An eigenproblem approach to classical screw theory

This paper presents a novel algebraic formulation of the central problem of screw theory, namely the determination of the principal screws of a given system. Using the algebra of dual numbers, it shows that the principal screws can be determined via the solution of a generalised eigenproblem of two real, symmetric matrices. This approach allows the study of the principal screws of the general two-, three-systems associated with a manipulator of arbitrary geometry in terms of closed-form expressions of its architecture and configuration parameters. We also present novel methods for the determination of the principal screws for four-, five-systems which do not require the explicit computation of the reciprocal systems. Principal screws of the systems of different orders are identified from one uniform criterion, namely that the pitches of the principal screws are the extreme values of the pitch.The classical results of screw theory, namely the equations for the cylindroid and the pitch-hyperboloid associated with the two-and three-systems, respectively have been derived within the proposed framework. Algebraic conditions have been derived for some of the special screw systems. The formulation is also illustrated with several examples including two spatial manipulators of serial and parallel architecture, respectively.

Interrelations of micro-organisms and mulberry II. Phyllosphere microflora and nitrogen fixation in leaf and root surfaces

The mulberry leaves were shown to harbour substantial populations of bacteria, streptomycetes, yeasts, and moulds. Azotobacter and Beijerinckia were observed to contribute to nearly 5 to 10 per cent of the bacterial population. When grown in water culture under sterile conditions, Azotobacter inoculation on the leaf or root surface was found to increase plant growth, dry wt, and nitrogen content of the mulberry. The beneficial effect of Azotobacter was largely influenced by the presence of a carbon source in the plant nutrient solution. The root inoculation in comparison to leaf application was found to confer greater benefits to the growing plant. The presence of carbohydrates and amino acids in the leaf leachates of mulberry was shown. The mutual beneficial nature of the association of the plant and Azotobacter has been brought to light.

Metabolism of Plasmodium bergheistar, open: III. Carbon dioxide fixation and role of pyruvate and dicarboxylic acids

Formation of C4 dicarboxylic acids in Plasmodium berghei by carbon dioxide fixation reaction has been demonstrated by the use of labeled NaH14CO3. The reactions require glucose, which may be required not only as an energy source but also to contribute to the formation of pyruvate in the process of carbon dioxide fixation. Intracellular concentration of pyruvate may play an important role in the metabolism of P. berghei; an increased intracellular level of pyruvate seems to be a prerequisite before some of these reactions could be detected. The distribution of the label indicates extensive randomization of amino acids and suggests an extensive cycling of the amino acid and organic acid pools of the parasites. This investigation formed part of the thesis submitted in 1965 for the doctoral degree at the Indian Institute of Science, Bangalore 12, India, and was supported in part by the Council of Scientific and Industrial Research, India.

Screw dynamo and the generation of nonaxisymmetric magnetic fields

A mechanism is presented here for the amplification of large-scale nonaxisymmetric magnetic fields as a manifestation of the dynamo effect. We generalize a result on restrictions of dynamo actions due to laminar flow originally derived by Zeldovich, Ruzmaikin, and Sokolov [Magnetic Fields in Astrophysics (Gordon and Breach, New York, 1983)]. We show how a screwlike motion having phi and z components of velocity can help to grow a magnetic field. This model postulates a large-scale flow having phi and z components with radial dependences (helical flow). Shear in the radial field, because of a near-flux-freezing condition, causes amplification of the phi component of the magnetic field. The radial and axial components grow due to the presence of turbulent diffusion. The shear in the large scale flow induces an indefinite growth of magnetic field without the a effect; nevertheless, turbulent diffusion forms an important part in the overall mechanism.

Classical screw theory: A fresh look using dual eigenvalue approach

This paper presents a novel algebraic formulation of the central problem of screw theory, namely the determination of the principal screws of a given system. Using the algebra of dual numbers, it shows that the principal screws can be determined via the solution of a generalised eigenproblem of two real, symmetric matrices. This approach allows the study of the principal screws of the general screw systems associated with a manipulator of arbitrary geometry in terms of closed-form expressions of its architecture and configuration parameters. The formulation is illustrated with examples of practical manipulators.

