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The first metallabenzene,[O[graphic omitted]H)(CO)(PPh3)2] has been prepared from [Os(Co)(CS)(PPh3)3] and ethyen; X- ray crystal structure determination reveals a planar six-membered ring with no significant alternation of C–C bond lengths thus supporting the idea of electron delocalization within the ring.

Even–odd alternation of the e.s.r. spectra of a series of irradiated linear alkanes starting from n-C11 H24 is found to be due to the prominent chain end alkyl radical formation in odd members of the series, suggesting that the radiation chemistry of crytstalline alkanes may be affected by the cyrtystal structure, e.g. by molecular packing and alignment.

Electron spin resonance spectra of paradinitrobenzene anions in methanoldioxane mixtures exhibit a very marked line-width alternation. It is shown that such alternation, stemming from a relatively small difference between the isotropic hyperfine coupling constants of the two nitrogen atoms can account for the apparently anomalous spectra in solvents of low dielectric constant.

The electron spin resonance (e.s.r.) spectrum of 4,4′-dimethoxybiphenyl in aluminium chloride–nitromethane is remarkably temperature dependent. The changes are explained by postulating the rapid interconversion of conformational isomers, leading to line-width alternation.

The concentration of the original monomers in the reaction medium influences the alteranation effect during the copolymerization of vinyl ethers with acrylates. A concentration of the active monomer may be chosen such that the polymer of methyl methacrylate will be formed at the beginning.

Simple products of singlet-coupled spin pairs are identified as exact eigenstates for a certain class of antiferromagnetically signed linear-chain Heisenberg models with both bond-length alternation and next-nearest-neighbor interactions. Where such an eigenstate becomes a ground state, a cusp is noted to arise in the ground-state energy. Differences between the spin-1/2 and higher-spin cases appear.

The ground-state energy per site, \ensuremath{\epsilon}(\ensuremath{\delta}), and the singlet-triplet gap, \ensuremath{\Delta}(\ensuremath{\delta}), of the linear spin-(1/2) alternating Heisenberg antiferromagnet are found by extrapolation of direct solutions to N\ensuremath{\le}26 sites for even rings and N\ensuremath{\le}21 sites for odd rings, whose orbital degeneracy leads to qualitatively different critical behavior. The \ensuremath{\epsilon}(\ensuremath{\delta}) accuracy of ${l10}^{\mathrm{\ensuremath{-}}4}$ (in units of J) decisively rules out power-law behavior for any alternation \ensuremath{\delta}g0.001 and is consistent with ${\ensuremath{\delta}}^{4/3}$/\ensuremath{\Vert}ln\ensuremath{\delta}\ensuremath{\Vert} for \ensuremath{\delta}l0.05. The gap \ensuremath{\Delta}(\ensuremath{\delta}) is slightly sublinear in \ensuremath{\delta}. Direct ground-state solutions are found via diagrammatic valence-bond methods and provide sensitive tests for theoretical approaches to linear spin systems.

Mass spectra of carbon \({{\rm{c}}^{\rm{ + }}}_{\rm{n}}{\rm{,}}{{\rm{c}}^{\rm{ - }}}_{\rm{n}}{\rm{,}}{{\rm{c}}^{{\rm{2 + }}}}_{\rm{n}}\) aggregates produced by various techniques show three different n regions. For n ≲ 10, an alternation behaviour appears with aggregates more abundant for a given parity of n. For 10 ≲ n ≲ 30, the mass spectra exhibit a modulo-4 periodicity. For n ≳ 40, an alternation behaviour appears again and some species as \({{\rm{c}}^{\rm{ + }}}_{60}\) are very intense. These results which are related to the stabilities of the aggregates are discussed.

Results of recent synthetic, structural, and magnetic work on exchange coupled copper (II) ions bridged by nonmagnetic ligands are discussed, including the quasi���linear chain compound bis (dimethyldithiocarbamato) copper (II) in which the copper (II) ions are antiferromagnetically exchange coupled. An unusual correlation exists in the structural and magnetic data for [Cu(dmtc)2]��� and other known sulfur bridged coppercompounds. Data are presented for the alternatingly spaced linear chain compounds di��������chlorobis���(4���methylpyridine)copper (II), and a series of dionebis���(thiosemicarbazato)copper (II) compounds. Exchange coupling constants and alternation parameters were obtained from expressions which were empirically generated from calculations on rings of ten S = 1/2 ions for kT/���J������0.5 and J

An example is constructed showing that best uniform approximation (local or global) from $R_{n}^{m}(\mathbf{c})$ can not be characterized by linearization techniques or by alternation properties of the error function. A class of local best approximations are characterized, and used to demonstrate approximation properties of $R_{n}^{m}(\mathbf{c})$.

