Complete characterization of the water dimer vibrational ground state and testing the VRT(ASP-W)III,SAPT-5st,and VRT(MCY-5f) surfaces

We report the observation of extensive a- and c-type rotation-tunnelling (RT) spectra of (H₂O)₂ for K_a = 0–3, and (D₂O)₂ for K_a = 0–4. These data allow a detailed characterization of the vibrational ground state to energies comparable to those of the low-lying (70–80 cm^?1) intermolecular vibrations. We present a comparison of the experimentally determined molecular constants and tunnelling splittings with those calculated on the VRT(ASP-W)III, SAPT-5st, and VRT(MCY-5f) intermolecular potential energy surfaces. The SAPT-5st potential reproduces the vibrational ground state properties of the water dimer very well. The VRT(MCY-5f) and especially the VRT(ASP-W)III potentials show larger disagreements, in particular for the bifurcation tunnelling splitting.     

Approximation of Parametric Derivatives by the Empirical Interpolation Method

We introduce a general a priori convergence result for the approximation of parametric derivatives of parametrized functions. We consider the best approximations to parametric derivatives in a sequence of approximation spaces generated by a general approximation scheme, and we show that these approximations are convergent provided that the best approximation to the function itself is convergent. We also provide estimates for the convergence rates. We present numerical results with spaces generated by a particular approximation scheme—the Empirical Interpolation Method—to confirm the validity of the general theory.     

Maintenance optimization on parallel production units

The optimal preventive-maintenance schedule for a productionsystem consisting of N identical parallel production units isinvestigated. The lifetimes of the units are IFR-distributed,i.e. with an increasing failure rate, and are supposed to bestatistically independent. The relevant costs are due to productionlosses, which are increasing and convex in the number of unitsthat are out of operation simultaneously. Actual maintenancecosts (either preventive or corrective) are supposed to be negligibleas compared to the costs due to these production losses. First we consider the apparently trivial case of geometric (discrete-time)or exponential (continuous-time) lifetime distributions forthe units. In this situation, preventive maintenance cannotimprove the condition of a unit. Hence, apparently the onlyrelevant policy is to do corrective maintenance on failed units.However, the analysis reveals that this conclusion is not correct.It turns out that taking non-failed units out of operation deliberatelycan be better than restricting to corrective maintenance only. We first show that, in the case of geometrically distributedlifetimes and unit repair times, the optimal preventive–maintenancepolicy is characterized by a single control limit K. Wheneverthe number of working units is less than or equal to K, no unitsare taken out of operation, while i – K units are setapart whenever i ( > K) units are operational. Next we consider the case with exponentially distributed lifetimesand repair times. Moreover, we assume that the repair capacityis limited, in the sense that only s ( N) units can be underrepair simultaneously. We show that, also in this case, it canbe optimal to take a working unit out of operation until thenext decision epoch (which is either a failure epoch or a repaircompletion epoch). It is shown that the optimal policy has aweak monotonicity property: the number of units which remainin operation increases with the number of available units. However,it is not necessarily true that, under the optimal policy, thenumber of units in standby position increases with the numberof available units. Numerical examples are presented which illustrate that, fora wide range of parameter values, the easiest policy (only performcorrective maintenance on failed units) performs rather wellas compared to the overall optimal policy. Finally we consider the possible extension to the practicallymore interesting case of non-exponential lifetime distributions.In particular, we assume that the lifetimes are composed oftwo non-identical exponential phases. A unit in its first lifephaseis called ‘good’, while a unit in its second phaseis called "doubtful". In this situation, one has the optionto put a good or doubtful unit in standby position until thenext decision epoch or to perform preventive maintenance ona doubtful unit. The latter brings a unit back from the doubtfulinto the good state. An indication is given of the problemsthat arise in generalizing the results obtained for the exponentialcase.     

