The octahedral manipulator: Geometry and mobility

In most Of the practical six-actuator in-parallel manipulators, the octahedral form is either taken as it stands or is approximated. Yet considerable theoretical attention is paid in the literature to more general forms. Here we touch on the general form, and describe some aspects of its behavior that vitiate strongly against its adoption as a pattern for a realistic manipulate,: We reach the conclusion that the structure for in-parallel manipulators must be triangulated as fully as possible, so leading to the octahedral form. In describing some of the geometrical properties of the general octahedron, we show how they apply to manipulators. We examine in detail the special configurations at which the 6 x 6 matrix of leg lines is singular presenting results from the point of view of geometry in preference to analysis. In extending and enlarging on some known properties, a few behavioral surprises materialize. In studying special configurations, we start with the most general situation, and every other case derives from this. Our coverage is more comprehensive than any that we have found. We bring to light material that is, we think, of significant use to a designer.

Achromatic optical phase shifter/modulator

We propose and demonstrate, theoretically and experimentally, a novel achromatic optical phase shifter modulator based on a frequency-domain optical delay line configured to maintain zero group delay as variable phase delay is generated by means of tilting a mirror. Compared with previously reported phase shifter modulators, e.g., based on the Pancharatnam (geometric) phase, our device is high speed and polarization insensitive and produces a large, bounded phase delay that, uniquely, is one-to-one mapped to a measurable parameter, the tilt angle.

A fast cross-entropy method for estimating buffer overflows in queuing networks

In this paper, we propose a fast adaptive importance sampling method for the efficient simulation of buffer overflow probabilities in queueing networks. The method comprises three stages. First, we estimate the minimum cross-entropy tilting parameter for a small buffer level; next, we use this as a starting value for the estimation of the optimal tilting parameter for the actual (large) buffer level. Finally, the tilting parameter just found is used to estimate the overflow probability of interest. We study various properties of the method in more detail for the M/M/1 queue and conjecture that similar properties also hold for quite general queueing networks. Numerical results support this conjecture and demonstrate the high efficiency of the proposed algorithm.

Iron(III) and iron(II) complexes of 1-thia-4,7-diazacyclononane ([9]aneN(2)S) and 1,4-dithia-7-azacyclononane ([9]aneNS(2)). X-Ray structural analyses, magnetic susceptibility, Mossbauer, EPR and electronic spectroscopy

The complexes [Fe([9]aneN(2)S)(2)][ClO4](2), [Fe([9]aneN(2)S)(2)][ClO4](3) and [Fe([9]aneNS(2))(2)][ClO4](2) ([9]aneN(2)S = 1-thia-4. 7-diazacyclononane and [9]aneNS(2) = 1,4-dithia-7-azacyclononane) have been prepared and the latter two characterised by X-ray crystallography. The Mossbauer spectra (isomer shift/mm s(-1), quadrupole splitting/mm s(-1), 4.2 K) for [Fe([9]aneN(2)S)(2)][ClO4](2) (0.52, 0.57), [Fe([9]aneN(2)S)(2)][ClO4](3) (0.25, 2.72) and [Fe([9]aneNS(2))(2)][ClO4](2) (0.43, 0.28) are typical for iron(II) and iron(III) complexes. Variable-temperature susceptibility measurements for [Fe([9]aneN(2)S)(2)][ClO4](2) (2-300 K) revealed temperature-dependent behaviour in both the solid state [2.95 mu(B) (300 K)-0.5 mu(B) (4.2 K)] and solution (Delta H degrees 20-22 kJ mol(-1), Delta S degrees 53-60 J mol(-1) K-1). For [Fe([9]aneN(2)S)(2)][ClO4](3) in the solid state [2.3 mu(B) (300 K)-1.9 mu(B) (4.2 K)] the magnetic data were fit to a simple model (H = -lambda L . S + mu L-z) to give the spin-orbit coupling constant (lambda) of -260 +/- 10 cm(-1). The solid-state X-band EPR spectrum of [Fe([9]aneN(2)S)(2)][ClO4](3) revealed axial symmetry (g(perpendicular to) = 2.607, g(parallel to) = 1.599). Resolution of g(perpendicular to) into two components at Q-band frequencies indicated a rhombic distortion. The low-temperature single-crystal absorption spectra of [Fe([9]aneN(2)S)(2)][ClO4](2) and [Fe([9]aneNS(2))(2)][ClO4](2) exhibited additional bands which resembled pseudotetragonal low-symmetry splitting of the parent octahedral (1)A(1g) --> T-1(2g) and (1)A(1g) ---> T-1(1g) transitions. However, the magnitude of these splittings was too large, requiring 10Dq for the thioether donors to be significantly larger than for the amine donors. Instead, these bands were tentatively assigned to weak, low-energy S --> Fe-II charge-transfer transitions. Above 200 K, thermal occupation of the high-spin T-5(2g) ground state resulted in observation of the T-5(2g) --> E-5(g) transition in the crystal spectrum of [Fe([9]aneN(2)S)(2)][ClO4](2). From a temperature-dependence study, the separation of the low-spin (1)A(1g) and high-spin T-5(2g) ground states was approximately 1700 cm(-1). The spectrum of the iron(III) complex [Fe([9]aneN(2)S)(2)][ClO4](3) is consistent with a low-spin d(5) configuration.

