Mathematical studies of the solution of Burgers' equations by Adomian decomposition method

In this paper, a novel Adomian decomposition method (ADM) is developed for the solution of Burgers' equation. While high level of this method for differential equations are found in the literature, this work covers most of the necessary details required to apply ADM for partial differential equations. The present ADM has the capability to produce three different types of solutions, namely, explicit exact solution, analytic solution, and semi-analytic solution. In the best cases, when a closed-form solution exists, ADM is able to capture this exact solution, while most of the numerical methods can only provide an approximation solution. The proposed ADM is validated using different test cases dealing with inviscid and viscous Burgers' equations. Satisfactory results are obtained for all test cases, and, particularly, results reported in this paper agree well with those reported by other researchers.     

A Novel Route to the Fused Maleic Anhydride Moiety of CP Molecules

A seven‐step cascade reaction —in which selective mesylation, epoxide formation, epoxide lysis, cyclization, reiterative oxidation, and nitrogen–oxygen exchange occur sequentially—facilitates the construction of the maleic anhydride moiety of CP molecules 1 and 2 (>93% yield per step). Unstable intermediates of this reaction sequence were detected, providing evidence for the proposed mechanism and resulting in the discovery of a new chemical entity.     

Biofuel cell controlled by enzyme logic network — Approaching physiologically regulated devices

A “smart” biofuel cell switchable ON and OFF upon application of several chemical signals processed by an enzyme logic network was designed. The biocomputing system performing logic operations on the input signals was composed of four enzymes: alcohol dehydrogenase (ADH), amyloglucosidase (AGS), invertase (INV) and glucose dehydrogenase (GDH). These enzymes were activated by different combinations of chemical input signals: NADH, acetaldehyde, maltose and sucrose. The sequence of biochemical reactions catalyzed by the enzymes models a logic network composed of concatenated AND/OR gates. Upon application of specific “successful” patterns of the chemical input signals, the cascade of biochemical reactions resulted in the formation of gluconic acid, thus producing acidic pH in the solution. This resulted in the activation of a pH-sensitive redox-polymer-modified cathode in the biofuel cell, thus, switching ON the entire cell and dramatically increasing its power output. Application of another chemical signal (urea in the presence of urease) resulted in the return to the initial neutral pH value, when the O₂-reducing cathode and the entire cell are in the mute state. The reversible activation–inactivation of the biofuel cell was controlled by the enzymatic reactions logically processing a number of chemical input signals applied in different combinations. The studied biofuel cell exemplifies a new kind of bioelectronic device where the bioelectronic function is controlled by a biocomputing system. Such devices will provide a new dimension in bioelectronics and biocomputing benefiting from the integration of both concepts.     

Polarographic Behavior of Bivalent Germanium in Alkaline Solution

Bivalent germanium was polarographically studied in sodium hydroxide solution at various concentrations. A well-defined reduction wave with half-wave potential varying from ?0.90 to ?0.98 volt vs. S.C.E. was observed for 1×10^?4 M Ge(II) in concentration range of 0.2 to 2.0 F with respect to NaOH, and from ?0.70 to ?0.88 volt vs. S.C.E. in the pH range 9.0–12.1 at 25°. The value of i_d/C is 5.43 μα/mM and that of i_d/C m^for t^1/8 is 5.21. Dependence of E_1/2 upon pH is expressed by —E_1/2 =0.18+0.058 pH. Experimental result suggests that the reaction proceeds in two-steps involving an irreversible two-electron reduction: Ge(OH)₂+OH^?→HGeO₂^?+H₂O and HGeO₂^?+H₂O+2e→Ge⁰+3OH^?.     

Mechanistic Insights into RNA Transphosphorylation from Kinetic Isotope Effects and Linear Free Energy Relationships of Model Reactions

Phosphoryl transfer reactions are ubiquitous in biology and the understanding of the mechanisms whereby these reactions are catalyzed by protein and RNA enzymes is central to reveal design principles for new therapeutics. Two of the most powerful experimental probes of chemical mechanism involve the analysis of linear free energy relations (LFERs) and the measurement of kinetic isotope effects (KIEs). These experimental data report directly on differences in bonding between the ground state and the rate‐controlling transition state, which is the most critical point along the reaction free energy pathway. However, interpretation of LFER and KIE data in terms of transition‐state structure and bonding optimally requires the use of theoretical models. In this work, we apply density‐functional calculations to determine KIEs for a series of phosphoryl transfer reactions of direct relevance to the 2′‐O‐transphosphorylation that leads to cleavage of the phosphodiester backbone of RNA. We first examine a well‐studied series of phosphate and phosphorothioate mono‐, di‐ and triesters that are useful as mechanistic probes and for which KIEs have been measured. Close agreement is demonstrated between the calculated and measured KIEs, establishing the reliability of our quantum model calculations. Next, we examine a series of RNA transesterification model reactions with a wide range of leaving groups in order to provide a direct connection between observed Brønsted coefficients and KIEs with the structure and bonding in the transition state. These relations can be used for prediction or to aid in the interpretation of experimental data for similar non‐enzymatic and enzymatic reactions. Finally, we apply these relations to RNA phosphoryl transfer catalyzed by ribonuclease A, and demonstrate the reaction coordinate–KIE correlation is reasonably preserved. A prediction of the secondary deuterium KIE in this reaction is also provided. These results demonstrate the utility of building up knowledge of mechanism through the systematic study of model systems to provide insight into more complex biological systems such as phosphoryl transfer enzymes and ribozymes.     

Synthesis,structure and catalytic polymerization activity of half‐sandwich cyclometallated iridium complexes

A series of mononuclear half‐sandwich cyclometallated iridium complexes with Schiff base ligands were synthesized in good yields. Five air‐stable C,N‐chelate mode complexes were obtained smoothly through metal‐mediated C─H bond activation. Treatments of dimeric metal complexes [Cp*IrCl₂]₂ with ligands L1–L5 afforded the corresponding C,N‐chelate mononuclear half‐sandwich iridium(III) complexes 1 – 5 . These iridium complexes exhibit high catalytic activity for norbornene polymerization. Both steric and electronic effects of the substituted groups have influences on the behaviors of the polymerization process. All complexes were characterized using infrared and NMR spectroscopies and elemental analysis. Molecular structures of complexes 1 , 2 and 5 were further confirmed using single‐crystal X‐ray analysis.     

Uranium assay and trace element analysis of the fourth collaborative material exercise samples by the modified Davies-Gray method and the ICP-MS/OES techniques

Journal of Radioanalytical and Nuclear Chemistry - An international group of laboratories participating in CMX-4 subjected three samples to comparative nuclear forensic analysis using uranium assay...