Analysis of G/D/1 Queueing Systems with Inputs Satisfying Large Deviation Principle under Weak* Topology

The large deviation principle (LDP) which has been effectively used in queueing analysis is the sample path LDP, the LDP in a function space endowed with the uniform topology. Chang [5] has shown that in the discrete-time G/D/1 queueing system under the FIFO discipline, the departure process satisfies the sample path LDP if so does the arrival process. In this paper, we consider arrival processes satisfying the LDP in a space of measures endowed with the weak^* topology (Lynch and Sethuraman [12]) which holds under a weaker condition. It is shown that in the queueing system mentioned above, the departure processes still satisfies the sample path LDP. Our result thus covers arrival processes which can be ruled out in the work of Chang [5]. The result is then applied to obtain the exponential decay rate of the queue length probability in an intree network as was obtained by Chang [5], who considered the arrival process satisfying the sample path LDP.     

An optimal service rate in a Poisson arrival queue with two-stage service policy*

We consider a two-stage service policy for a Poisson arrival queueing system. The idle server starts to work with ordinary service rate when a customer arrives. If the number of customers in the system reaches N, the service rate gets faster and continues until the system becomes empty. Otherwise, the server finishes the busy period with ordinary service rate. After assigning various operating costs to the system, we show that there exists a unique fast service rate minimizing the long-run average cost per unit time.This work was supported by Korea Research Foundation Grant(KRF-2002-070-C00021).     

Self-assembly approach toward chiral bimetallic catalysts: bis-urea-functionalized (salen)cobalt complexes for the hydrolytic kinetic resolution of epoxides

A series of novel bis-urea-functionalized (salen)Co complexes has been developed. The complexes were designed to form self-assembled structures in solution through intermolecular urea-urea hydrogen-bonding interactions. These bis-urea (salen)Co catalysts resulted in rate acceleration (up to 13 times) in the hydrolytic kinetic resolution (HKR) of rac-epichlorohydrin in THF by facilitating cooperative activation, compared to the monomeric catalyst. In addition, one of the bis-urea (salen)Co(III) catalyst efficiently resolves various terminal epoxides even under solvent-free conditions by requiring much shorter reaction time at low catalyst loading (0.03-0.05 mol %). A series of kinetic/mechanistic studies demonstrated that the self-association of two (salen)Co units through urea-urea hydrogen bonds was responsible for the observed rate acceleration. The self-assembly study with the bis-urea (salen)Co by FTIR spectroscopy and with the corresponding (salen)Ni complex by (1)H NMR spectroscopy showed that intermolecular hydrogen-bonding interactions exist between the bis-urea scaffolds in THF. This result demonstrates that self-assembly approach by using non-covalent interactions can be an alternative and useful strategy toward the efficient HKR catalysis.     

ab initio calculations and thermochemical analysis on C1 atom abstractions of chlorine from chlorocarbons and the reverse alkyl abstractions: Cl2 + R· ↔ Cl· + RCl