Application of a modified jogged-screw model for creep of titanium aluminides: evaluation of the key substructural parameters

A modification of the jogged-screw model has been adopted recently by the authors to explain observations of 1/2[110]-type jogged-screw dislocations in equiaxed Ti-48Al under creep conditions. The aim of this study has been to verify and validate the parameters and functional dependencies that have been assumed in this previous work. The original solution has been reformulated to take into account the finite length of the moving jog. This is a better approximation of the tall jog. The substructural model parameters have been further investigated in light of the Finite Length Moving Line (FLML) source approximation. The original model assumes that the critical jog height (beyond which the jog is not dragged) is inversely proportional to the applied stress. By accounting for the fact that there are three competing mechanisms (jog dragging, dipole dragging, dipole bypass) possible, we can arrive at a modified critical jog height. The critical jog height was found to be more strongly stress dependent than assumed previously. The original model assumes the jog spacing to be invariant over the stress range. However, dynamic simulation using a line tension model has shown that the jog spacing is inversely proportional to the applied stress. This has also been confirmed by TEM measurements of jog spacings over a range of stresses. Taylor's expression assumed previously to provide the dependence of dislocation density on the applied stress, has now been confirmed by actual dislocation density measurements. Combining all of these parameters and dependencies, derived both from experiment and theory, leads to an excellent prediction of creep rates and stress exponents. The further application of this model to other materials, and the important role of atomistic and dislocation dynamics simulations in its continued development is also discussed.

Structure of 5-Bromo-2',3'-O-isopropylideneuridine, C12H15BrN206

Mr= 363.17, orthorhombic, P21212 ~, a= 5.251(4), b=14.962(5), c=19.112(5)A, U= 1501.41/k 3, Z=4, Dx=1.61Mgm -3, /t(CuKa)= 3.02 mm -1, 2(Cu Ka)= 1.5418/~, final R = 7.0% for 1091 reflections with Fo> 2e(Fo). The glycosidic torsion angle ZCN is 13"1 (12) °. The ribose has a C (3')-exo,C (4)-endo twist geometry. The dioxolane ring assumes an envelope conformation with 0(3') displaced by 0.453 (10)/k from the plane of the other four atoms. The conformation about the C(4')-C(5') bond is gauche-gauche. The structure is stabilized by two hydrogen bonds between screw-axis-related molecules. The crystal packing and the conformation of the molecule are very similar to those found in the structure of 2',3'-O-isopropylideneuridine which lacks the Br atom at the 5-position.

Structure of 2',3'-O-Isopropylidene-5'-O-tosyluridine, C19H22N 2Oas

M r = 438.45, trigonal, P32, a = b = 13.385 (4), c = 9.900 (5) A,, V = 1536.0 A 3, Z = 3, D x = 1.42, D m = 1.42 Mg m -3, 2(Cu Ka) = 1.5418 A,,g(CuKa) = .800mm -], T=290K, F(000)=690, R=6.0% for 1222 unique reflections with F o>_2o(Fo). This is the first 2',3'-O-isopropylidene pyrimidine nucleoside with the base in a syn orientation with respect to the ribose [Xcy= 116.0(7)°]. The ribose has a C(3')-endo conformation with the phase angle of pseudorotation P = 16.36 (2) °. The dioxolane ring assumes an envelope conformation with 0(2') displaced from the best four-atom plane by 0.50 (1) k. The crystal structure is possibly stabilized by a bifurcated hydrogen bond between N(3) and the 0(2) and 0(4) atoms of screw-related molecules.

Evolution of cooperation by reciprocation within structured demes

The iterative two-person Prisoners’ Dilemma game has been generalised to theN-person case. The evolution of cooperation is explored by matching the Tit For Tat (TFT) strategy (Axelrod and Hamilton 1981) against the selfish strategy. Extension of TFT toN-person situations yields a graded set of strategies from the softest TFT, which continues cooperation even if only one of the opponents reciprocates it, to the hardest, which would do so only when all the remaining opponents cooperate. The hardest TFT can go to fixation against the selfish strategy provided it crosses a threshold frequencypc. All the other TFT are invadable by the selfish (D) or the pure defector strategy, while none can invadeD. Yet, provided a thresholdpc is crossed, they can coexist stably withD. AsN, the size of the group increases, the threshold pc also increases, indicating that the evolution of cooperation is more difficult for larger groups. Under certain conditions, only the soft TFT can coexist stably against the selfish strategyD, while the harder ones cannot. An interesting possibility of a complete takeover of the selfish population by successive invasions by harder and harder TFT strategies is also presented.

