Ultraspherical polynomials approach to the study of third-order non-linear systems

In this study, the Krylov-Bogoliubov-Mitropolskii-Popov asymptotic method is used to determine the transient response of third-order non-linear systems. Instead of averaging the non-linear functions over a cycle, they are expanded in ultraspherical polynomials and the constant term is retained. The resulting equations are solved to obtain the approximate solution. A numerical example is considered and the approximate solution is compared with the digital solution. The results show that there is good agreement between the two values.

Study of third-order non-linear systems- Variation of parameters approach

In this paper, the transient response of a third-order non-linear system is obtained by first reducing the given third-order equation to three first-order equations by applying the method of variation of parameters. On the assumption that the variations of amplitude and phase are small, the functions are expanded in ultraspherical polynomials. The expansion is restricted to the constant term. The resulting equations are solved to obtain the response of the given third-order system. A numerical example is considered to illustrate the method. The results show that the agreement between the approximate and digital solution is good thus vindicating the approximation.

Second-order statistical structure of geomagnetic field reversals

From the autocorrelation function of geomagnetic polarity intervals, it is shown that the field reversal intervals are not independent but form a process akin to the Markov process, where the random input to the model is itself a moving average process. The input to the moving average model is, however, an independent Gaussian random sequence. All the parameters in this model of the geomagnetic field reversal have been estimated. In physical terms this model implies that the mechanism of reversal possesses a memory.

Application of Laplace transform technique to the solution of certain third-order non-linear systems

A number of papers have appeared on the application of operational methods and in particular the Laplace transform to problems concerning non-linear systems of one kind or other. This, however, has met with only partial success in solving a class of non-linear problems as each approach has some limitations and drawbacks. In this study the approach of Baycura has been extended to certain third-order non-linear systems subjected to non-periodic excitations, as this approximate method combines the advantages of engineering accuracy with ease of application to such problems. Under non-periodic excitations the method provides a procedure for estimating quickly the maximum response amplitude, which is important from the point of view of a designer. Limitations of such a procedure are brought out and the method is illustrated by an example taken from a physical situation.

Kinetics of formalization of poly(vinyl acetate)

Kinetic information on the formation of poly(vinyl formal) by the reaction of poly(vinyl acetate) and formaldehyde in presence of aqueous acid has been derived from the spectroscopic analysis of polymer samples after different periods of reaction. The hydroxyl content of poly(vinyl formal) is found to be nearly independent of reaction time and only slightly affected by temperature while the fall of acetate content and the increase in formal content are most rapid in the initial period and are largely influenced by temperature. The rate expression formulated on the assumption that the formalization reaction is of first order with respect to both poly(vinyl acetate) and formaldehyde explains the observed variation of polymer composition with reaction time. The activation energy for the reaction is found to be 17.3 kcal/mol.

Rate Model and Mechanism of Liquid-Phase Oxidation of Propionaldehyde

A rate equation is developed for the liquid-phase oxidation of propionaldehyde with oxygen in the presence of manganese propionate catalyst in a sparged reactor. The equation takes into account diffusional limitations based on Brian's solution for mass transfer accompanied by a pseudo m-. nth-order reaction. Sauter-mean bubble diameter, gas holdup, interfacial area, and bubble rise velocity are measured, and rates of mass transfer within the gas phase and across the gas-liquid interface are computed. Statistically designed experiments show the adequacy of the equation. The oxidation reaction is zero order with respect to oxygen concentration, 3/2 order with respect to aldehyde concentration, and order with respect to catalyst concentration. The activation energy is 12.1 kcal/g mole.

