Review of AdS/CFT Integrability: An Overview

This is the introductory chapter of a review collection on integrability in the context of the AdS/CFT correspondence. In the collection, we present an overview of the achievements and the status of this subject as of the year 2010.     

Reactions of methyl fluoride with atomic transition-metal and main-group cations: gas-phase room-temperature kinetics and periodicities in reactivity

Reactions of CH(3)F have been surveyed systematically at room temperature with 46 different atomic cations using an inductively coupled plasma/selected-ion flow tube tandem mass spectrometer. Rate coefficients and product distributions were measured for the reactions of fourth-period atomic ions from K(+) to Se(+), of fifth-period atomic ions from Rb(+) to Te(+) (excluding Tc(+)), and of sixth-period atomic ions from Cs(+) to Bi(+). Primary reaction channels were observed corresponding to F atom transfer, CH(3)F addition, HF elimination, and H(2) elimination. The early-transition-metal cations exhibit a much more active chemistry than the late-transition-metal cations, and there are periodic features in the chemical activity and reaction efficiency that maximize with Ti(+), As(+), Y(+), Hf(+), and Pt(+). F atom transfer appears to be thermodynamically controlled, although a periodic variation in efficiency is observed within the early-transition-metal cations which maximizes with Ti(+), Y(+), and Hf(+). Addition of CH(3)F was observed exclusively (>99%) with the late-fourth-period cations from Mn(+) to Ga(+), the fifth-period cations from Ru(+) to Te(+), and the sixth-period cations from Hg(+) to Bi(+) as well as Re(+). Periodic trends are observed in the effective bimolecular rate coefficient for CH(3)F addition, and these are consistent with expected trends in the electrostatic binding energies of the adduct ions and measured trends in the standard free energy of addition. HF elimination is the major reaction channel with As(+), while dehydrogenation dominates the reactions of W(+), Os(+), Ir(+), and Pt(+). Sequential F atom transfer is observed with the early-transition-metal cations, with the number of F atoms transferred increasing across the periodic table from two to four, maximizing at four for the group 5 cations Nb(+)(d(4)) and Ta(+)(d(3)s(1)), and stopping at two with V(+)(d(4)). Sequential CH(3)F addition was observed with many atomic cations and all of the metal mono- and multifluoride cations that were formed.     

Gas-phase reactions of atomic lanthanide cations with CO2 and CS2: room-temperature kinetics and periodicities in reactivity

Gas-phase reactions of atomic lanthanide cations (excluding Pm+) have been surveyed systematically with CO2 and CS2 using an inductively coupled plasma/selected-ion flow tube (ICP/SIFT) tandem mass spectrometer. Observations are reported for reactions with La+, Ce+, Pr+, Nd+, Sm+, Eu+, Gd+, Tb+, Dy+, Ho+, Er+, Tm+, Yb+, and Lu+ at room temperature (295 +/- 2 K) in helium at a total pressure of 0.35 +/- 0.02 Torr. The observed primary reaction channels correspond to X-atom transfer (X = O, S) and CX2 addition. X-atom transfer is the predominant reaction channel with La+, Ce+, Pr+, Nd+, Gd+, Tb+, and Lu+, and CX2 addition occurs with the other lanthanide cations. Competition between these two channels is seen only in the reactions of CS2 with Nd+ and Lu+. Rate coefficient measurements indicate a periodicity in the reaction efficiencies of the early and late lanthanides. With CO2 the observed trends in reactivity across the row and with exothermicity follow trends in the energy required to achieve two unpaired non-f valence electrons by electron promotion within the Ln+ cation that suggest the presence of a kinetic barrier, in a manner much like those observed previously for reactions with isoelectronic N2O. In contrast, no such barrier is evident for S-atom transfer from the valence isolectronic CS2 molecule which proceeds at unit efficiency, and this is attributed to the much higher polarizability of CS2 compared to CO2 and N2O. Up to five CX2 molecules were observed to add sequentially to selected Ln+ and LnX+ cations.     

Gas-phase reactions of carbon dioxide with atomic transition-metal and main-group cations: room-temperature kinetics and periodicities in reactivity

The chemistry of carbon dioxide has been surveyed systematically with 46 atomic cations at room temperature using an inductively-coupled plasma/selected-ion flow tube (ICP/SIFT) tandem mass spectrometer. The atomic cations were produced at ca. 5500 K in an ICP source and allowed to cool radiatively and to thermalize by collisions with Ar and He atoms prior to reaction downstream in a flow tube in helium buffer gas at 0.35 +/- 0.01 Torr and 295 +/- 2 K. Rate coefficients and products were measured for the reactions of first-row atomic ions from K(+) to Se(+), of second-row atomic ions from Rb(+) to Te(+) (excluding Tc(+)), and of third-row atomic ions from Cs(+) to Bi(+). CO(2) was found to react in a bimolecular fashion by O atom transfer only with 9 early transition-metal cations: the group 3 cations Sc(+), Y(+), and La(+), the group 4 cations Ti(+), Zr(+), and Hf(+), the group 5 cations Nb(+) and Ta(+), and the group 6 cation W(+). Electron spin conservation was observed to control the kinetics of O atom transfer. Addition of CO(2) was observed for the remaining 37 cations. While the rate of addition was not measurable some insight was obtained into the standard free energy change, DeltaG(o), for CO(2) ligation from equilibrium constant measurements. A periodic variation in DeltaG(o) was observed for first row cations that is consistent with previous calculations of bond energies D(0)(M(+)-CO(2)). The observed trends in D(0) and DeltaG(o) are expected from the variation in electrostatic attraction between M(+) and CO(2) which follows the trend in atomic-ion size and the trend in repulsion between the orbitals of the atomic cations and the occupied orbitals of CO(2). Higher-order CO(2) cluster ions with up to four CO(2) ligands also were observed for 24 of the atomic cations while MO(2)(+) dioxide formation by sequential O atom transfer was seen only with Hf(+), Nb(+), Ta(+), and W(+).     