N-Acetylglycyl-L-lysine methyl ester acetate

C llH22 N 30 + . C2H302, orthorhombic, P2~2~2~, a = 5.511(2), b = 14.588(4), c = 21.109 (4)A, Z = 4. The structure has been solved using MULTAN and refined to R = 0.079 for 993 observed reflections. The fully extended lysine side chain in the molecule is staggered between the main-chain amino and carbonyl groups. The dipeptide molecules in the crystal structure are arranged in twofold helices centred on 21 screw axes. These helices are interconnected through interactions involving the acetate and the side-chain amino groups. Each acetate group bridges two adjacent side-chain amino groups, related by an a translation, giving rise to an infinitely long chain of alternating negatively charged carboxylate and positively charged amino groups.

Proton NMR spectra including 13C- and 77Se-satellites in organoselenium compounds oriented in the nematic phase : Part 1. The spectrum of 2,1,3-benzoselenadiazole

The vibrationally corrected structure of 2,1,3-benzoselenadiazole is derived from the proton NMR spectrum including 13C-H and 77Se-H satellites, in a nematic solvent. The results indicate considerable bond-fixation in the 6-membered ring. References

N-Acetylglycyl-L-lysine methyl ester acetate

C llH22 N 30 + . C2H302, orthorhombic, P2~2~2~, a = 5.511(2), b = 14.588(4), c = 21.109 (4)A, Z = 4. The structure has been solved using MULTAN and refined to R = 0.079 for 993 observed reflections. The fully extended lysine side chain in the molecule is staggered between the main-chain amino and carbonyl groups. The dipeptide molecules in the crystal structure are arranged in twofold helices centred on 21 screw axes. These helices are interconnected through interactions involving the acetate and the side-chain amino groups. Each acetate group bridges two adjacent side-chain amino groups, related by an a translation, giving rise to an infinitely long chain of alternating negatively charged carboxylate and positively charged amino groups.

Nitrogenase activity (acetylene reduction) associated with leaves of different cultivars of paddy

An investigation was conducted to study the levels of nitrogen fixation on the leaf or sheath surfaces of four cultivars of paddy plants by using acetylene reduction technique. Varying levels of positive nitrogenase activity were observed on all the leaf surfaces. Sheath of IET 1991 cultivar showed a higher rate of fixation than the leaf surface. All the nitrogen-fixing organisms on the leaf or sheath surfaces belonged to the genus Beijerinckia. There was no correlation between the bacterial density and the level of fixation. Scanning electron microscopic data revealed that the upper surface of IET 1991 leaf was highly silicified and the microflora was either scanty or nil while the lower surface appeared quite different and harboured more micro-organisms. Similarly, the inner surface of sheath was devoid of silicification and showed the presence of micro-organisms.

Nitrogenase activity (acetylene reduction) associated with leaves of different cultivars of paddy (Oryza sativa L.)

An investigation was conducted to study the levels of nitrogen fixation on the leaf or sheath surfaces of four cultivars of paddy plants by using acetylene reduction technique. Varying levels of positive nitrogenase activity were observed on all the leaf surfaces. Sheath of IET 1991 cultivar showed a higher rate of fixation than the leaf surface. All the nitrogen-fixing organisms on the leaf or sheath surfaces belonged to the genus Beijerinckia. There was no correlation between the bacterial density and the level of fixation. Scanning electron microscopic data revealed that the upper surface of IET 1991 leaf was highly silicified and the microflora was either scanty or nil while the lower surface appeared quite different and harboured more micro-organisms. Similarly, the inner surface of sheath was devoid of silicification and showed the presence of micro-organisms.