Immobilized 2-(4-hydrazinocarbonylphenyl)-4,5-diphenylimidazole as solid phase luminophore in peroxyoxalate chemiluminescence

A new luminophore for application in peroxyoxalate chemiluminescence is presented. An analogue of the well-known chemiluminescence compound lophine, i.e. 2-(4-hydrazinocarbonylphenyl)-4,5-diphenylimidazole (HCPI), has been covalently immobilized to controlled pore glass and a porous methacrylate resin. By using this reagent in a solid phase detection reactor, sensitive determinations of hydrogen peroxide have been demonstrated. In homogeneous solution HCPI emits poorly as a result of 1,1-oxalyldiimidazole excitation, but when immobilized its efficiency is almost comparable to highly efficient luminophores such as 3-aminofluoranthene. Linearity extends in the single stream flow system over several orders of magnitude with both materials. The limit of detection was 1 nmol/l (10 fmole injected), when using the porous methacrylate support.     

Potentiometric micro-titration of potassium

Summary The potentiometric micro titration of potassium tetraphenylborate in acetone/water mixtures using a silver nitrate solution gives a sharper end-point than with indicators. The silver nitrate titer obtained against K(Ph)₄B in acetone/water mixtures varies with the acetone concentration. This applies particularly for solutions which contain less than ca. 40 Vol.% acetone.

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Zusammenfassung Die potentiometrische Mikrotitration von Kaliumtetraphenylborat in Aceton-Wasser-Gemischen mit Silbernitrat gibt einen schärferen Endpunkt als bei Verwendung eines Indikators. Der Silbernitrattiter gegen K(Ph)₄B in Aceton-Wasser-Gemischen variiert mit der Acetonkonzentration, besonders wenn der Acetongehalt der Lösungen geringer ist als 40 Vol.-%.

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Résumé Le microtitrage potentiométrique du tétraphénylborate de potassium dans des mélanges d'eau et d'acétone à l'aide d'une solution titrante de nitrate d'argent donne un point final de titrage plus net que les indicateurs. Le titre du nitrate d'argent déterminé à l'aide de K(Ph)₄B dans des mélanges acétone-eau varie avec la concentration en acétone. Cette observation s'applique particulièrement aux solutions qui contiennent moins de 40% environ en volume d'acétone.

     

Structural Aspects of Lithium Arenethiolate Complexes with Intramolecular Coordinating Amine Donors

Reaction of aryllithium reagents LiR (R = C(6)H(4)((R)-CH(Me)NMe(2))-2 (1a), C(6)H(3)(CH(2)NMe(2))(2)-2,6 (1b), C(6)H(4)(CH(2)N(Me)CH(2)CH(2)OMe)-2 (1c)) with 1 equiv of sulfur (1/8 S(8)) results in the quantitative formation of the corresponding lithium arenethiolates [Li{SC(6)H(4)((R)-CH(Me)NMe(2))-2}](6) (3), [Li{SC(6)H(3)(CH(2)NMe(2))(2)-2,6}](6) (4), and [Li{SC(6)H(4)(CH(2)N(Me)CH(2)CH(2)OMe)-2}](2) (5). Alternatively, 3 can be prepared by reacting the corresponding arenethiol HSC(6)H(4)((R)-CH(Me)NMe(2))-2 (2) with (n)BuLi. X-ray crystal structures of lithium arenethiolates 3 and 4, reported in abbreviated form, show them to have hexanuclear prismatic and hexanuclear planar structures, respectively, that are unprecedented in lithium thiolate chemistry. The lithium arenethiolate [Li{SC(6)H(4)(CH(2)N(Me)CH(2)CH(2)OMe)-2}](2) (5) is dimeric in the solid state and in solution, and crystals of 5 are monoclinic, space group P2(1)/c, with a = 17.7963(9) ?, b = 8.1281(7) ?, c = 17.1340(10) ?, beta = 108.288(5) degrees, Z = 4, and final R = 0.047 for 4051 reflections with F > 4sigma(F). Hexameric 4 reacts with 1 equiv of lithium iodide and 2 equiv of tetrahydrofuran to form the dinuclear adduct [Li(2)(SAr)(I)(THF)(2)] (6). Crystals of 6 are monoclinic, space group P2(1)/c, with a = 13.0346(10) ?, b = 11.523(3) ?, c = 16.127(3) ?, beta = 94.682(10) degrees, Z = 4, and final R = 0.059 for 3190 reflections with F > 4sigma(F).