hydrogen Production by Surface Modification of Pt-TiO2 Nanoparticles with a Double Layer of Photosensitizers

To investigate the effect of the surface structure of dye-sensitized photocatalyst nanoparticles, we prepared three types of Ru^II-photosensitizer (PS)-double-layered Pt-cocatalyst-loaded TiO₂ nanoparticles with different surface structures, Zr- RuCP⁶ -Zr- RuP⁶ @N wt %Pt-TiO₂, RuCP⁶ -Zr- RuP⁶ @N wt %Pt-TiO₂, and RuCP² -Zr- RuP⁶ @N wt %Pt-TiO₂ (N=0.2, 1, and 5), and evaluated their photocatalytic H₂ evolution activity in the presence of redox-reversible iodide as the electron donor. Although the driving force of the electron injection from I⁻ to the photo-oxidized Ru^III PS is comparable, the activity increased in the following order: RuCP² -Zr- RuP⁶ @1 wt %Pt-TiO₂ < RuCP⁶ -Zr- RuP⁶ @1 wt %Pt-TiO₂ < Zr- RuCP⁶ -Zr- RuP⁶ @1 wt %Pt-TiO₂. The apparent quantum yield of Zr- RuCP⁶ -Zr- RuP⁶ @1 wt %Pt-TiO₂ in the first hour reached 1 %. Zeta-potential measurements suggest that the surface Zr⁴⁺-phosphate groups attracted I⁻ anions to the nanoparticle–solution interface. Our results indicate that the surface modification of dye-sensitized photocatalysts is a promising approach to enhance photocatalytic activity with various redox mediators.     

Reversible and Stepwise Single-Crystal-to-Single-Crystal Transformation of a Platinum(II) Complex with Vapochromic Luminescence

The vapochromic single-crystal-to-single-crystal (SCSC) transformation of a highly luminescent Pt^II complex bearing an N-heterocyclic carbene [Pt(CN)₂(tBu-impy)] (tBu-impyH⁺=1-tert-butyl-3-(2-pyridyl)-1H-imidazolium) is reported. The trihydrate form of the complex, which exhibits blue ³MMLCT emission owing to weak Pt⋅⋅⋅Pt interactions, changed its luminescence color from blue to yellowish-green upon the desorption of water molecules while keeping the high emission quantum yield of more than 0.45. Variable-temperature and continuous in-situ tracking of single-crystal X-ray diffraction measurements revealed that the SCSC transformation proceeds reversibly by the release and reabsorption of water molecules, thereby changing the stacked structure slightly. As a result, the dynamics of vapor-induced SCSC transformation were elucidated: that the anhydrous form returned to the original trihydrate form in a two-step process under a water vapor atmosphere. In addition, the Pt^II complex exhibited a similar SCSC response accompanied by a luminescence color change in the presence of methanol vapor, while being inactive toward ethanol vapor.