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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  相似文献   
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A method for flow-through liquid scintillation counting in reversed-phase liquid chromatography (RP-LC) based on the continuous extraction of aqueous column eluates with a water-immiscible liquid scintillator is evaluated in terms of sensitivity, reproducibility and extra-column band broadening. 3H- and 14C-labelled phenylthiohydantoinamino acid derivatives of widely different polarity serve as model compounds. For extractable derivatives, counting efficiencies of over 30 and 80% can be obtained for 3H and 14C, respectively. The reproducibility and extra-column band broadening depend on the mixing ratio of scintillator and LC eluent; relative standard deviations (peak areas) of less than 3% can be obtained. The sensitivity of flow-through counting can be increased at least 150-fold by storing the segmented scintillator/eluate stream in a capillary storage loop. After the separation is complete, the stream is re-introduced into the radioactivity detector at reduced flow-rates to increase the mean residence time, i.e., the counting time, in the detector.  相似文献   
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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.  相似文献   
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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).  相似文献   
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It is well‐known that the self‐assembly of AB diblock copolymers in solution can produce various morphologies depending on the relative volume fraction of each block. Recently, polymerization‐induced self‐assembly (PISA) has become widely recognized as a powerful platform technology for the rational design and efficient synthesis of a wide range of block copolymer nano‐objects. In this study, PISA is used to prepare a new thermoresponsive poly(N‐(2‐hydroxypropyl) methacrylamide)‐poly(2‐hydroxypropyl methacrylate) [PHPMAC‐PHPMA] diblock copolymer. Remarkably, TEM, rheology and SAXS studies indicate that a single copolymer composition can form well‐defined spheres (4 °C), worms (22 °C) or vesicles (50 °C) in aqueous solution. Given that the two monomer repeat units have almost identical chemical structures, this system is particularly well‐suited to theoretical analysis. Self‐consistent mean field theory suggests this rich self‐assembly behavior is the result of the greater degree of hydration of the PHPMA block at lower temperature, which is in agreement with variable temperature 1H NMR studies.  相似文献   
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Based on our analysis of the hopcount of the shortest path between two arbitrary nodes in the class G p (N) of random graphs, the corresponding flooding time is investigated. The flooding time T N (p) is the minimum time needed to reach all other nodes from one node. We show that, after scaling, the flooding time T N (p) converges in distribution to the two-fold convolution (2*) of the Gumbel distribution function (z)=exp (–e z ), when the link density p N satisfies Np N /(log N)3 if N .  相似文献   
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