Dynamic complexity of optimal paths and discount factors for strongly concave problems

We study the relationship between the dynamical complexity of optimal paths and the discount factor in general infinite-horizon discrete-time concave problems. Given a dynamic systemx _t+1=h(x _t ), defined on the state space, we find two discount factors 0 < ^{* **} < 1 having the following properties. For any fixed discount factor 0 < < ^*, the dynamic system is the solution to some concave problem. For any discount factor ^** < < 1, the dynamic system is not the solution to any strongly concave problem. We prove that the upper bound ^** is a decreasing function of the topological entropy of the dynamic system. Different upper bounds are also discussed.This research was partially supported by MURST, National Group on Nonlinear dynamics in Economics and Social Sciences. The author would like to thank two anonymous referees for helpful comments and suggestions.     

Initial data truncation for multivariate output of discrete-event simulations using the Kalman filter

Data truncation is a commonly accepted method of dealing with initialization bias in discrete-event simulation. An algorithm for determining the appropriate initial-data truncation point for multivariate output is proposed. The technique entails averaging across independent replications and estimating a steady-state output model in a state-space framework. A Bayesian technique called Multiple Model Adaptive Estimation (MMAE) is applied to compute a time varying estimate of the output's steady-state mean vector. This MMAE implementation features the use, in paralle, of a bank of Kalman filters. Each filter is constructed under a different assumption concerning the output's steady-state mean vector. One of the filters assumes that the steady-state mean vector is accurately reflected by an estimate, called the assumed steady-state mean vector, taken from the last half of the simulation data. As the filters process the output through the effective transient, this particular filter becomes more likely (in a Bayesian sense) to be the best filter to represent the data and the MMAE mean estimator is influenced increasingly towards the assumed steady-state mean vector. The estimated truncation point is selected when a norm of the MMAE mean vector estimate is within a small tolerance of the assumed steady-state mean vector. A Monte Carlo analysis using data from simulations of open and closed queueing models is used to evaluate the technique. The evaluation criteria include the ability to construct accurate and reliable confidence regions for the mean response vector based on the truncated sequences.     

Theoretical study of structure and stability of fullerene derivative: C50O

A total of eight possible isomers of C₅₀O, an oxide of fullerene C₅₀ (D_5h), have been investigated by B3LYP/3‐21G calculations. The isomer, which has an annulene‐like structure with oxygen bridging across a [5,6] type C? C bond at the site between the pole and the equatorial belt, is found being the ground state of C₅₀O. Four isomers are relatively more stable and the energy differences between them are not large. This result indicates that more than one C₅₀O isomer will coexist once C₅₀O is synthesized. The relative stabilities of the C₅₀O isomers may be determined mainly by the strain release and by the formation of the cyclic phenylene substructure at the equatorial belt of the cage. The calculated nucleus independent chemical shifts (NICS) of the C₅₀O isomers will be useful because from them one can expect outstanding NMR properties that can lead to their identification and characterization. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Norvancomycin-capped silver nanoparticles: Synthesis and antibacterial activities against E. coli

The synthesis of norvancomycin (NVan)-capped silver nanoparticles (Ag@NVan) and their notable in vitro antibacterial activities against E. coli, a Gram-negative bacterial strain (GNB), are reported here. Mercaptoacetic acid-stabilized spherical silver nanoparticles with a diameter of 16±4 nm are prepared by a simple chemical reaction. The formation process of the silver nanoparticles is investigated by UV-visible (UV-vis) spectroscopy and transmission electron microscopy (TEM). NVan is then grafted to the terminal carboxyl of the mercaptoacetic acid in the presence of N-(3-Dimethylaminopropyl)-N′-ethylcarbodiimide hydrochloride (EDAC). The TEM images of single bacteria treated with Ag@NVan show that plenty of Ag@NVan aggregate in the cell wall of E. coli. A possible antibacterial mechanism is proposed that silver nanoparticles may help destroy the stability of the outer membrane of E. coli, which makes NVan easier to bind to the nether part of the peptidoglycan structure. The antibacterial activities of silver nanoparticles on their own, together with the rigid polyvalent interaction between Ag@NVan and cell wall, enables Ag@NVan to be an effective inhibitor of GNB. This kind of bionanocomposites might be used as novel bactericidal materials and we also provide an effective synthesis method for preparing functional bioconjugated nanoparticles here. Supported by the National Natural Science Foundation of China (Grant No. 50373036) and Fok Ying Tung Education Foundation (Grant No. J20040212)     

橡胶中简单剪切与纯剪切的关系

研究了简单剪切与纯剪切的关系，得出了：（１）简单剪切可看成纯剪切加转动，转动角θ有；（２）若简单剪切椭圆的长轴与坐标轴Ｘ的夹角为φ，相应的纯剪椭圆长袖与坐标轴ｙ的夹角为β０，则φ＝β０；（３）橡胶在双向拉伸时剪应变γ的一般表达式为，对简单剪切而言即为     

Synthesis,Structure, and Fluxionality of Strained Hypercoordinate Silicon‐Bridged [1]Ferrocenophanes