Carbon disulfide reactions with atomic transition-metal and main-group cations: gas-phase room-temperature kinetics and periodicities in reactivity

The reactions of 46 atomic-metal cations with CS2 have been investigated at room temperature using an inductively-coupled plasma/selected-ion flow tube (ICP/SIFT) tandem mass spectrometer. Rate coefficients and products were measured for the reactions of fourth-period atomic ions from K+ to Se+, of fifth-period atomic ions from Rb+ to Te+ (excluding Tc+), and of sixth-period atomic ions from Cs+ to Bi+. Primary reaction channels were observed leading to S-atom transfer, CS2 addition and, with Hg+, electron transfer. S-atom transfer appears to be thermodynamically controlled and occurs exclusively, and with unit efficiency, in the reactions with most early transition-metal cations (Sc+, Ti+, Y+, Zr+, Nb+, La+, Hf+, Ta+, and W+) and with several main-group cations (As+, Sb+) and less efficiently with Se+, Re+ and Os+. Other ions, including most late transition and main-group metal cations, react with CS2 with measurable rates mostly through CS2 addition or not at all (K+, Rb+, Cs+). Traces of excited states (< 10%) were seen from an inspection of the observed product ions to be involved in the reactions with Mo+, Te+, Ba+ and Au+ and possibly Pt+ and Ir+. The primary products YS+, ZrS+, NbS+, HfS+, TaS+, WS+, ReS+ and OsS+ react further by S-atom transfer to form MS2(+), and TaS2(+) reacts further to form TaS3(+). CS2 addition occurs with the cations MCS2(+), MS+, MS2(+), CS2(+), and TaS3(+) to form M+(CS2)(n) (n < or = 4), MS+(CS2)(n) (n < or = 4), MS2(+)(CS2)(n) (n < or = 3), (CS2)2(+) and TaS3(+)(CS2). Up to four CS2 molecules add sequentially to bare metal cations and monosulfide cations, and three to disulfide cations. Equilibrium constant measurements are reported that provide some insight into the standard free energy change for CS2 ligation. Periodic variations in deltaG degrees are as expected from the variation in electrostatic attraction, which follows the trend in atomic-ion size and the trend in repulsion between the orbitals of the atomic cations and the occupied orbitals of CS2.     

Application of Hamiltonian of ray motion to room acoustics

Based on a standard Hamiltonian of acoustic ray, it is shown that a ray motion in a finite region can be treated as a particle motion inside a potential well. The boundary reflections of ray can be described by introducing a so-called confining potential to confine a ray motion in a closed domain. It is shown that the square well potential model for the ray motion can reproduce the reverberation time in a two-dimensional room with irregular walls which is consistent with the Norris-Eyring law. It is also shown that the sound reverberation relates the ray chaos of the billiards in polygons with smooth convex walls.     

An assignment problem for a parallel queueing system with two heterogeneous servers

In this paper, we consider an optimization problem for a parallel queueing system with two heterogeneous servers. Each server has its own queue and customers arrive at each queue according to independent Poisson processes. Each service time is independent and exponentially distributed. When a customer arrives at queue 1, the customers in queue 1 can be transferred to queue 2 by paying an assignment cost which is proportional to the number of moved customers. Holding cost is a function of the pair of queue lengths of the two servers. Our objective is to minimize the expected total discounted cost. We use the dynamic programming approach for this problem. Considering the pair of queue lengths as a state space, we show that the optimal policy has a switch over structure under some conditions on the holding cost.     

3nπ* spectra of benzaldehyde. I. Vapor phosphorescence

Vibrational analysis of the vapor ³nπ* phosphorescence for three isotopic benzaldehydes (B-h₆, B-1d₁, B-Rd₅) shows that the out-of-plane aldehyde hydrogen wagging vibration (ν₂₆) is the most active non-totally symmetric mode in the spectrum. Since the intensity of 26₂⁰ ? 26₁⁰ the mechanism of ν₂₆ activity is primarily as a Franck—Condon mode. The only other out-of-plane mode definitely attributed to the vapor phosphorescence is the weakly active CHO torsional vibration (ν₃₆) with I (36₁⁰) > I (26₁⁰). Other Franck—Condon modes are ν₇, ν₂₅, ν₂₀, ν₁₇ and ν₈.     

Nucleophilic substitutions of 2-chloronaphtho[2,3-b]furan-4,9-dione with amines

2-Chloronaphtho[2,3-b]furan-4,9-dione 4 was allowed to react with pyrrolidine to produce 2-(1-pyrrolidinyl)naphtho[2,3-b]furan-4,9-dione 8 in 64% yield. In a similar manner, the reaction of 4 with cyclic amines (piperidine, morpholine, 4-substituted piperazines, etc.) gave the desired compounds. 2-Dimethylaminonaphtho[2,3-b]furan-4,9-dione 20 and 2-propylaminonaphtho[2,3-b]furan-4,9-dione 23 were obtained from the reactions of 4 with amines in 67% and 48% yields, respectively. Furthermore, the reactions of 4 with acyclic amines (diethylamine, dipropylamine, isopropylamine, butylamine, etc.) gave the desired compound. Compound 4 was treated with sodium azide to give 2-azidonaphtho[2,3-b]furan-4,9-dione 28 in 42% yield. All these nucleophilic substitutions were carried out at room temperature. It was found that 4 showed high reactivity for amines. Unexpectedly, 2-morpholinonaphtho[2,3-b]furan-4,9-dione 13 was obtained from the reaction of 4 with 1-morpholino-1-cyclohexene.