Description de l'application du concept d'alternance de charge a la distribution de charge dans les diions de molecules mono- et polycycliques. Determination de la densite de charge par etude theorique et experimentale (RMN 13 C)

The series of structurally ordered bimetallic chains formulated as MM′ (EDTA).6H2O, in short (MM′), provides the most versatile known example of 1-dimensional ferrimagnets, since on the same structural support many different magnetic ions (Mn, Co, Ni and Cu(II)) can be selectively accommodated.1 Consequently, many choices of alternating magnetic moments with Heisenberg or Ising exchange couplings can be investigated. Moreover, taking into account that the M-M′ distances along the chain are alternating, this series could show at the same time an alternation of the exchange parameter2.

The modulated structure of Na2CO3 at room temperature, formerly analyzed in the sinusoidal approximation (van Aalst c.s., Acta Cryst. approximation using 3766 non‐zero reflection intensities. These belong to 751 main reflections and 1159, 951, 518, 387 satellites of 1st, 2nd, 3rd, and 4th order respectively. The final R for the weighted set is 9.3%.The average coordinates and the first harmonic components of all modulation functions agree with the former values to within 3σ. The improbable second harmonic variations in the internal distances of the CO3 ion in that former structure are almost eliminated. On the other hand, the large variations in several Na3‐0 distances are now found to approach square‐wave form, indicating a tendency to alternation between two opposite coordinations of Na3. Plots of F0 against fc for each satellite order m show a significant decrease of their ratio with increasing m; for m=4, fo/fc is about 0.8. This effect points to some disorder in the modulation, apart from the normal ...

Publisher Summary Cyanine dyes and related compounds cover the whole visible spectrum and have high tinctorial power but owing to their poor stability to light they are not important as textile dyes. Some of these dyes show high light stability on acrylonitrile homo-and co-polymers, and have attained technological importance. For convenience, cyanine dyes and related compounds are studied under the groups: Cyanines; Azacyanines; Polynuclear cyanines; Dye bases; Merocyanines; Linear tri- and poly-nuclear cyanines and merocyanines; Oxonols; nonheterocyclic cyanines; Styryl dyes and N-hemicyanines. The vast majority of cyanine dyes are mono-acid salts, in which two heterocyclic nuclei containing nitrogen are linked through an odd numbered methine chain in such a way that resonance occurs through the conjugated system between tertiary and quaternary nitrogen atoms. Azacyanines are dyes, in which one or more of the methine groups in the conjugated chain have been replaced by nitrogen. When cyanine dyes are heated with a high-boiling amine, such as N,N-diethylaniline, the more basic heterocyclic ring becomes dequaternized to produce the dye base. Merocyanines may be defined as nonionic dyes, in which a double bond or an even-numbered methine chain unites a dihydrogenated nitrogen-containing heterocycle with the residue of a compound having an active methylene group, usually a cyclic ketomethylene compound.

The temperature dependence of the susceptibility of solvent-free DPPH powder measured by means of the hyperfine splitting in the proton magnetic resonance spectrum fits a one-dimensional alternating antiferranagnetic Heisenberg chain with activation energy |J|= 10 K and an alternation parameter estimated to be about 0.2.

The concept of stabilization of polyanionic and polycationic compounds by charge alternation was introduced to explain the course of polymetalation of hydrocarbons and enolates. This concept is generalized to the positional stabilization of polar compounds containing two or more donor or acceptor groups and reconciled with the different known stabilizations of compounds containing a donor and an acceptor group. Various properties of other classes of compounds such as relative acidities and basicities of heterocyclic compounds, charge distribution in cyanines, mesocyanines,oxonoles and aromatic dianions, as well as the regioselectivity of some reactions seem also to obey the rules based on this concept.

Yet, this condition of the cosmic system was still different from the world as it is today, since all of this diakosmesis was still unfit to bring about an alternation of day and night. For still the entire perichoresis was everywhere taking place around the one axis chosen in the beginning when Nous started cosmogony from that tiny district. Consequently, the circles described around that axis by the sun and the moon could only lie in the plane of the earth disk itself, and the orbits of the other stars were either in this very plane or parallel with it.

