Efficient QR Decomposition Using Low Complexity Column-wise Givens Rotation (CGR)

QR decomposition (QRD) is a widely used Numerical Linear Algebra (NLA) kernel with applications ranging from SONAR beamforming to wireless MIMO receivers. In this paper, we propose a novel Givens Rotation (GR) based QRD (GR QRD) where we reduce the computational complexity of GR and exploit higher degree of parallelism. This low complexity Column-wise GR (CGR) can annihilate multiple elements of a column of a matrix simultaneously. The algorithm is first realized on a Two-Dimensional (2 D) systolic array and then implemented on REDEFINE which is a Coarse Grained run-time Reconfigurable Architecture (CGRA). We benchmark the proposed implementation against state-of-the-art implementations to report better throughput, convergence and scalability.

Conformational Stability and Intramolecular Hydrogen Bonding in 1,2-Ethanediol and 1,4-Butanediol

The gas-phase infrared spectra of 1,2-ED and 1,4-BD have been, recorded at three different temperatures using a multipass gas cell of 6 m optical path length. DFT calculation has also been carried out using 6-311++G** and aug-cc-pVDZ basis sets to look for the existence of intramolecular hydrogen bonding, in them from the red shift and infrared absorption intensity enhancement of the bonded O-H band compared to that of the free O-H hand. Equilibrium population analysis With 10 conformers of 1,2-ED and 1,4-BD at experimental temperatures were-carried out for the reconstruction of the Observed vibrational spectra at that temperature,using standard statistical relationships. The most abundant conformer at experimental temperatures, was identified. In 1,2-ED a red shift of 45 cm(-1) in the intramolecularly interacting O-H stretching vibrational band position and no significant intensity enhancement compared to that of-the free O-H have been observed. On the contrary, in one of the hydrogen bonded conformers of 1,4-BD, a 124 cm(-1) red shift in the O-H stretching frequency and 8.5 times-intensity enhancement for the ``bonded'' O-H compared to that of the ``free'' O-H is seen. On the basis of this comparative study, we have concluded that strong intramolecular hydrogen bonding exists in 1,4-BD. But there appears, to be weak intramolecular hydrogen bonding in 1,2-ED at temperatures of 303, 313, and 323 Km the gas phase We have found that most stable hydrogen-bonded conformers of 1,4-BD are less populated than some of the non-hydrogen-bonded conformers. Even for the 1,4-BD, the relative population of the g'GG'Gt conformer, which has a strong intramolecular,hydrogen bond, is less than what is predicted. Perhaps the intramolecular hydrogen bond plays a less Significant role in the relative stability,of the various Conformers than what has been predicted from calculations and prevails in the literature.

``Conformational Simulation'' of Sulfamethizole by Molecular Complexation and Insights from Charge Density Analysis: Role of Intramolecular S center dot center dot center dot O Chalcogen Bonding

Intramolecular S center dot center dot center dot O chalcogen bonding and its potential to lock molecular conformation have been examined in the crystal forms of sulfamethizole, a sulfonamide antibiotic. Molecular complexes of sulfamethizole, including salts and cocrystal, have been synthesized, and their crystal structures were analyzed in order to examine the possible conformational preferences of the molecule in various ionic states and supramolecular environments (neutral/cocrystal, anionic salt, and cationic salt forms). The electrostatic potential mapped on Hirshfeld surfaces generated for these crystal forms provides insights into the possible binding modes of the drug in different environments. Further, the observed conformation locking feature has been rationalized in terms of the experimental charge density features of the intramolecular S center dot center dot O chalcogen bonding in sulfamethizole. The study quantitatively illustrates and rationalizes an intriguing case of a local minimum of molecular conformation being exclusively preferred over the global minimum, as it facilitates more efficient intermolecular interactions in a supramolecular environment.

Intramolecular hydrogen bonds involving organic fluorine in the derivatives of hydrazides: an NMR investigation substantiated by DFT based theoretical calculations

The rare examples of intramolecular hydrogen bonds (HB) of the type the N-H center dot center dot center dot F-C, detected in a low polarity solvent in the derivatives of hydrazides, by utilizing one and two-dimensional solution state multinuclear NMR techniques, are reported. The observation of through-space couplings, such as, (1h)J(FH), and (1h)J(FN), provides direct evidence for the existence of intra-molecular HB. Solvent induced perturbations and the variable temperature NMR experiments unambiguously establish the presence of intramolecular HB. The existence of multiple conformers in some of the investigated molecules is also revealed by two dimensional HOESY and N-15-H-1 HSQC experiments. The H-1 DOSY experimental results discard any possibility of self or cross dimerization of the molecules. The derived NMR experimental results are further substantiated by Density Function Theory (DFT) based Non Covalent Interaction (NCI), and Quantum Theory of Atom in Molecule (QTAIM) calculations. The NCI calculations served as a very sensitive tool for detection of non-covalent interactions and also confirm the presence of bifurcated HBs.

Intramolecular hydrogen bond: Can it be part of the basis set of valence internal coordinates in normal mode analysis?

