On the direct parallel solution of systems of linear equations: New algorithms and systolic structures

The paper presents two new algorithms for the direct parallel solution of systems of linear equations. The algorithms employ a novel recursive doubling technique to obtain solutions to an nth-order system in n steps with no more than 2n(n −1) processors. Comparing their performance with the Gaussian elimination algorithm (GE), we show that they are almost 100% faster than the latter. This speedup is achieved by dispensing with all the computation involved in the back-substitution phase of GE. It is also shown that the new algorithms exhibit error characteristics which are superior to GE. An n(n + 1) systolic array structure is proposed for the implementation of the new algorithms. We show that complete solutions can be obtained, through these single-phase solution methods, in 5n−log2n−4 computational steps, without the need for intermediate I/O operations.

Push-pull ethylenes: the structures of 3-(2-imidazolidinylidene)-2,4-pentanedione (I), C8H12N2O2, and 3-(1,3-dimethyl-2-imidazolidinylidene)-2,4-pentanedione trihydrate (II), C10H16N2O2.3H2O

(I): Mr= 168, triclinic, P1, Z=2, a= 5.596 (2), b = 6.938 (3), c = 10.852 (4) A, ~t= 75.64 (3), fl= 93.44 (3), ),= 95.47 (3) °, V= 406.0A 3, Din= 1.35 (by flotation using carbon tetrachloride and n-hexane), D x= 1.374 Mg m -3, g(Mo Kct, 2 = 0.7107 A) = 1.08 cm -l, _F(000) = 180, T= 293 K. (II): Mr= 250, triclinic, P1, Z= 2, a = 7.731(2), b=8.580(2), c=11.033(3)A, a= 97-66 (2), fl= 98.86 (2), y= 101.78 (2) °, V= 697.5 A 3, D m = 1.18 (by flotation using KI solution), Dx= 1.190Mgm -3, g(MoKa, 2=0.7107A)= 1.02 cm -1, F(000) = 272, T= 293 K. Both structures were solved by direct methods and refined to R = 4.4% for 901 reflexions for (I) and 5.7% for 2001 reflexions for (II). The C=C bond distances are 1.451 (3) A in (I) and 1.468 (3)A in (II), quite significantly longer than the C=C bond in ethylene [1.336 (2).~; Bartell, Roth, Hollowell, Kuchitsu & Young (1965). J. Chem. Phys. 42, 2683-2686]. The twist angle about the C=C bond in (II) is 72.9 (5) ° but molecule (I) is essentially planar, the twist angle being only 4.9 (5) ° .

The structures of the ammonium halides

A comparison with the alkali halides suggests that all the ammonium halides should occur in the NaCl centre-of-mass structure. Experimentally, at room temperature and atmospheric pressure, only NH4I crystallizes in this structure, while NH4F is found in the ZnO structure, and NH4C1 and NH4Br occur in the CsCl structure. We show that a distributed charge on the NH4+ ion can explain these structures. Taking charges of + 0.2e on each of the five atoms in NH4+, as suggested by other studies, we have recomputed the Madelung energy in the cases of interest. A full ionic theory including electrostatic, van der Waals and repulsive interactions then explains the centre-of-mass structures of all the four ammonium halides. The thermal and pressure transitions are also explained reasonably well. The calculated phase diagram of NH4F compares well with experiment. Barring the poorly understood NH4F(II) phase, which is beyond the scope of this work, the other features are in qualitative agreement. In particular, the theory correctly predicts a pressure transition at room temperature from the ZnO structure directly to the CsCl structure without an intermediate NaCl phase. A feature of our approach is that we do not need to invoke hydrogen bonding in NH4F.