The first hypercoordinate sila[1]ferrocenophanes [fcSiMe(2‐C₆H₄CH₂NMe₂)] ( 5 a ) and [fcSi(CH₂Cl)(2‐C₆H₄CH₂NMe₂)] ( 5 b ) (fc=(η⁵‐C₅H₄)Fe(η⁵‐C₅H₄)) were synthesized by low‐temperature (?78 °C) reactions of Li[2‐C₆H₄CH₂NMe₂] with the appropriate chlorinated sila[1]ferrocenophanes ([fcSiMeCl] ( 1 a ) and [fcSi(CH₂Cl)Cl] ( 1 d ), respectively). Single‐crystal Xray diffraction studies revealed pseudo‐trigonal bipyramidal structures for both 5 a and 5 b , with one of the shortest reported Si???N distances for an sp³‐hybridized nitrogen atom interacting with a tetraorganosilane detected for 5 a (2.776(2) Å). Elongated Si? C_ipso bonds trans to the donating NMe₂ arms (1.919(2) and 1.909(2) Å for 5 a and 5 b , respectively) were observed relative to both the non‐trans bonds ( 5 a : 1.891(2); 5 b : 1.879(2) Å) and the Si? C_ipso bonds of the non‐hypercoordinate analogues ([fcSiMePh] ( 1 b ): 1.879(4), 1.880(4) Å; [fcSi(CH₂Cl)Ph] ( 1 e ): 1.881(2), 1.884(2)). Solution‐state fluxionality of 5 a and 5 b , suggestive of reversible coordination of the NMe₂ group to silicon, was demonstrated by means of variable‐temperature NMR studies. The ΔG^≠ of the fluxional processes for 5 a and 5 b in CD₂Cl₂ were estimated to be 35.0 and 37.6 kJ mol^?1, respectively (35.8 and 38.3 kJ mol^?1 in [D₈]toluene). The quaternization of 5 a and 5 b by MeOTf, to give [fcSiMe(2‐C₆H₄CH₂NMe₃)][OTf] ( 7 a‐ OTf) and [fcSi(CH₂Cl)(2‐C₆H₄CH₂NMe₃)][OTf] ( 7 b‐ OTf), respectively, supported the reversibility of NMe₂ coordination at the silicon center as the source of fluxionality for 5 a and 5 b . Surprisingly, low room‐temperature stability was detected for 5 b due to its tendency to intramolecularly cyclize and form the spirocyclic [fcSi(cyclo‐CH₂NMe₂CH₂C₆H₄)]Cl ( 9 ‐Cl). This process was observed in both solution and the solid state, and isolation and Xray characterization of 9 ‐Cl was achieved. The model compound, [Fc₂Si(2‐C₆H₄CH₂NMe₂)₂] ( 8 ), synthesized through reaction of [Fc₂SiCl₂] with two equivalents of Li[2‐C₆H₄CH₂NMe₂] at ?78 °C, showed a lack of hypercoordination in both the solid state and in solution (down to ?80 °C). This suggests that either the reduced steric hindrance around Si or the unique electronics of the strained sila[1]ferrocenophanes is necessary for hypercoordination to occur.     

Pion absorption by16O using realistic interactions—II: Free pion absorption followed by emission of proton

Matrix element of the Gallilean invariant nonrelativistic reduction of the pseudoscalar-pseudovector interaction has been calculated for free pion absorption by a single nucleon inside the nucleus of¹⁶O. The Hartree-Fock wavefunctions obtained with the unitary-model-operator approach starting with the hard-core nucleon-nucleon interaction have been used for the π-capturing nucleon in the initial state. The initial pion distortion in the presence of nuclear field of the absorbing nucleus prior to its absorption together with the Coulomb interaction with the finite nuclear size has been taken into account. The distortion of the emitted proton in the field of the residual nucleus has also been considered. The differential cross-sections have been obtained and calculated results are compared with the previous experimental and theoretical work.     

An approach to sequence-specific antibody proteases

We describe here a novel strategy for the isolation of antibodies with sequence-specific protease activity: the synthesis of dipeptide haptens in which the targeted peptide bond has been replaced by a ring-strained or torsionally strained hydroxyethylene transition-state analog. Thus, the analogs mimic both a peptide bond in a distorted, reactive conformation and the transition state for peptide bond hydrolysis. In order to obtain sequence-specific antibody proteases, these analogs have been flanked with additional amino acid residues in preparation for immunization. In particular, we have synthesized peptides containing analogs such as 2-cis-amino-3-cis-hydroxycyclobutane carboxylic acid andendo-(3-amino-2-hydroxy)bicyclo[2.2.1]heptane-7-anti-carboxylic acid. We have also prepared a series of peptide derivatives containing analogs, such as 2-[3-amino-2-oxo-1-azetidinyl]-3-methylbutanoic acid, in which the targeted peptide bond has been incorporated into a β-lactam ring. Since the “peptide bond” has been left intact, these species mimic only a distorted ground state. At present, antibodies are being elicited against a number of the above peptide derivatives.     

Effect of conformational rigidity on the glass transition and initial decomposition temperatures of polyimides

The dependence of the glass transition and initial decomposition temperatures of polyperyleneimide and polynaphthylimide on the conformational rigidity was studied by the Monte Carlo, Kuhn segment, and quantum chemical AM1 methods. The corresponding linear plots can be used for estimation of the glass transition and initial decomposition temperatures when experimental determination is difficult.     

Ring strain energies: substituted rings, norbornanes, norbornenes and norbornadienes

Ring strain energies (RSEs) are predicted using homodesmotic reactions at the B3LYP/6-31G^* level of theory. Substituents are conserved in the acyclic reference and any difference in energy between the ring and the acyclic reference corresponds exclusively to RSE. Small rings are stabilized by alkyl substituents and this stabilization decreases as the size of the ring increases. There is a destabilization of medium sized rings. Greater stabilization is found upon alkyl substitution at a double bond in an unsaturated ring and this stabilization decreases as ring size increases. The effects of cis-1,2-disubstitution on RSEs have been evaluated and indicate stabilization for both small and medium sized rings. RSEs of saturated and unsaturated polycyclic systems agree well with the RSEs derived from experimental thermochemical data. RSEs are reported for substituted norbornanes, norbornenes, and norbornadienes to complement experimental studies.