It has been shown earlier1] that the relaxed force constants (RFCs) could be used as a measure of bond strength only when the bonds form a part of the complete valence internal coordinates (VIC) basis. However, if the bond is not a part of the complete VIC basis, its RFC is not necessarily a measure of bond strength. Sometimes, it is possible to have a complete VIC basis that does not contain the intramolecular hydrogen bond (IMHB) as part of the basis. This means the RFC of IMHB is not necessarily a measure of bond strength. However, we know that IMHB is a weak bond and hence its RFC has to be a measure of bond strength. We resolve this problem of IMHB not being part of the complete basis by postulating `equivalent' basis sets where IMHB is part of the basis at least in one of the equivalent sets of VIC. As long as a given IMHB appears in one of the equivalent complete VIC basis sets, its RFC could be used as a measure of bond strength parameter.

Partial rotation of the isopropyl group in the solid state: single-crystal-to-single-crystal phase transformation in a carvacrol derivative

A hitherto unseen rotation of the isopropyl group in the solid state, predicted to be forbidden based on theoretical investigations, is reported. This C-C rotation observed during the temperature dependent single-crystal-to-single-crystal transformation is attributed to the concomitant changes in molecular structure and intermolecular packing.

Organic fluorine involved intramolecular hydrogen bonds in the derivatives of imides: NMR evidence corroborated by DFT based theoretical calculations

The rare occurrence of intramolecular hydrogen bonds (HBs) of the type N-H center dot center dot center dot F-C is detected in the derivatives of imides in a low polarity solvent by using multi-dimensional and multinuclear NMR experiments. The observation of (1h)J(FH), (2h)J(FN), and (2h)J(FF), where the spin magnetization is transmitted through space among the interacting NMR active nuclei, provided strong and unambiguous evidence for the existence of intra-molecular HBs. The variation in the chemical shifts of labile protons depending on physical conditions, such as the solvent dilution and the systematic alteration of temperature confirmed the presence of weak interactions through intramolecular HBs in all the investigated fluorine substituted molecules. The self or cross dimerization of molecules is unequivocally discarded by the analysis of the rates of diffusion obtained using pseudo-two dimensional DOSY experiments. The Density Function Theory (DFT) calculations based on the Quantum Theory of Atoms In Molecules (QTAIM) and Non Covalent Interaction (NCI), are in close agreement with the NMR experimental findings.

Gold catalyzed intramolecular hydroalkoxylation assisted ring opening of furans to the corresponding saturated gamma-keto esters

A facile ring opening of furans in furyl propargyl alcohols to the corresponding saturated gamma-keto esters is observed in the gold(III) chloride catalyzed reaction with MeOH. It is found that the ring opening of furan is driven by the intramolecular hydroalkoxylation. Mitigating the intramolecular hydroalkoxylation led to the expected conjugated enyne resulting from the dehydration. (C) 2015 Elsevier Ltd. All rights reserved.

Study of H/D exchange rates to derive the strength of intramolecular hydrogen bonds in halo substituted organic building blocks: An NMR spectroscopic investigation

Rates of hydrogen/deuterium (H/D) exchange determined by H-1 NMR spectroscopy are utilized to derive the strength of hydrogen bonds and to monitor the electronic effects in the site-specific halogen substituted benzamides and anilines. The theoretical fitting of the time dependent variation of the integral areas of H-1 NMR resonances to the first order decay function permitted the determination of HID exchange rate constants (k) and their precise half-lives (t(1/2)) with high degree of reproducibility. The comparative study also permitted the unambiguous determination of relative strength of hydrogen bonds and the contribution from electronic effects on the HID exchange rate. (C) 2015 Elsevier B.V. All rights reserved.

Rotation Numbers Of Invariant Manifolds Around Unstable Periodic Orbits For The Diamagnetic Kepler Problem

In this paper, a method to construct topological template in terms of symbolic dynamics for the diamagnetic Kepler problem is proposed. To confirm the topological template, rotation numbers of invariant manifolds around unstable periodic orbits in a phase space are taken as an object of comparison. The rotation numbers are determined from the definition and connected with symbolic sequences encoding the periodic orbits in a reduced Poincare section. Only symbolic codes with inverse ordering in the forward mapping can contribute to the rotation of invariant manifolds around the periodic orbits. By using symbolic ordering, the reduced Poincare section is constricted along stable manifolds and a topological template, which preserves the ordering of forward sequences and can be used to extract the rotation numbers, is established. The rotation numbers computed from the topological template are the same as those computed from their original definition.

Distribution, stability, bifurcations and catastrophe of steady rotation of a symmetrical heavy gyroscope with viscous-liquid-filled cavity

The number, the angles of orientation and the stability in Rumyantsev Movchan's sense of oblique steady rotations of a symmetric heavy gyroscope with a cavity completely filled with a uniform viscous liquid, possessing a fixed point 0 on its symmetric axis. are given for various values of the parameters. By taking the square of the upright component of the angular momentum M2 as a control parameter, three types of bifurcation diagrams of the steady rotations, two types of jumps and two kinds of local catastrophes, one being the symmetric reduced cusp type and the other being of the symmetric reduced butterfly type, are obtained. By taking account of the M2-damping owing to the moment of unavoidable faint friction, two different modes for the gyroscope, initially in a stable quasi-steady upright rotation with a nutation angle theta(s) equal to zero, to topple over are found.