Thermodynamic properties (ΔH°_f(298), S°₍₂₉₈₎ and Cp(T) from 300 to 1500 K) for reactants, adducts, transition states, and products in reactions of CH₃ and C₂H₅ with Cl₂ are calculated using CBSQ//MP2/6‐311G(d,p). Molecular structures and vibration frequencies are determined at the MP2/6‐311G(d,p), with single‐point calculations for energy at QCISD(T)/6‐311 + G(d,p), MP4(SDQ)/CbsB4, and MP2/CBSB3 levels of calculation with scaled vibration frequencies. Contributions of rotational frequencies for S°₍₂₉₈₎ and Cp(T)'s are calculated based on rotational barrier heights and moments of inertia using the method of Pitzer and Gwinn [1]. Thermodynamic parameters, ΔH°_f(298), S°₍₂₉₈₎, and C_P(T), are evaluated for C₁ and C₂ chlorocarbon molecules and radicals. These thermodynamic properties are used in evaluation and comparison of Cl₂ + R· → Cl· + RCl (defined forward direction) reaction rate constants from the kinetics literature for comparison with the calculations. Data from some 20 reactions in the literature show linearity on a plot of Ea_fwd vs. ΔH_rxn,fwd, yielding a slope of (0.38 ± 0.04) and intercept of (10.12 ± 0.81) kcal/mole. A correlation of average Arrhenius preexponential factor for Cl· + RCl → Cl₂ + R· (reverse rxn) of (4.44 ± 1.58) × 10¹³ cm³/mol‐sec on a per‐chlorine basis is obtained with Ea_Rev = (0.64 ± 0.04) × ΔH_rxn,Rev + (9.72 ± 0.83) kcal/mole, where Ea_Rev is 0.0 if ΔH_rxn,Rev is more than 15.2 kcal/mole exothermic. Kinetic evaluations of literature data are also performed for classes of reactions. Ea_fwd = (0.39 ± 0.11) × ΔH_rxn,fwd + (10.49 ± 2.21) kcal/mole and average A_fwd = (5.89 ± 2.48) × 10¹² cm³/mole‐sec for hydrocarbons: Ea_fwd = (0.40 ± 0.07) × ΔH_rxn,fwd + (10.32 ± 1.31) kcal/mole and average A_fwd = (6.89 ± 2.15) × 10¹¹ cm³/mole‐sec for C₁ chlorocarbons: Ea_fwd = (0.33 ± 0.08) × ΔH_rxn,fwd + (9.46 ± 1.35) kcal/mole and average A_fwd = (4.64 ± 2.10) × 10¹¹ cm³/mole‐sec for C₂ chlorocarbons. Calculation results on the methyl and ethyl reactions with Cl₂ show agreement with the experimental data after an adjustment of +2.3 kcal/mole is made in the calculated negative Ea's. © 2000 John Wiley & Sons, Inc. Int J Chem Kinet 32: 548–565, 2000     

Late‐Stage Peptide Diversification through Cobalt‐Catalyzed C−H Activation: Sequential Multicatalysis for Stapled Peptides

Bioorthogonal late‐stage diversification of structurally complex peptides has enormous potential for drug discovery and molecular imaging. In recent years, transition‐metal‐catalyzed C?H activation has emerged as an increasingly viable tool for peptide modification. Despite major accomplishments, these strategies largely rely on expensive palladium catalysts. We herein report an unprecedented cobalt(III)‐catalyzed peptide C?H activation, which enables the direct C?H functionalization of structurally complex peptides, and sets the stage for a multicatalytic C?H activation/alkene metathesis/hydrogenation strategy for the assembly of novel cyclic peptides.     

Non-associative algebras containing the matrix ring

The Lie admissible non-associative algebra is defined in the papers [Seul Hee Choi, Ki-Bong Nam, Derivations of a restricted Weyl type algebra I, Rocky Mountain J. Math. 37 (6) (2007) 1813–1830; Seul Hee Choi, Ki-Bong Nam, Weyl type non-associative algebra using additive groups I, Algebra Colloq. 14 (3) (2007) 479–488; Ki-Bong Nam, On Some Non-associative Algebras using Additive Groups, Southeast Asian Bull. Math., vol. 27, Springer-Verlag, 2003, 493–500]. We define in this work the algebra which generalizes the previous one and is not Lie admissible. We prove that the antisymmetrized Lie algebra is simple and contains the simple Lie algebra . We also prove that the matrix ring is embedded in .     

Enantioselective Alkynylation of Trifluoromethyl Ketones Catalyzed by Cation‐Binding Salen Nickel Complexes

Cation‐binding salen nickel catalysts were developed for the enantioselective alkynylation of trifluoromethyl ketones in high yield (up to 99 %) and high enantioselectivity (up to 97 % ee). The reaction proceeds with substoichiometric quantities of base (10–20 mol % KOt‐Bu) and open to air. In the case of trifluoromethyl vinyl ketones, excellent chemo‐selectivity was observed, generating 1,2‐addition products exclusively over 1,4‐addition products. UV‐vis analysis revealed the pendant oligo‐ether group of the catalyst strongly binds to the potassium cation (K⁺) with 1:1 binding stoichiometry (K_a=6.6×10⁵ m ^?1).     