Involvement of Synthesis and Phosphorylation of Nuclear Protein Factors That Bind to the Positivecis-Acting Element in the Transcriptional Activation of the CYP2B1/B2 Gene by Phenobarbitonein Vivo

The synthesis and phosphorylation of protein factor(s) that bind to the positivecis-acting element (−69 to −98 nt) of the CYP2B1/B2 gene have been examinedin vivoin the rat. Treatment of rats with cycloheximide, a protein synthetic inhibitor, suppresses basal as well as phenobarbitone-induced levels of CYP2B1/B2 mRNA and its run-on transcription. Under these conditions, complex formation of the nuclear extract with the positive element is also inhibited, as judged by gel shift assays. Treatment of rats with 2-aminopurine, a general protein kinase inhibitor, blocks the phenobarbitone-mediated increase in CYP2B1/B2 mRNA, cell-free transcription of a minigene construct containing the positive element, pP450e179DNA, and binding of nuclear proteins to the positive element. Treatment of rats with okadaic acid, a protein phosphatase inhibitor, mimics the effects of phenobarbitone, but only partially. Thus, both phenobarbitone and okadaic acid individually enhance binding of the nuclear protein(s) to the positive element, cell-free transcription of the minigene construct, and phosphorylation of the not, vert, similar26- and 94-kDa proteins binding to the positive element. But unlike phenobarbitone, okadaic acid is not an inducer of CYP2B1/B2 mRNA or its run-on transcription. Thus, phenobarbitone-responsive positive element interactions constitute only a minimal requirement, and okadaic acid is perhaps not able to bring about the total requirement for activation of CYP2B1/B2 gene transcription that should include interaction between the minimal promoter and further upstream elements. An intriguing feature is the antagonistic effect of okadaic acid on phenobarbitone-mediated effects on CYP2B1/B2 mRNA levels, cell-free and run-on transcription, and nuclear protein binding to the positive element. The reason for this antagonism is not clear. It is concluded that phenobarbitone treatment enhancesin vivothe synthesis and phosphorylation of protein factors binding to the positive element and these constitute a minimal requirement for the transcriptional activation of the CYP2B1/B2 gene.

Origin of activation of Lattice Oxygen and Synergistic Interaction in Bimetal-Ionic Ce0.89Fe0.1Pd0.01O2-delta Catalyst

Flourite-type nanocrystalline Ce0.9Fe0.1O2-delta and Ce0.89Fe0.1Pd0.01O2-delta solid solutions have been synthesized by solution combustion method,'.which show higher oxygen storage/release property (OSC) compared to CeO2 and Ce0.8Zr0.2O2. Temperature programmed reduction an XPS study reveal that the presence of Pd ion in Ce0.9Fe0.1O2-delta facilitates complete reduction of Fe3+ to Fe2+ state and partial reduction of Ce4+ to Ce3+ state at.temperatures as low as 105 degrees C compared to 400 degrees C for monometal-ionic Ce0.9Fe0.1O2-delta. Fe3+ ion is reduced to Fe2+ and not to Feo due to favorable redox potential for Ce4+ + Fe2+ -> Ce3+ + Fe3+ reaction. Using first-principles density functional theory calculation we determine M-O (M = Pd, Fe, Ce) bond lengths, and find that bond lengths vary from shorter (2.16 angstrom) to longer (2.9 angstrom) bond distances compared to mean Ce-O bond distance of 2.34 angstrom. for CeO2. Using these results in bond valence analysis, we show that oxygen with bond valences as low as -1.55 are created, leading to activation of lattice oxygen in the bimetal ionic catalyst. Temperatures of CO oxidation and NO reduction by CO/H-2 are lower with the bimetalionic Ce0.89Fe0.1Pd0.01O2-delta catalyst compared to monometal-ionic Ce0.9Fe0.1O2-delta and Ce0.99Pd0.01O2-delta catalysts. From XPS studies of Pd impregnated on CeO2 and Fe2O3 oxides, we show that the synergism leading to low temperature activation of lattice oxygen in bimetal-ionic catalyst Ce0.89Fe0.1Pd0.01O2-delta is due to low-temperature reduction of Pd2+ to Pd-0, followed by Pd-0 + 2Fe(3+) -> Pd2+ + 2Fe(2+), Pd-0 + 2Ce(4+) -> Pd2+ + 2Ce(3+) redox reaction.

