Combined Metal-Metal and Metal-Ligand Cooperativity in Dicopper-Catalyzed Azide-Alkyne Cycloaddition Reactions. [PDF]
van Beek CB +7 more
europepmc +1 more source
Exploration of the associations between violent and aggressive behaviors risk and NHHR, TyG in patients with schizophrenia: an SHAP interpretable machine learning prediction and FAERS pharmacovigilance analysis. [PDF]
Qing G, Taorigen H, Zhou Y, Wang G.
europepmc +1 more source
Identification of a Novel Lipidomic Biomarker for Hepatocyte Carcinoma Diagnosis: Advanced Boosting Machine Learning Techniques Integrated with Explainable Artificial Intelligence. [PDF]
Yagin FH +5 more
europepmc +1 more source
Molecular Principles of Proton-Coupled Quinone Reduction in the Membrane-Bound Superoxide Oxidase. [PDF]
Riepl D +7 more
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On an Elementary Proof of Some Asymptotic Formulas in the Theory of Partitions
The Annals of Mathematics, 1942Let \(p(n)\) be the number of partitions of the positive integer \(n\) and let \(p_k(n)\) be the number of partitions of \(n\) into exactly \(k\) summands. The author gives an elementary proof that \(\lim_{n \to \infty} n p(n) \exp\{-\pi(2n/3)^{1/2}\}\) exists and is positive, but does not determine its value (known to be \(48^{-1/2}\)).
openaire +4 more sources
Partitions of Positive Integers: An Elementary Topic of Number Theory
The Mathematics Teacher, 1974The author presents some interesting aspects of number theory and graphing that should be appealing to students.
openaire +1 more source
1-Shell totally symmetric plane partitions (TSPPs) modulo powers of 5
Ramanujan Journal, 2020Shane Chern
exaly
Elementary proofs of infinite families of congruences for Merca’s cubic partitions
Ramanujan Journal, 2022exaly