Almost all compounds of the AIIBVI type crystallize in such a manner that each atom of one element is located at the center of a regular tetrahedron, the apices of which are occupied by atoms of the other element. Two possible structures can be formed from such tetrahedra: the sphalerite (cubic type) and the wurtzite (hexagonal) type. The sphalerite structure is very similar to the structure of diamond, but it differs from the latter by the alternation of atoms of two different elements. In the sphalerite structure, the atoms of one element are located at the sites of an fcc lattice, while the atoms of the second element occupy centers of four (out of a total of eight) small cubes (Fig. 1). The space group is F43m Td 2. The coordination number is 4 for atoms of both elements.

4,10b-Methano-8H-benzo[ab]cyclodecen-8-one (C14H10O), a stable derivative of so-called 1,6-methano[10]annulene, forms reddish orange crystals of the space group Pbca, with eight molecules in a unit cell with dimensions of a=16.567, b=14.090, and c=8.418 A. The structure was solved by the symbolic addition method and refined by the block-diagonal least-squares method. The final R factor was 0.080 for the 1386 independent observed reflections. The lengths of the peripheral bonds of the [10]annulene nucleus do not exhibit any apparent alternation. The peripheral eight atoms are approximately coplanar. The C–O distance (1.236 A) is longer than those in quinones and tropones, and it is consistent with the large dipole moment and high basicity of the present molecule.

We introduce the natural class ${\bf\,S}^P_2$ containing those languages that may be expressed in terms of two symmetric quantifiers. This class lies between $\Delta^P_2$ and $\Sigma^P_2\,\cap\,\Pi^P_2$ and naturally generates a “symmetric” hierarchy corresponding to the polynomial-time hierarchy. We demonstrate, using the probabilistic method, new containment the theorems for BPP. We show that MA (and hence BPP) lies within ${\bf\,S}^P_2$ , orems for BPP. We show that MA (and hence BPP) lies within ${\bf\,S}^P_2$ , improving the constructions of Sipser and Lautemann which show that ${\bf BPP}\subseteq\,\Sigma^P_2\,\cap\,\Pi^P_2$ . Symmetric alternation is shown to enjoy two strong structural properties which are used to prove the desired containment results. We offer some evidence that ${\bf S}^P_2\,\neq\,\Sigma^P_2\,\cap\,\Pi^P_2$ by constructing an oracle O such that ${\bf S}^{P,O}_2\,\neq\,\Sigma^{P,O}_2\,\cap\,\Pi^{P,O}_2$ , assuming that the machines make only “positive” oracle queries.

Using sum rules for spectral moments of linear and nonlinear absorption we show that the jth order off-resonant polarizabilities of polyacetylene chains scale as $\ensuremath{\sim}j{\ensuremath{\Delta}}^{\ensuremath{-}j}{N}^{j+1}/(N+L{)}^{j}$; $N$ is the number of carbon atoms, $\ensuremath{\Delta}$ the bond-length alternation, and $L(\ensuremath{\Delta})$ the exciton coherence size. This result is in excellent agreement with time-dependent Hartree-Fock calculations performed for chains with up to 200 carbon atoms.

The traditional studies of multi-prover interactive proof systems have concentrated on cooperating provers. These are systems in which a verifier interacts with a set of provers who collaborate in their attempt to convince the verifier that a word $ \omega $ is in a prespecified language L. Results on probabilistically checkable proofs coupled with parallel repetition techniques characterize NP in terms of multi-prover proof systems: languages in NP can be verified through a one-round interaction with two cooperating provers using limited randomness and communication.¶Less attention has been paid to the study of competition in this complexity-theoretic setting of interactive proof systems. We consider, for example, one-round proof systems where the first prover is trying to convince the verifier to accept and the second prover is trying to convince the verifier to reject. We build into these proof systems a (crucial) asymmetry between the provers, analogous to quantifier alternation. We show that such proof systems capture, with restrictions on communication and randomness, languages in NP. We generalize this model by defining alternating prover proof systems which we show characterize each level of the polynomial hierarchy. Alternating oracle proof systems are also examined.¶The main contribution of this work is the first exact characterization of the polynomial hierarchy in terms of interactive (prover) proof systems.

We report the detailed X-ray structure of the fully blocked tetrapeptide Z-D-Val-(Aib)2-L-Phe-OMe. The compound crystallizes in the space group P21 with four independent tetrapeptide molecules aligned in a parallel arrangement along the c axis. There is a regular alternation of right- and left-handed 310-helices hydrogen bonded head-to-tail along this axis. Pairs of molecules with the same handedness differ in the conformation of the side chains and of the N- and C-terminal blocking groups. This is the first observation, to the best of our knowledge, of a helical peptide containing chiral α-monosubstituted α-amino acids without a preferred screw sense. Conformational energy computations confirmed that those helices with different handedness have comparable stabilities. This work is a part of our studies on fully protected tetrapeptides containing homo and hetero chiral residues at N- and C-termini spaced by an achiral dipeptide segment, in order to understand the structural features responsible for the diastereoselective separation by reversed-phase HPLC.