The pulse response of non-linear third order systems

The response of a third order non-linear system subjected to a pulse excitation is analysed. A transformation of the displacement variable is effected. The transformation function chosen is the solution of the linear problem subjected to the same pulse. With this transformation the equation of motion is brought into a form in which the method of variation of parameters is applicable for the solution of the problem. The method is applied to a single axis gyrostabilized platform subjected to an exponentially decaying pulse. The analytical results are compared with digital and analog computer solutions.

Which One Is Preferred: Myers-Saito Cyclization of Ene-Yne-Allene or Garratt-Braverman Cyclization of Conjugated Bisallenic Sulfone? A Theoretical and Experimental Study

A competitive scenario between Myers-Saito (MS) and Garraff-Braverman (GB) cyclization has been created in a molecule. High-level computations indicate a preference for GB over MS cyclization. The activation energies for the rate-determining steps of the GB and MS cyclizations were found to be the same (24.4 kcal/mol) at the B3LYP/6-31G* level of theory; thus, from the kinetic point of view, both reactions are feasible. However, the main biradical intermediate GB2 of the GB reaction is 6.2 kcal/mol lower in energy than the biradical MS2, which is the main intermediate of MS reaction, so GB cyclization is thermodynamically favored over MS cyclization. To verify the prediction by computational techniques, bisenediynyl sulfones 1-4 and bisenediynyl sulfoxide 17 were synthesized. Under basic conditions, these molecules isomerized to a system possessing both the ene-yne-allene and the bisallenic sulfone. The isolation of only one product, identified as the corresponding naphthalene- or benzene-fused sulfone 8-11, indicated the occurrence of GB cyclization as the sole reaction pathway. No product corresponding to the MS cyclization pathway could be isolated. Though the theoretical prediction showed a preference for the GB pathway over the MS pathway, the exclusive preference for GB over MS cyclization is very striking. Further analysis showed that the intramolecular self-quenching nature of the GB pathway may play an important role in the complete preference for this reaction. Apart from the mechanistic studies, these sulfones showed DNA cleavage activity that had an inverse relation with the reactivity order. Our findings are important for the design of artificial DNA-cleaving agents.

Farnesyltransferase Inhibitors Reduce Ras Activation and Ameliorate Acetaminophen-Induced Liver Injury in Mice

Hepatotoxicity due to overdose of the analgesic and antipyretic acetaminophen (A-PAIP) is a major cause of liver failure in adults. To better understand the contributions of different signaling pathways, the expression and role of Ras activation was evaluated after oral dosing of mice with APAP (400-500 mg/kg). Ras-guanosine triphosphate (GTP) is induced early and in an oxidative stress-dependent manner. The functional role of Ras activation was studied by a single intraperitoneal injection of the neutral sphingomyelinase and farnesyltransferase inhibitor (FTI) manumycin A (I mg/kg), which lowers induction of Ras-GTP and serum amounts of alanine aminotransferase (ALT). APAP dosing decreases hepatic glutathione amounts, which are not affected by manumycin A treatment. However, APAP-induced activation of c-Jun N-terminal kinase, which plays an important role, is reduced by manumycin A. Also, APAP-induced mitochondrial reactive oxygen species are reduced by manumycin A at a later time point during liver injury. Importantly, the induction of genes involved in the inflammatory response (including iNos, gp91phox, and Fasl) and serum amounts of proinflammatory cytokines interferon-gamma (IFN gamma) and tumor necrosis factor alpha, which increase greatly with APAP challenge, are suppressed with manumycin A. The FTI ctivity of manumycin A is most likely involved in reducing APAP-induced liver injury, because a specific neutral sphingomyelinase inhibitor, GW4869 (I mg/kg), did not show any hepatoprotective effect. Notably, a structurally distinct FTI, gliotoxin (I mg/kg), also inhibits Ras activation and reduces serum amounts of ALT and IFN-gamma after APAP dosing. Finally, histological analysis confirmed the hepatoprotective effect f manumycin A and gliotoxin during APAP-induced liver damage. Conclusion: This study identifies a key role for Ras activation and demonstrates the therapeutic efficacy of FTIs during APAP-induced liver injury.