X-ray Studies on Crystalline Complexes Involving Amino Acids and Peptides. XIII. Effect of Chirality on Molecular Aggregation: The Crystal Structures of L-Arginine D-Aspartate and L-Arginine D-Glutamate Trihydrate

The crystal structures of (1) L-arginine D-asparate, C6HIsN40~.C4H6NO4 [triclinic, P1, a=5.239(1), b=9.544(1), c=14.064(2)A, a=85"58(1), /3=88.73 (1), ~/=84.35 (1) °, Z=2] and (2) L-arginine D-glutamate trihydrate, C6H15N40~-.CsHsNO4.3H20 [monoclinic, P2~, a=9.968(2), b=4.652(1), c=19.930 (2) A, fl = 101.20 (1) °, Z = 2] have been determined using direct methods. They have been refined to R =0.042 and 0.048 for 2829 and 2035 unique reflections respectively [I>2cr(I)]. The conformations of the two arginine molecules in the aspartate complex are different from those observed so far in the crystal structures of arginine, its salts and complexes. In both complexes, the molecules are organized into double layers stacked along the longest axis. The core of each double layer consists of two parallel sheets made up of main-chain atoms, each involving both types of molecules. The hydrogen bonds within each sheet and those that interconnect the two sheets give rise to EL-, DD- and DE-type head-to-tail sequences. Adjacent double layers in (1) are held together by side-chain-side-chain interactions whereas those in (2) are interconnected through an extensive network of water molecules which interact with sidechain guanidyl and carboxylate groups. The aggregation pattern observed in the two LD complexes is fundamentally different from that found in the corresponding EL complexes.

Conformations Of Peptides Containing 1-Aminocyclohexane-Carboxylic Acid (Acc6) - Crystal-Structures Of 2 Model Peptides

The crystal structures of two peptides containing 1-aminocyclohexanecarboxylic acid (Acc6) are described. Boc-Aib-Acc6-NHMe · H2O adopts a β-turn conformation in the solid state, stabilized by an intramolecular 4 → 1 hydrogen bond between the Boc CO and methylamide NH groups. The backbone conformational angles (φAib = – 50.3°, ψAib = – 45.8°; φAcc6 = – 68.4°, ψAcc6 = – 15°) lie in between the values expected for ideal Type I or III β-turns. In Boc-Aib-Acc6-OMe, the Aib residue adopts a partially extended conformation (φAib = – 62.2°, ψAib = 143°) while the Acc6residue maintains a helical conformation (φAcc6 = 48°, ψAcc6= 42.6°). 1H n.m.r. studies in CDCl3 and (CD3)2SO suggest that Boc-Aib-Acc6-NHMe maintains the β-turn conformation in solution.

Ultrasonic attenuation in strongly disordered electronic systems

The attenuation of long-wavelength phonons due to their interaction with electronic excitations in disordered systems is investigated here. Lattice strain couples to electronic stress, and thus ultrasonic attenuation measures electronic viscosity. The enhancement and critical divergence of electronic viscosity due to localization effects is calculated for the first time. Experimental consequences for the anomalous increase of ultrasonic attenuation in disordered metals close to the metal-insulator transition are discussed. In the localized regime, the appropriate model is one of electronic two-level systems (TLS’s) coupled to phonons. The TLS consists of a pair of states with one localized state occupied and the other unoccupied. The density of such low-excitation-energy TLS’s is nonzero due to long-range Coulomb interactions. The question of whether these could be significant low-energy excitations in glasses is touched upon.

Large cryptic internal sequence repeats in protein structures from Homo sapiens

Amino acid sequences are known to constantly mutate and diverge unless there is a limiting condition that makes such a change deleterious. However, closer examination of the sequence and structure reveals that a few large, cryptic repeats are nevertheless sequentially conserved. This leads to the question of why only certain repeats are conserved at the sequence level. It would be interesting to find out if these sequences maintain their conservation at the three-dimensional structure level. They can play an active role in protein and nucleotide stability, thus not only ensring proper functioning but also potentiating malfunction and disease. Therefore, insights into any aspect of the repeats - be it structure, function or evolution - would prove to be of some importance. This study aims to address the relationship between protein sequence and its three-dimensional structure, by examining if large cryptic sequence repeats have the same structure.

