The infrared spectra (600-140 cm−1 of the imidazole,pyrazine and pyrimidine adducts of cobalt(II), nickel(II) and zinc(II) acetylacetonates

Summary The complexes M(acac)₂(imidazole)₂ (M = Co or NO and [M(acac)₂B]_n (M = Co, Ni or Zn; B = pyrazine or pyrimidine) have been prepared and their i.r. spectra determined over the 600–140 cm^–1. range. The metal-oxygen and metal-nitrogen stretching frequencies, (M-O) and v(M-N), are assigned on the basis of the band shifts induced by deuteriation of the adducted base and by substitution of the metal ion. Three or fourv(M-O) bands are observed within the 600-200 cm^–1 range. The twov(M-O) bands of higher frequency are considered to the coupled with internal ligand modes. TwovM-N) bands are observed within the 280–170 cm^–1. range. The metal-ligand stretching frequencies are in good agreement with the values previously established for these vibrations in the [M(imidazole)₆]²⁺ and Ni(acac)₂(pyridine)₂ complexes.     

The effect of pressure on the dissociation constant of hydrofluoric acid and the association constant of the NaF ion pair at 25°C

The effect of pressure on the dissociation constant of hydrofluoric acid was determined by using the indicator technique at 25°C at an ionic strength of 0.1m over a pressure range of 1 to 2000 atm. A value of 3.14 for pK _a ^* at I =0 was obtained by extrapolation to zero ionic strength at 1 atm. The pressure dependence yielded a partial molar volume change of –9.6 cm³-mol^–1 and a compressibility change of — 35×10^–3 cm³-mol^–1 –atm^–1 for the dissociation. The dependence of ionic strength on the association constant K _A ^* of NaF was studied at 25°C and 1 atm. Extrapolation to I=0 yielded a pK _A ^* of –0.78. The pressure dependence of K _A ^* gave a change of volume of 3.26 cm³-mol^–1 and a change in compressibility of 6×10^–3 cm³-mol^–1-atm^–1 for the formation of the ion pair.     

Photoreactivation of tobacco mosaic virus and potato virus X ribonucleic acids inactivated by acetone-sensitized photoreaction

Abstract— Acetone-sensitized photoinactivation and subsequent in vivo photoreactivation of tobacco mosaic virus (TMV) and potato virus X (PVX) ribonucleic acids (RNA's) were demonstrated. The photoreactivable sectors were comparable to those obtained for the same RNA's irradiated at 253·7 nm. Only dimers were detected in these RNA's. Irradiation of E. coli rRNA at a higher dose indicated that photoreversible pyrimidine dimers were the main photoproducts detected in the sensitized reaction, whereas pyrimidine hydrates were formed only in negligible amounts. These results have led us to conclude that photoreversible pyrimidine dimers constitute both a lethal and photorepairable type of lesion in u.v.-damaged viral RNA.     

Structural similarities and differences among mixed-metal clusters containing a single M(PPh3) (M = Cu, Ag or Au) fragment

The heteronuclear metal clusters [H₃MRu₄(CO)₁₂(PPh₃)] and [MFe₃(μ-COMe)(CO)₁₀(PPh₃)] (M = Cu, Ag or Au) have been prepared; the gold-tetraruthenium cluster has a different metal core geometry to that adopted by the copper and silver analogues, whereas all three iron-Group IB mixed-metal clusters have the same geometry.     

An efficient synthesis of 4-(phenylsulfonyl)-4H-furo[3,4-b]indoles

The fused heterocycle 4-(phenylsulfonyl)-4H-furo[3,4-b]indole, which is an indole-2,3-quinodimethane synthetic analogue, is prepared in five steps from indole in 46% yield. A similar sequence is used to synthesize C-3 derivatives (3-methyl, 3-phenyl, and 3-heptyl). Thus, indole-3-carbaldehyde (1) is protected as the N-phenylsulfonyl derivative 2 and converted to the ethylene acetal 6. Lithiation at C-2 followed by treatment with an aldehyde affords the expected hydroxy acetals 7 and 8. Exposure to acid effects cyclization to the furoindoles 5 and 9. Furthermore, C-1 lithiation of furo[3,4-b]indole 9c followed by treatment with methyl iodide affords disubstituted furo[3,4-b]indole 10.     

Ultrafast digital soliton logic gates

We demonstrate all-optical fibre switches, including soliton-dragging logic gates, soliton-interaction gates and soliton-trapping AND-gates, that have the potential of operating up to speeds of 0.2 Tbps. Solitons in fibres are attractive for ultrafast timedomain switching because they avoid pulse distortion during propagation and because they exhibit particle-like properties. Soliton-dragging logic gates satisfy all requirements for a digital optical processor and having switching energies approaching 1 pJ. In addition, soliton-dragging logic gates are one example of a more general timedomain chirp switch architecture in which a dispersive delay line acts as a lever-arm to reduce the switching energy. Soliton-interaction gates are based on elastic collisions between solitons and illustrate that solitons can be used to implement conservative, billiard-ball logic operations. Soliton-trapping AND-gates are sensitive to the timing of the input pulses and display on/off contrast ratios greater than 201. The soliton-trapping AND-gate can serve as the final stage in an all-optical system and as the interface to electronics. These ultrafast gates may prove advantageous in applications where the switch bandwidth limits the performance of the system     

Self-avoiding walk in five or more dimensions I. The critical behaviour

We use the lace expansion to study the standard self-avoiding walk in thed-dimensional hypercubic lattice, ford5. We prove that the numberc _n ofn-step self-avoiding walks satisfiesc _n ~A ⁿ , where is the connective constant (i.e. =1), and that the mean square displacement is asymptotically linear in the number of steps (i.e.v=1/2). A bound is obtained forc _n(x), the number ofn-step self-avoiding walks ending atx. The correlation length is shown to diverge asymptotically like (^––Z)^1/2. The critical two-point function is shown to decay at least as fast as x^–2, and its Fourier transform is shown to be asymptotic to a multiple ofk ^–2 ask0 (i.e. =0). We also prove that the scaling limit is Gaussian, in the sense of convergence in distribution to Brownian motion. The infinite self-avoiding walk is constructed. In this paper we prove these results assuming convergence of the lace expansion. The convergence of the lace expansion is proved in a companion paper.Supported by the Nishina Memorial Foundation and NSF grant PHY-8896163.Supported by NSERC grant A9351     

Probability and expectation inequalities

Summary This paper introduces a mathematical framework within which a wide variety of known and new inequalities can be viewed from a common perspective. Probability and expectation inequalities of the following types are considered: (a)P(ZA) P(ZA) for some class of setsA, (b)k(Z)k(Z) for some class of functionsk, and (c)l(Z)k(Z) for some class of pairs of functionsl andk. It is shown, sometimes using explicit constructions ofZ andZ, that, in several cases, (a) (b) (c); included here are cases of normal and elliptically contoured distributions. A case where (a) (b) (c) is studied and is expressed in terms ofn monotone functions for (some of) which integral representations are obtained. Also, necessary and sufficient conditions for (c) are given.Research supported by the Air Force Office of Scientific Research under Grants AFOSR-75-2796 and AFOSR-80-0080Research supported by the National Science Foundation under Grants MCS78-01240 and MCS81-00748