Asymptotic distribution for the birthday problem with multiple coincidences,via an embedding of the collision process

We study the random variable B(c, n), which counts the number of balls that must be thrown into n equally‐sized bins in order to obtain c collisions. The asymptotic expected value of B(1, n) is the well‐known appearing in the solution to the birthday problem; the limit distribution and asymptotic moments of B(1, n) are also well known. We calculate the distribution and moments of B(c, n) asymptotically as n goes to ∞ and c = O(n). We have two main tools: an embedding of the collision process — realizing the process as a deterministic function of the standard Poisson process — and a central limit result by Rényi. © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 48, 480–502, 2016     

Oxidative diamination of alkenes with ureas as nitrogen sources: mechanistic pathways in the presence of a high oxidation state palladium catalyst

A first palladium-catalyzed intramolecular diamination of unfunctionalized terminal alkenes has recently been reported. This study investigates the details of its mechanistic course based on NMR titration, kinetic measurements competition experiments, and deuterium labeling. It concludes a two-step procedure consisting of syn-aminopalladation with an unligated palladium(II) catalyst state followed by oxidation to palladium(IV) and subsequent C-N bond formation to give the final products as cyclic diamines. Related reactions employing sulfamides give rise to aminoalkoxy-functionalization of alkenes. This process was investigated employing deuterated alkenes and found to follow an identical mechanism where stereochemistry is concerned. It exemplifies the importance of cationic palladium(IV) intermediates prior to the final reductive elimination from palladium and proves that the nucelophile for this step stems from the immediate coordination sphere of the palladium(IV) precursor. These results have important implications for the general development of alkene 1,2-difunctionalization and for the individual processes of aminopalladation and palladium-catalyzed C(alkyl)-N bond formation.     

Defined Palladium–Phthalimidato Catalysts for Improved Oxidative Amination

New palladium(II)–phthalimidato complexes have been synthesized, isolated, and structurally characterized. As demonstrated from over 30 examples, they constitute superior catalysts for oxidative amination reactions of alkenes with phthalimide as the nitrogen source. This work streamlines vicinal difunctionalization of alkenes and provides access to significantly improved and experimentally simplified synthetic protocols.     

DFT Rationalization of the Diverse Outcomes of the Iodine(III)‐Mediated Oxidative Amination of Alkenes

A computational study of the mechanism for the iodine(III)‐mediated oxidative amination of alkenes explains the experimentally observed substrate dependence on product distribution. Calculations with the M06 functional have been carried out on the reaction between PhI(N(SO₂Me)₂)₂ and three different representative substrates: styrene, α‐methylstyrene, and (E)‐methylstilbene. All reactions start with electrophilic attack by a cationic PhI(N(SO₂Me)₂)⁺ unit on the double bond, and formation of an intermediate with a single C?I bond and a planar sp² carbocationic center. The major path, leading to 1,2‐diamination, proceeds through a mechanism in which the bissulfonimide initially adds to the alkene through an oxygen atom of one sulfonyl group. This behavior is now corroborated by experimental evidence. An alternative path, leading to an allylic amination product, takes place through deprotonation at an allylic C?H position in the common intermediate. The regioselectivity of this amination depends on the availability of the resonant structures of an alternate carbocationic intermediate. Only in cases where a high electronic delocalization is possible, as in (E)‐methylstilbene, does the allylic amination occur without migration of the double bond.     

Capillary electrophoresis speciation of chromium in leather tanning liquor

We present a method for the speciation of chromium by capillary electrophoresis. Cr(III) was complexed with diethylenetriaminepentaacetic acid (DTPA) to form a negatively charged complex. Using 20 mM phosphate buffer of pH 8 containing 0.5 mM tetradecyltrimethylammonium hydroxide (TTAOH) at a separation voltage of -15 kV, both forms of chromium CrDTPA(2-) and CrO(4) (2-) were separated in less than 6 min. Direct UV detection at 214 nm was used. The effect of the presence of interfering ions was investigated. The application of the developed method to speciation of chromium in tanning liquor is demonstrated. The obtained results have shown a good correlation with those of flame atomic absorbance spectrometry (FAAS), inductively coupled plasma-mass spectrometry (ICP-MS) and UV/VIS spectrophotometry.     

η3‐Allyl Coordination at Tin(II)—Reactivity towards Alkynes and Benzonitrile

We herein report the synthesis and characterization of a terphenyl‐substituted Sn^II allyl compound featuring an η³ coordination mode in solution and in the solid state. Two examples for the interesting reactivity of the allyl Sn^II molecule are presented: Reactions with terminal alkynes result in the formation of tricyclic compounds by C? C bond formation and the dimerization of two Sn moieties whereas the reaction with benzonitrile leads to a sixteen‐membered ring system through C? H activation.     

The Molecular Basis of Different Approaches for the Study of Cancer Stem Cells and the Advantages and Disadvantages of a Three-Dimensional Culture

Cancer stem cells (CSCs) are a rare tumor subpopulation with high differentiation, proliferative and tumorigenic potential compared to the remaining tumor population. CSCs were first discovered by Bonnet and Dick in 1997 in acute myeloid leukemia. The identification and isolation of these cells in this pioneering study were carried out through the flow cytometry, exploiting the presence of specific cell surface molecular markers (CD34⁺/CD38⁻). In the following years, different strategies and projects have been developed for the study of CSCs, which are basically divided into surface markers assays and functional assays; some of these techniques also allow working with a cellular model that better mimics the tumor architecture. The purpose of this mini review is to summarize and briefly describe all the current methods used for the identification, isolation and enrichment of CSCs, describing, where possible, the molecular basis, the advantages and disadvantages of each technique with a particular focus on those that offer a three-dimensional culture.     

The Maxwell-Contact

In multibody systems, two alternative approaches exist to compute contact forces between bodies. The unilateral constraint contact and the unilateral regularized contact do not take into account the influence of the deformation due to other contacts on a body using rigid body dynamics. In this paper, a third alternative, i.e. the Maxwell-Contact, is derived coupling the deformations of different contacts on one body quasi-statically. An academic example validates the fundamental properties of the contact model and the application in a simulation of a pushbelt CVT shows improved results. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)