Reaction of H + ketene to formyl methyl and acetyl radicals and reverse dissociations

Thermochemical properties for reactants, intermediates, products, and transition states important in the ketene (CH₂?C?O) + H reaction system and unimolecular reactions of the stabilized formyl methyl (C·H₂CHO) and the acetyl radicals (CH₃C·O) were analyzed with density functional and ab initio calculations. Enthalpies of formation (ΔH_f°₂₉₈) were determined using isodesmic reaction analysis at the CBS‐QCI/APNO and the CBSQ levels. Entropies (S°₂₉₈) and heat capacities (C_p°(T)) were determined using geometric parameters and vibrational frequencies obtained at the HF/6‐311G(d,p) level of theory. Internal rotor contributions were included in the S and C_p(T) values. A hydrogen atom can add to the CH₂‐group of the ketene to form the acetyl radical, CH₃C·O (E_a = 2.49 in CBS‐QCI/APNO, units: kcal/mol). The acetyl radical can undergo β‐scission back to reactants, CH₂?C?O + H (E_a = 45.97), isomerize via hydrogen shift (E_a = 46.35) to form the slight higher energy, formyl methyl radical, C·H₂CHO, or decompose to CH₃ + CO (E_a = 17.33). The hydrogen atom also can add to the carbonyl group to form C·H₂CHO (E_a = 6.72). This formyl methyl radical can undergo β scission back to reactants, CH₂?C?O + H (E_a = 43.85), or isomerize via hydrogen shift (E_a = 40.00) to form the acetyl radical isomer, CH₃C·O, which can decompose to CH₃ + CO. Rate constants are estimated as function of pressure and temperature, using quantum Rice–Ramsperger–Kassel analysis for k(E) and the master equation for falloff. Important reaction products are CH₃ + CO via decomposition at both high and low temperatures. A transition state for direct abstraction of hydrogen atom on CH₂?C?O by H to form, ketenyl radical plus H₂ is identified with a barrier of 12.27, at the CBS‐QCI/APNO level. ΔH_f°₂₉₈ values are estimated for the following compounds at the CBS‐QCI/APNO level: CH₃C·O (?3.27), C·H₂CHO (3.08), CH₂?C?O (?11.89), HC·CO (41.98) (kcal/mol). © 2002 Wiley Periodicals, Inc. Int J Chem Kinet 35: 20–44, 2003     

Generation of Ultra‐High‐Molecular‐Weight Polyethylene from Metallocenes Immobilized onto N‐Doped Graphene Nanoplatelets

Catalytic natures of organometallic catalysts are modulated by coordinating organic ligands with proper steric and electronic properties to metal centers. Carbon‐based nanomaterials such as graphene nanoplatelets are used with and without N‐doping and multiwalled carbon nanotube as a ligand for ethylene polymerizations. Zirconocenes or titanocenes are immobilized on such nanomaterials. Polyethylenes (PEs) produced by such hybrids show a great increase in molecular weight relative to those produced by free catalysts. Specially, ultra‐high‐molecular‐weight PEs are produced from the polymerizations at low temperature using the hybrid with N‐doped graphene nanoplatelets. This result shows that such nanomaterials act a crucial role to tune the catalytic natures of metallocenes.     

A double‐lined metasurface for plasmonic complex‐field generation

Since the surface plasmon polariton (SPP) has received a great deal of attention because of its capability of guiding light within the subwavelength scale, finding methods for arbitrary SPP field generation has been a significant issue in the area of integrated optics. To achieve such a goal, it will be necessary to generate a plasmonic complex field. In this paper, we propose a novel method for generating a plasmonic complex field propagating with arbitrary curvatures by using double‐lined distributed nanoslits. As a unit cell, two facing nanoslits are used for tuning both the amplitude and the phase of excited SPPs as a function of their tilted angles. For verification of the proposed design rule, the authors experimentally demonstrate some plasmonic caustic curves and Airy plasmons.