Solid-State Acyl Migration In Salicylamides - An X-Ray Study Of The Ortho-Propionyl And Normal-Propionyl Derivatives

In recent years there has been an upsurge of interest in the study of organic reactions in the solid state. It is now realised that the crystalline matrix provides an extra-ordinary spatial control on the initiation and progress of these reactions. Electronic and dipolar effects which are important in solution are replaced by structural and geometric effects in solids. These 'spatial' or 'topochemical' aspects are important in understanding the mechanistic details of the reaction. In our laboratory, the thermally induced acyl migration in salicylamides from 0- to N- position in the solid state has been under study (Scheme 1). The structures of the acetyl and benzoyl derivatives (Ia,IIa, Ib and IIb) have been reported.

Thermally Induced Acyl Migration in Salicylamides. 1. Structures of the Reactants, O-Acetylsalicylamide and O-Benzoylsalicylamide

O-Acetylsalicylamide (Ia), C9H9NO3, M r =179.18, monoclinic, P2Jc, a=8.155(5), b=8.571 (2), c= 13.092 (3)A, fl=99.54 (5) ° , V= 902.4(6)A 3, Z=4, Dm=l.31, Dx=l.319gcm -3, 2(Mo Ka) = 0.71069 A,/~ = 1.08 cm -1, F(000) = 376, T = 295 K, R = 0.076 for 1604 reflections. O-Benzoylsalicylamide (Ib), C14HtlNO 3, M,=241.2, monoclinic, P2t/e, a=9.423(1), b=5.116(1), e= 26.424 (2) A, fl= 103.97 (1)% V= 1236.2 (3)/~3, Z= 4, D~ = 1.28, D x = 1.296 gcm -3, ,;L(Cu Ks) = 1.5418 A, p = 7.71 cm-', F(000) = 504, T= 295 K, R =0.050 for 2115 reflections. The dihedral angles between the amide group and the benzene ring are 39.9 ° (Ia) and 37.9 ° (Ib), whereas between the acyl group and the benzene ring they are 78.1 ° (Ia) and 93.4 ° (Ib). The differences in the packing of the two structures are brought out in terms of the observed hydrogen-bonding patterns. Based on the crystallographic results, an intramolecular mechanism for the migration of the acyl group from the O to the N position is suggested in both compounds.

Photochemical Oxidation of Thioketones: Steric and Electronic Aspects

Oxidation of diaryl, aryl alkyl, and dialkyl thioketones by singlet oxygen generated via self-sensitization and other independent methods yielded the corresponding ketone and sulfine in varying amounts. A zwitterionic/ diradical intermediate arising out of the primary interaction of singlet oxygen with the thiocarbonyl chromophore is believed to be the common intermediate for the ketone and sulfine. While closure of the zwitterion/diradical to give 1,2,3-dioxathietane would lead to the ketone, competing oxygen elimination is believed to lead to the sulfine. This partitioning is governed by steric and electronic factors operating on the zwitterionic/diradical intermediate.

The structures of the ammonium halides

A comparison with the alkali halides suggests that all the ammonium halides should occur in the NaCl centre-of-mass structure. Experimentally, at room temperature and atmospheric pressure, only NH,1 crystallizes in this structure, while NH,F is found in the ZnO structure, and NH&I and NH,Br occur in the CsCl structure. We show that a distributed charge on the NH,+ ion can explain these structures. Taking charges of + 0.2e on each of the five atoms in NH,+, as suggested by other studies, we have recomputed the Madelung energy in the cases of interest. A full ionic theory including electrostatic, van der Waals and repulsive interactions then explains the centre-of-mass structures of all the four ammonium halides. The thermal and pressure transitions are also explained reasonably well. The calculated phase diagram of NH,F compares well with experiment. Barring the poorly understood NH,F(II) phase, which is beyond the scope of this work, the other features are in qualitative agreement. In particular, the theory correctly predicts a pressure transition at room temperature from the ZnO structure directly to the CsCl structure without an intermediate NaCl phase. A feature of our approach is that we do not need to invoke hydrogen bonding in NH,F.