Crystal and molecular structure of 2-hydroxy-1-naphthaldehyde isonicotinoyl hydrazone (NIH) and its iron(III) complex: an iron chelator with anti-tumour activity

Previous studies have demonstrated that 2-hydroxy-1-naphthaldehyde isonicotinoyl hydrazone (NIH) and several other aroylhydrazone chelators possess anti-neoplastic activity due to their ability to bind intracellular iron. In this study we have examined the structure and properties of NIH and its Fe-III complex in order to obtain further insight into its anti-tumour activity. Two tridentate NIH ligands deprotonate upon coordination to Fe-III in a meridional fashion to form a distorted octahedral, high-spin complex. Solution electrochemistry of [Fe(NIH-H)(2)](+) shows that the trivalent oxidation state is dominant over a wide potential range and that the Fe-II analogue is not a stable form of this complex. The fact that [Fe(NIH-H)(2)](+) cannot-cycle between the Fe-II and Fe-III states suggests that the production of toxic free- radical species, e.g. OH. or O2(.-),is not part of this ligand's cytotoxic action. This suggestion is supported by cell culture experiments demonstrating that the addition of Fe-III to NIH prevents its anti-proliferative effect. The chemistry of this chelator and its Fe-III complex are discussed in the context of understanding its anti-tumour activity.

Bonding effects and the crystal structures of (NH4)(2)[Cu(H2O)(6)](SO4)(2) and its (H2O)-O-18 substituted form at 9.5 K

The crystal structures of the Tutton salts (NH4)(2)[Cu(H2O)(6)](SO4)(2), diammonium hexaaquacopper disulfate, formed with normal water and isotopically substituted (H2O)-O-18, have been determined by X-ray diffraction at 9.5 K and are very similar, with Cu-O(7) the longest of the Cu-O bonds of the Jahn-Teller distorted octahedral [Cu(H2O)(6)](2+) complex. It is known that structural differences accompany deuteration of (NH4)(2)[Cu(H2O)(6)](SO4)(2), the most dramatic of which is a switch to Cu-O(8) as the longest such bond. The present result suggests that the structural differences are associated with hydrogen-bonding effects rather than with increased mass of the water ligands affecting the Jahn-Teller coupling. The Jahn-Teller distortions and hydrogen-bonding contacts in the compounds are compared with those reported for other Tutton salts at ambient and high pressure.

Synthesis and complexes of the sexidentate macrocycle 15-methyl-1,4,7,10,13-pentaazacyclohexadecan-15-amine

The potentially sexidentate polyamine macrocycle 15-methyl-1,4,7,10,13-pentaazacyclohexadecan-15-amine (1) was prepared via a copper(II)-templated route from 3,6,9-triazaundecan-1,ll-diamine, formaldehyde and nitroethane which first formed the copper(II) complex of the macrocycle 15-methyl-15-nitro-1,4,7,10,13-pentaazacyclohexadecane (2), reduced subsequently with zinc and aqueous acid to yield 1. The hexaamine 1, with five secondary amine groups in the macrocyclic ring and one pendant primary amine group, forms inert sexidentate octahedral complexes with cobalt(III), chromium(III) and iron(III). An X-ray structure of [Co(1)](ClO4)(3) defines the distorted octahedron of the complex cation and shows it is a symmetrical isomer with all nitrogens bound and the central aza group trans to the pendant primary amine group. The [M(1)](3+) ions are all stable indefinitely in aqueous solution and exhibit spectra consistent with MN6 d(3) (Cr), low-spin d(5) (Fe) and low-spin d(6) (Co) electronic ground states. For each complex, a reversible M(III/II) redox couple is observed. (C) 2000 Elsevier Science S.A. All rights reserved.

