On the covariance of the level sizes in random recursive trees

In this paper we study the covariance structure of the number of nodes k and l steps away from the root in random recursive trees. We give an analytic expression valid for all k, l and tree sizes N. The fraction of nodes k steps away from the root is a random probability distribution in k. The expression for the covariances allows us to show that the total variation distance between this (random) probability distribution and its mean converges in probability to zero. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 20: 519–539, 2002     

Spirophostins: conformationally restricted analogues of adenophostin A

The synthesis, biological evaluation, and molecular modeling of two conformationally restricted analogues of adenophostinA (1), denominated as spirophostin (3R)-10 and (3S)-11, as novel ligands for the D-myo-inositol 1,4,5-trisphosphate receptor (IP3R), is presented. These diastereoisomeric spiroketals are synthesized by spiroketalization of D-glucose derivatives (2S)-15 and (2R)-16, separation of the protected isomers (3R)-19 and (3S)-20, followed by phosphorylation and deprotection. The spirophostins (3R)-10 and (3S)-11 display comparable biological activity, with a 3H-IP3-displacing and Ca2+-releasing potency less than IP3 and adenophostin A.     

Asymmetric Information in a Capital Accumulation Differential Game with Spillover and Learning Effects

Journal of Optimization Theory and Applications - This paper considers a capital accumulation game where the installation costs of investments are lowered by the firm’s own capital stock...     

Optimal Double Stopping Problems for Maxima and Minima of Geometric Brownian Motions

Methodology and Computing in Applied Probability - We present closed-form solutions to some double optimal stopping problems with payoffs representing linear functions of the running maxima and...     

A unified orbital model of delocalised and localised currents in monocycles, from annulenes to azabora-heterocycles

Why are some (4n+2)π systems aromatic, and some not? The ipsocentric approach to the calculation of the current density induced in a molecule by an external magnetic field predicts a four‐electron diatropic (aromatic) ring current for (4n+2)π carbocycles and a two‐electron paratropic (antiaromatic) current for (4n)π carbocycles. With the inclusion of an electronegativity parameter, an ipsocentric frontier‐orbital model also predicts the transition from delocalised currents in carbocycles to nitrogen‐localised currents in alternating azabora‐heterocycles, which rationalises the differences in (magnetic) aromaticity between these isoelectronic π‐conjugated systems. Ab initio valence‐bond calculations confirm the localisation predicted by the naïve model, and coupled‐Hartree–Fock calculations give current‐density maps that exhibit the predicted delocalised‐to‐localised/carbocycle–heterocycle transition.     

Ring currents as probes of the aromaticity of inorganic monocycles : P5-, As5-, S2N2, S3N3-, S4N3+, S4N42+, S5N5+, S42+ and Se42+

Current-density maps were calculated by the ipsocentric CTOCD-DZ/6-311G** (CTOCD-DZ=continuous transformation of origin of current density-diamagnetic zero) approach for three sets of inorganic monocycles: S(4) (2+), Se(4) (2+), S(2)N(2), P(5) (-) and As(5) (-) with 6 pi electrons; S(3)N(3) (-), S(4)N(3) (+) and S(4)N(4) (2+) with 10 pi electrons; and S(5)N(5) (+) with 14 pi electrons. Ipsocentric orbital analysis was used to partition the currents into contributions from small groups of active electrons and to interpret the contributions in terms of symmetry- and energy-based selection rules. All nine systems were found to support diatropic pi currents, reinforced by sigma circulations in P(5) (-), As(5) (-), S(3)N(3) (-), S(4)N(3) (+), S(4)N(4) (2+) and S(5)N(5) (+), but opposed by them in S(4) (2+), Se(4) (2+) and S(2)N(2). The opposition of pi and sigma effects in the four-membered rings is compatible with height profiles of calculated NICS (nucleus-independent chemical shifts).