Quantum behaved Particle Swarm Optimization (QPSO) for multi-objective design optimization of composite structures

We present a new, generic method/model for multi-objective design optimization of laminated composite components using a novel multi-objective optimization algorithm developed on the basis of the Quantum behaved Particle Swarm Optimization (QPSO) paradigm. QPSO is a co-variant of the popular Particle Swarm Optimization (PSO) and has been developed and implemented successfully for the multi-objective design optimization of composites. The problem is formulated with multiple objectives of minimizing weight and the total cost of the composite component to achieve a specified strength. The primary optimization variables are - the number of layers, its stacking sequence (the orientation of the layers) and thickness of each layer. The classical lamination theory is utilized to determine the stresses in the component and the design is evaluated based on three failure criteria; Failure Mechanism based Failure criteria, Maximum stress failure criteria and the Tsai-Wu Failure criteria. The optimization method is validated for a number of different loading configurations - uniaxial, biaxial and bending loads. The design optimization has been carried for both variable stacking sequences as well as fixed standard stacking schemes and a comparative study of the different design configurations evolved has been presented. Also, the performance of QPSO is compared with the conventional PSO.

Structures of mannose-6-phosphate isomerase from Salmonella typhimurium bound to metal atoms and substrate: implications for catalytic mechanism

Mannose-6-phosphate isomerase (MPI) catalyzes the inter-conversion of mannose 6-phosphate and fructose 6-phosphate. X-ray crystal structures of MPI from Salmonella typhimurium in the apo form (with no metal bound) and in the holo form (with bound Zn2+) and two other structures with yttrium bound at an inhibitory site and complexed with Zn2+ and fructose 6-phosphate (F6P) were determined in order to gain insights into the structure and the isomerization mechanism. Isomerization involves acid/base catalysis with proton transfer between the C1 and C2 atoms of the substrate. His99, Lys132, His131 and Asp270 are close to the substrate and are likely to be the residues involved in proton transfer. The interactions observed at the active site suggest that the ring-opening step is probably catalyzed by His99 and Asp270. An active-site loop consisting of residues 130-133 undergoes conformational changes upon substrate binding. Zn2+ binding induces structural order in the loop consisting of residues 50-54. The metal atom appears to play a role in substrate binding and is probably also important for maintaining the architecture of the active site. Isomerization probably follows the previously suggested cis-enediol mechanism.

Photochemical oxidation of thio ketones: steric and electronic aspects

Oxidation of diaryl, aryl alkyl, and dialkyl thioketones by singlet oxygen generated via self-sensitization and other independent methods yielded the corresponding ketone and sulfine in varying amounts. A zwitterionic/ diradical intermediate arising out of the primary interaction of singlet oxygen with the thiocarbonyl chromophore is believed to be the common intermediate for the ketone and sulfine. While closure of the zwitterion/diradical to give 1,2,3-dioxathietane would lead to the ketone, competing oxygen elimination is believed to lead to the sulfine. This partitioning is governed by steric and electronic factors operating on the zwitterionic/diradical intermediate.

A Pulsewidth Modulated Control of Induction Motor Drive Using Multilevel 12-Sided Polygonal Voltage Space Vectors

In this paper, a novel 12-sided polygonal space vector structure is proposed for an induction motor drive. The space vector pattern presented in this paper consists of two 12-sided concentric polygons with the outer polygon having a radius double the inner one. As compared to previously reported 12-sided polygonal space vector structures, this paper subdivides the space vector plane into smaller sized triangles. This helps in reducing the switching frequency of the inverters without deteriorating the output voltage quality. It also reduces the device ratings and dv/dt stress on the devices to half. At the same time, other benefits obtained from the existing 12-sided space vector structure, such as increased linear modulation range and complete elimination of 5th and 7th order harmonics in the phase voltage, are also retained in this paper. The space vector structure is realized by feeding an open-end induction motor with two conventional three-level neutral point clamped (NPC) inverters with asymmetric isolated dc link voltage sources. The neutral point voltage fluctuations in the three-level NPC inverters are eliminated by utilizing the switching state multiplicities for a space vector point. The pulsewidth modulation timings are calculated using sampled reference waveform amplitudes and are explained in detail in this paper. Experimental verification on a laboratory prototype shows that this configuration may be considered suitable for high power drives.