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An Asymptotic Robin Inequality
The conjectured Robin inequality for an integer $n>7!$ is $\sigma(n)<e^\gamma n \log \log n,$ where $\gamma$ denotes Euler constant, and $\sum_{d | n} d$ denotes Chebyshev summatory function. Expand
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A unique Au-Ag-Au triangular motif in a trimetallic halonium dication: silver incorporation in a gold(I) catalyst.
As a result of explorations into the solution chemistry of silver/gold mixtures, a unique diphosphine trimetallic chloronium dication was discovered that incorporates silver-arene chelation and aExpand
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Synthesis and Structure of Cationic Phosphine Gold(I) Enol Ether Complexes
Cationic {[(t-Bu)2(o-biphenyl)P]Au(enol ether)}+SbF6– and {[(t-Bu)3P]Au(enol ether)}+SbF6– complexes were isolated and characterized by NMR spectroscopy and X-ray crystallography. For three of theExpand
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Synthesis and structure of an extremely air-stable binuclear hafnocene perfluorooctanesulfonate complex and its use in Lewis acid-catalyzed reactions.
Stable complexes: An extremely air-stable mu(2)-hydroxy-bridged binuclear hafonocene perfluorooctanesulfoante complex shows high catalytic efficiency in Lewis acid-catalyzed reactions, such asExpand
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Structure and Dynamic Behavior of Phosphine Gold(I)-Coordinated Enamines: Characterization of α-Metalated Iminium Ions
Cationic gold(I) enamine complexes with the (t-Bu)2(o-biphenyl)phosphine ligand were isolated and characterized by NMR spectroscopy and X-ray crystallography. The complexes display highly distortedExpand
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Insights into Alkene Activation by Gold: Nucleophile Activation with Base as a Trigger for Generation of Lewis Acidic Gold
Previously, the generation of alkyl gold intermediates (B) from nucleophilic addition to inactivated alkenes was limited by the use of trigold oxo complexes (A) with arylphosphine ligands,Expand
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Bisbiphenyl Phosphines: Structure and Synthesis ofGold(I) Alkene π‑Complexes with Variable Phosphine Donicityand Enhanced Stability
This paper describes the synthesis and characterization of RP­(o-biphenyl)2 phosphine ligands (where R = PhO, Ph, and t-Bu), corresponding gold­(I) chloride precatalysts, gold­(I) triflate catalysts,Expand
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The probability of Riemann's hypothesis being true is equal to 1
  • Y. Zhu
  • Mathematics
  • 24 September 2016
Let $P$ be the set of all prime numbers, ${q_1},{q_2}, \cdots ,{q_m} \in P$, $P_k$ be the k-th $(k = 1,2, \cdots m)$ element of $P$ in ascending order of size, ${\alpha _1},{\alpha _2}, \cdotsExpand
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A Fast Algorithm to Calculate Power Sum of Natural Numbers
Permutations can be represented as linear combinations of natural numbers with different powers. In this paper, its coefficient matrix and inverse matrix is derived, and the results show theExpand