ESR spectra of a tetrasilaspirobiindane anion radical (1−) showed a doublet of doublet hfs pattern at low temperatures and significant line-width alternation, indicating that there is remarkable difference in the electron-accepting effects between two silyl substituents at the benzene ring with the unpaired electron due to the ring conformation.

Three structures of silicon light emitting sources are described, each presenting higher electrical-to-optical conversion efficiency. The advantage of these structures lay in the fact that they were all fabricated using conventional standard VLSI technology, without any alternation of the processing procedure.

The electronic structure of a single monatomic gold wire is presented for the first time. It has been obtained with state-of-the-art ab-initio full-potential density-functional (DFT) LMTO (linearized muffin-tin orbital) calculations taking into account relativistic effects. For stretched structures in the experimentally accessible range the conduction band is exactly half-filled, whereas the band structures are more complex for the optimized structure. By studying the total energy as a function of unit-cell length and of a possible bond-length alternation we find that the system can lower its total energy by letting the bond lengths alternate leading to a structure containing separated dimers with bond lengths of about 2.5 \AA, largely independent of the stretching. However, first for fairly large unit cells (above roughly 7 \AA), is the total-energy gain upon this dimerization comparable with the energy costs upon stretching. We propose that this together with band-structure effects is the reason for the larger interatomic distances observed in recent experiments. We find also that although spin-orbit couplings lead to significant effects on the band structure, the overall conclusions are not altered, and that finite Au_2, Au_4, and Au_6 chains possess electronic properties very similar to those of the infinite chain., Comment: (14 pages, 5 figures; Elsevier Preprint style elsart.sty)

The trigonal structure of a new member of the eudialyte group was established from X-ray single-crystal diffraction, λ(MoKα ) = 0.71073 Å; space group R3m; a = 14.153(9) Å, c = 60.72(5) Å, V = 10546.1 Å3; M = 3050; D x = 2.88 g/cm3; Z = 3; μ = 28cm−1; R(hkl) = 0.068 for 3402 reflections. Due to the ordered replacement of Zr with Ti, the new mineral is characterized by a doubling of c and an alternation along [001] of two microdomains, containing (Zr, Ti) or (Ti, Zr)-octahedra, respectively. The key positions on the triad axis are accommodated by Si, Mn and Al atoms. Mn is four-fold coordinated and dominates in one nine-membered ring of the Ti microdomain while Al is six-fold coordinated in the ring of the Zr microdomain. The second key sites are related to Fe atoms which are situated in a slightly aplanar oxygen squares similarly to other relevant examples. These two positions are completed with some neighbour subsites. The axial Al octahedron is connected with three Ti octahedra around the triad axis forming a polyhedral cluster. The splitting and isomorphic substitution of the Na dominant positions are similar to other eudialyte minerals. It was also reported for kentbrooksite. The Na(8b) and Na(9b) atoms are the most disordered around the 18c site with 25% occupancy. The unusual doubling of the structure in the new mineral may be interpreted as a commensurate modulation with wave displacements along the c axis. Other original features of this new representative in the eudialyte family are also discussed.

If an electric field is applied to a planar layer of a cholesteric liquid crystal with a large negative dielectric anisotropy ( Δ ϵ = -5), an alternation of square grid perturbations and planar textures is observed when the voltage is increased. This effect, which is contrary to the usual behaviour, is accompanied by an increase in the number of helix turns.

ALTERNATION in many of the properties of successive members in homologous series of solid long-chain compounds is well known. We are reporting the direct observation of a similar alternation in the maximum adsorptions of mono-1 and di-carboxylic acids from aqueous solutions on two series of coconut shell charcoals of different degrees of activation. Some alternation in the adsorptions of these acids on a single ‘Norite’ charcoal was found indirectly by Linner and Gortner2, who made a Langmuir extrapolation of their isotherms to maximum adsorption.

THE well-known alternation of the melting points with chain-length of a homologous series of compounds (for example, the normal paraffins, mono- and di-basic fatty acids, n-acetyl L-amino-acids) has been observed in the series of αω-dimethanesulphonoxyalkanes CH3SO2O(CH2)nOSO2CH3 1. The melting points of this series are shown plotted in Fig. 1, from which it is observed that the butane derivative (n = 4) exhibits a melting point which is very much larger than the rest of the series. A discontinuity of this kind is unusual, and it is of interest to examine it further.