A Novel Invertase from a Thermophilic FungusThermomyces lanuginosus:Its Requirement of Thiol and Protein for Activation

Unlike the invertases from the mesophilic fungi and yeasts, invertase from a thermophilic fungus,Thermomyces lanuginosus,was unusually unstable bothin vivoandin vitro.The following observations suggested that the unstable nature of the enzyme activity in the cell-free extracts was due to the oxidation of the cysteine residue(s) in the enzyme molecule: (a) the addition of dithiothreitol or reduced glutathione stabilized invertase activity during storage of the extracts and also revived enzyme activity in the extracts which had become inactive with time; (b)N-ethylmaleimide, iodoacetamide, oxidized glutathione, cystine, or oxidized coenzyme A-inactivated invertase; (c) invertase activity was low when the ratio reduced/oxidized glutathione was lower and high when this ratio was higher, suggesting regulation of the enzyme by thiol/disulfide exchange reaction. In contrast to the activation of invertase by the thiol compounds and its inactivation by the disulfides in the cell-free extracts, the purified enzyme did not respond to these compounds. Following its inactivation, the purified enzyme required a helper protein in addition to dithiothreitol for maximal activation. A cellular protein was identified that promoted activation of invertase by dithiothreitol and it was called “PRIA” for theprotein which helps inrestoringinvertaseactivity. The revival of enzyme activity was due to the conversion of the inactive invertase molecules into an active form. A model is presented to explain the modulation of invertase activity by the thiol compounds and the disulfides, both in the crude cell-free extracts and in the purified preparations. The requirement of free sulfhydryl group(s) for the enzyme activity and, furthermore, the reciprocal effects of the thiols and the disulfides on invertase activity have not been reported for invertase from any other source. The finding of a novel invertase which shows a distinct mode of regulation demonstrates the diversity in an enzyme that has figured prominently in the development of biochemistry.

Transcriptional activation of the Escherichia coli bgl operon: negative regulation by DNA structural elements near the promoter

The bgl operon of Escherichia coil is transcriptionally inactive in wild-type cells. DNA insertion sequences (IS) constitute a major class of spontaneous mutations that activate the cryptic bgl promoter. In an attempt to study the molecular mechanism of activation mediated by insertion sequences, transcription of the bgl promoter was carried out in vitro. Stimulation of transcription is observed when a plasmid containing an insertionally activated bgl promoter is used as a template in the absence of proteins other than RNA polymerase. Deletions that remove sequences upstream of the bgl promoter, and insertion of a 1.2 kb DNA fragment encoding resistance to kanamycin, activate the promoter. Point mutations within a region of dyad symmetry upstream of the promoter, which has the potential to extrude into a cruciform structure under torsional stress, also lead to activation, Introduction of a sequence with dyad symmetry, upstream of an activated bgl promoter carrying a deletion of upstream sequences, results in a fourfold reduction in transcription, These results suggest that the cryptic nature of the bgl promoter is because of the presence of DNA structural elements near the promoter that negatively affect transcription.

Suppression of the zero-order term in off-axis digital holography through nonlinear filtering

We present experimental validation of a new reconstruction method for off-axis digital holographic microscopy (DHM). This method effectively suppresses the object autocorrelation,namely, the zero-order term,from holographic data,thereby improving the reconstruction bandwidth of complex wavefronts. The algorithm is based on nonlinear filtering and can be applied to standard DHM setups with realistic recording conditions.We study the robustness of the technique under different experimental configurations,and quantitatively demonstrate its enhancement capabilities on phase signals.