Ni-II and Zn-II complexes of the hexadentate macrocyclic ligand cis-6,13-dimethyl-1,4,8,11-tetraazacyclotetra- decane-6,13-diamine

The title pendent-arm macrocyclic hexaamine ligand binds stereospecifically in a hexadentate manner, and we report here its isomorphous Ni-II and Zn-II complexes (both as perchlorate salts), namely (cis-6,13-dimethyl-1,4,8,11-tetraazacyclotetradecane-6,13-diamine-kappa(6)N)nickel(II) diperchlorate, [Ni(C12H30N6)](ClO4)(2), and (cis-6,13-dimethyl-1,4,8,11-tetraazacyclotetradecane-6,13-diamine-kappa(6)N)zinc(II) diperchlorate, [Zn(C-12 H30N6)](ClO4)(2). Distortion of the N-M-N valence angles from their ideal octahedral values becomes more pronounced with increasing metal-ion size and the present results are compared with other structures of this ligand.

Metal-directed synthesis routes to a 16-membered tetraazamacrocycle with two pendant primary amine groups

The reaction of the bis(propane-1,3-diamine)copper(II) ion with paraformaldehyde and nitroethane in dry methanol under basic conditions produces a macrocyclic product, (cis-3,11-dimethyl-3,11-dinitro-1,5,9,13-tetraazacyclohexadecane)copper(II) perchlorate, in low yield, compared with the good yield obtained in the parallel chemistry possible even under aqueous conditions using palladium(II) as a template. The palladium complex was reduced with zinc amalgam in dilute aqueous acid to yield the metal-free 16-membered macrocyclic hexaamine, in this case re-complexed and characterised by an X-ray crystal structure as the (cis-3,11-dimethyl-1,5,9,13-tetraazacyclohexadecane-3,11-diamine)copper(II) perchlorate. The copper ion is found in a tetragonally elongated and trigonally-distorted octahedral environment, with all six of the ligand nitrogens coordinated, the two primary amine pendant groups occupying cis sites. (C) 2000 Elsevier Science S.A. All rights reserved.

Mesoionic pyridopyrimidinylium and pyridooxazinylium olates and non-mesoionic pyridopyrimidinones. Structures in the solid state, solution, and matrices

X-Ray crystal structures, C-13 NMR spectra and theoretical calculations (B3LYP/6-31G*) are reported for the mesoionic (zwitterionic) pyridopyrimidinylium- and pyridooxazinyliumolates 2a, 3a and 5a,b as well as the enol ether 11b and the enamine 11c. The 1-NH compounds like 1a, 2a and 3a exist in the mesoionic form in the crystal and in solution, but the OH tautomers such as 1b and 2b dominate in the gas phase as revealed by the Ar matrix IR spectra in conjunction with DFT calculations. All data indicate that the mesoionic compounds can be regarded as intramolecular pyridine-ketene zwitterions (cf. 16 --> 17) with a high degree of positive charge on the pyridinium nitrogen, a long pyridinium N-CO bond (ca. 1.44-1.49 Angstrom), and normal C=O double bonds (ca. 1.22 Angstrom). All mesoionic compounds exhibit a pronounced tilting of the olate C=O groups (the C=O groups formally derived from a ketene) towards the pyridinium nitrogen, giving NCO angles of 110-118 degrees. Calculations reveal a hydrogen bond with 6-CH, analogous to what is found in ketene-pyridine zwitterions and the C3O2-pyridine complex. The 2-OH tautomers of type 1b, 2b, and 11 also show a high degree of zwitterionic character as indicated by the canonical structures 11 12.

Embracing ligands. A synthetic strategy towards new nitrogen-thioether multidentate ligands and characterization of the cobalt(III) complexes