THE electron spin resonance spectra of semiquinone–alkali metal systems in 1,2-dimethoxyethane (DME) have recently been interpreted1 in terms of (a) two types of ion-pair, A or solvated type and B or contact type, which appear separately or together depending on the temperature and (b) an equilibrium between these two types of ion-pair which is thought to be the cause of marked line-width alternation. We have also studied these systems over a wide temperature range, but have drawn quite different conclusions.

ONE of the most interesting features of long chain compounds in the solid state is the well-known alternation in properties depending upon whether the chain contains an even or an odd number of carbon atoms. The X-ray work of Muller on single crystals and of Piper, and Muller and Shearer on the long crystal spacings has shown that long chain compounds crystallise in long zigzag chains lying perpendicular or tilted with regard to the planes formed by the terminal groups. It follows at once that there will be a difference between chains containing an odd and an even number of carbon atoms; the terminal groups being respectively in the cis and trans positions. It has been suggested by Pauly1 and Nekrassow2 that this is the cause of alternation, and Muller,3 apparently unaware of this, came independently to the same conclusions.

The radical anion of 1,4-naphthoquinone has been prepared by electrochemical reduction in dimethylformamide and by alkali-metal reduction in 1,2-dimethoxyethane. The e.s.r. spectrum of the radical anion in dimethylformamide can be readily interpreted in terms of three pairs of equivalent protons. However, in 1,2-dimethoxyethane, association of the alkali-metal counter-ion with one of the carbonyl groups removes the equivalence within each of these pairs. Linewidth alternation is observed in the e.s.r. spectrum when either Na+, K+ or Cs+ is the counter-ion as a result of intramolecular cation migration between equivalent sites adjacent to the two carbonyl groups. The rate of migration varies in the sequence Cs+ > K+ > Na+ > Li+, indicating that Li+ interacts more strongly with the radical anion than (say) Cs+. The disruption of the spin distribution within the radical anion, which is also greatest when Li+ is the counter-ion, supports this conclusion.

An X-ray crystal structure determination of the title compound (I)(monoclinic, space group C2/c, a= 14.929(2), b= 4.281 (1), c= 18.630(2)A, β= 100.60(1)°, Z= 4) shows systematic alternation of long and short bond distances (means 1.46 and 1.34 A) in the perimeter ring. The configuration of the double bonds follows the order trans, cis, cis. The molecule has a twisted conformation and crystallographic symmetry 2 (C2), with the two-fold axis running through the carbon atom of the methano-bridge. Simple HMO calculations for the present compound and other [4n]annulenes are in quite good agreement with experimental results. The structure was determined by the heavy-atom method and refined by least-squares techniques to R 0.037 for 1 249 observed reflections measured by diffractometer.

The existence of best Chebyshev approximations by an alternating family on closed subsets of an interval is considered. In varisolvent approximation, existence on subsets of sufficiently low density is guaranteed if the best approximation on the interval is of maximum degree. The paper studies the case in which the best approximation is not of maximum degree and shows that in many common cases, no such guarantee is possible. Let Y be a compact subset of [a,,/]] and C(Y) be the space of continuous functions on Y. For g E C(Y) define llglly = sup{lg(x)A: x E Y}, lIlgH = 110[al. Let F be an approximating function on [a,,8/] with parameter space P. The Chebyshev problem on Y is, given f E C(Y), to find a parameter A * to minimize lif F(A, .)IIy over A E P. Such a parameter A* is called best and F(A*, ) is called best to f on Y. We will consider only approximating functions for which best approximations on [a,,8]1 are characterized by alternation [10, pp. 17-21], [6], which implies uniqueness of best approximations. Following Cheney, we define the density of Y in [a,,8]1 to be IYI = max{inf{x -yl: y Y} a 0, there is a parameter B E P such that IF(B, a) -y < e and Received by the editors October 2, 1975. AMS (MOS) subject classifications (1970). Primary 41A50. Copyright ? 197'. Aniwrican Mathematical Society

The crysta and molecular structure of the title compound has been solved by both X-ray and neutron diffraction methods. It has been shown to exist in the enolic form, with the enolic hydrogen atom located in a clearly asymmetric position. An alternation of short and long bond lengths about the monothio-β-diketone ring is also observed. The structure is compared with those of analogous β-diketone structures. Crystals are monoclinic, space group P21/c, with a= 12.549(5), b= 7.416(4), c= 13.290(5)A, β= 98.289(12)°, Z= 4.