The synthesis of the hexadentate ligand 2,2,9,9-tetra(methyleneamine)-4,7-dithiadecane (EtN(4)S(2)amp) is reported. The ligand is of a type in which bifurcations of the chain occur at atoms other than donor atoms. The cobalt(III) complex [Co(EtN(4)S(2)amp)](3+) (1) was isolated and characterized. The synthetic methodology also results in a number of by-products, notably 2,9,9-tris(methyleneamine)-9-methylenehydroxy-4,7-dithiadecane (Et(HO)N(3)S(2)amp) and an eleven-membered pendant arm macrocyclic ligand 6,10-dimethyl-6,10-bis(methyleneamine)-1,4-dithia-8-azaacycloundec-7- ene (dmatue). The complexes [Co(Et(HO)N(3)S(2)amp)](3+) (2), in which the alcohol is coordinated to the metal ion, and [Co(dmatue)Cl](2+) (4) were isolated and characterized. Et(HO)N(3)S(2)amp also undergoes complexation with cobalt(III) to produce two isomers endo-[Co(Et(HO) N(3)S(2)amp)Cl](2+) (endo-3) and exo-[Co(Et(HO) N(3)S(2)amp)Cl](2+) (exo-3), both with an uncoordinated alcohol group. endo- 3 has the alcohol positioned cis, and exo-3 trans, to the sixth metal coordination site. Reaction of 1 with isobutyraldehyde, paraformaldehyde and base in dimethylformamide results in the encapsulated complex [Co(1,5,5,9,13,13-hexamethyl-18,21-dithia-3,7,11,15-tetraazabicyclo[7.7.6]docosa- 3,14-diene)](ClO4)(3) . 2H(2)O ([Co(Me(6)docosadieneN(4)S(2))](3+) ( 5). All complexes have been characterized by single crystal X-ray study. The low-temperature (11 K) absorption spectrum of 1 has been measured in Nafion films with spin-allowed (1)A(1g) --> T-1(1g) and (1)A(1g) --> T-1(2g) and spin forbidden (1)A(1g) --> T-3(1g) and (1)A(1g) --> T-3(2g) bands observed. The octahedral ligand-field parameters were determined (10Dq = 22570 cm(-1), B = 551 cm(-1); C = 3500 cm(-1)). For 5 10Dq and B were determined (20580 cm(-1); 516 cm(-1), respectively) and compared with those for similar expanded cavity complexes [Co(Me(8)tricosatrieneN(6))](3+) and [Co(Me(5)tricosatrieneN(6))](3+).

Cyanocobalt(III) complexes of penta- and tetradentate-coordinated macrocyclic hexaamines

The pendent-arm macrocyclic hexaamine trans-6,13-dimethyl-1,4,8,11-tetraazacyclotetradecane-6,13-diamine (L) may coordinate in tetra-, penta- or hexadentate modes, depending on the metal ion and the synthetic procedure. We report here the crystal structures of two pseudo-octahedral cobalt(III) complexes of L, namely sodium trans-cyano(trans-6,13-dimethyl-1,4,8,11-tetraazacyclotetradecane-6,13-diamine)cobalt(III) triperchlorate, Na[Co(CN)(C13H30N6)](ClO4)(3) or Na{trans-[CoL(CN)]}(ClO4)(3), (I), where L is coordinated as a pentadentate ligand, and trans-dicyano(trans-6,13-dimethyl-1,4,8,11-tetraazacyclotetradecane-6,13-diamine) cobalt (III) trans-dicyano (trans-6,13-dimethyl-1,4,8,11-tetraazacyclotetradecane-6,13-diaminium)cobalt(III) tetraperchlorate tetrahydrate, [Co(CN)(2)(Cl4H32N6)][Co(CN)(2)(Cl4H30N6)](ClO4)(4)•-4H(2)O or trans-[CoL(CN)(2)]trans-[Co(H2L)(CN)(2)] (ClO4)(4)•-4H(2)O, (II), where the ligand binds in a tetradentate mode, with the remaining coordination sites being filled by C-bound cyano ligands. In (I), the secondary amine Co-N bond lengths lie within the range 1.944 (3)-1.969 (3) &ANGS;, while the trans influence of the cyano ligand lengthens the Co-N bond length of the coordinated primary amine [Co-N = 1.986 (3) &ANGS;]. The Co-CN bond length is 1.899 (3) &ANGS;. The complex cations in (11) are each located on centres of symmetry. The Co-N bond lengths in both cations are somewhat longer than in (I) and span a narrow range [1.972 (3)-1.982 (3) &ANGS;]. The two independent Co-CN bond lengths are similar [1.918 (4) and 1.926 (4) &ANGS;] but significantly longer than in the structure of (1), again a consequence of the trans influence of each cyano ligand.

A continuum model for periodic two-dimensional block structures

A continuum model for regular block structures is derived by replacing the difference quotients of the discrete equations by corresponding differential quotients. The homogenization procedure leads to an anisotropic Cosserat Continuum. For elastic block interactions the dispersion relations of the discrete and the continuous models are derived and compared. Yield criteria for block tilting and sliding are formulated. An extension of the theory for large deformation is proposed. (C) 1997 by John Wiley & Sons, Ltd.

Tris(ethylenediamine-N,N')zinc(II) dinitrate

The Zn-II atom in [Zn(C2H8N2)(3)](NO3)(2) has a distorted octahedral geometry of D-3 symmetry With three ethylenediamine bidentate Ligands completing the coordination.

Calcium potassium tris(oxalato-O-1, O-2)-chromate(III) pentahydrate

The Cr-III atom in CaK[Cr(C2O4)(3)].5H(2)O, has a regular octahedral geometry with three oxalato groups completing the coordination, Both the calcium and potassium cations are coordinated to the O atom of the oxalate group.