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.     

Enhanced ethanol sensing properties of WO3 modified TiO2 nanorods

Pristine and WO₃ decorated TiO₂ nanorods (NRs) were synthesised to investigate n-n-type heterojunction gas sensing properties. TiO₂ NRs were fabricated via hydrothermal method on fluorine-doped tin oxide coated glass (FTO) substrates. Then, tungsten was sputtered on the TiO₂ NRs and thermally oxidised to obtain WO₃ nanoparticles. The heterostructure was characterised by X-ray diffraction (XRD), scanning electron microscopy (SEM), and energy-dispersive X-ray (EDX) spectroscopy. Fabricated sensor devices were exposed to VOCs such as toluene, xylene, acetone and ethanol, and humidity at different operation temperatures. Experimental results demonstrated that the heterostructure has better sensor response toward ethanol at 200 °C. Enhanced sensing properties are attributed to the heterojunction formation by decorating TiO₂ NRs with WO₃.     

Flowerlike hybrid horseradish peroxidase nanobiocatalyst for the polymerization of guaiacol

In this study, the catalytic activity and stability of flowerlike hybrid horseradish peroxidase (HRP) nanobiocatalyst (HRP-Cu ²⁺ ) obtained from Cu ²⁺ ions and HRP enzyme in the polymerization reaction of guaiacol were analyzed. We demonstrated that HRP-Cu ²⁺ and hydrogen peroxide (H ₂ O ₂ ) initiator showed significantly increased catalytic activity and stability on the polymerization of guaiacol compared to that of free HRP enzyme. Poly(guaiacol) was observed with quite high yields (88%) and molecular weights (38,000 g/mol) under pH 7.4 phosphate-buffered saline (PBS) conditions at 60 °C with 5 weight% of HRP-Cu ²⁺ loading. HRP-Cu ²⁺ also shows very high thermal stability and works even at 70 °C reaction temperature; free HRP enzyme denatures at that temperature. Furthermore, HRP-Cu ²⁺ provided considerable repeated use and showed some degree of catalytic activity, even after the fourth recycle, in the polymerization of guaiacol.     

Chemical composition,antimicrobial, and lipase enzyme activity of essential oil and solvent extracts from Serapias orientalis subsp. orientalis

The volatile components of essential oil (EO), SPME, and SPME of solvent extracts ( n -hexane, methanol, and water) obtained from fresh Serapias orientalis subsp. orientalis ( Soo ) were analyzed by GC-FID/MS. EO of Soo gave 11 compounds in the percentage of 99.97%; capronaldehyde (37.01%), 2-( E )-hexenal (23.19%), and n -nonanal (19.05%) were found to be major constituents. SPME GC-FID/MS analyses of fresh plant and solvent extracts of Soo revealed 7, 12, 7, and 4 compounds within the range of 99.7% to 99.9%. Limonene (76.5%, 41.7%, and 61.3%) was the major compound in SPMEs of the n -hexane and methanol extracts. α -Methoxy- p -cresol (52.9%) was the main component in its water extract. The antimicrobial activity of EO and the solvent extracts of Soo were screened against 9microorganisms. EO showed the best activity against Mycobacterium smegmatis , with 79.5 µg/mL MIC value. The n -hexane, methanol, and water extracts were the most active against the Staphylococcus aureus within the range of 81.25–125.0 µg/mL (MIC). IC ₅₀ values for the lipase enzyme inhibitory activity of EO and solvent extracts ( n -hexane, methanol, and water) were determined to be 59.87 µg/mL, 64.03 µg/mL, 101.91 µg/mL, and 121.24 µg/mL, respectively.     

Weak maximum principle and accessory problem for control problems on time scales

In this paper we derive the first and second variations for a nonlinear time scale optimal control problem with control and state-endpoints equality constraints. Using the first variation, a first order necessary condition for weak local optimality is obtained under the form of a weak maximum principle generalizing the Dubois–Reymond Lemma to the optimal control setting and time scales. A second order necessary condition in terms of the accessory problem is derived by using the nonnegativity of the second variation at all admissible directions. The control problem is studied under a controllability assumption, and with or without the shift in the state variable. These two forms of the problem are shown to be equivalent.     

Weak shock waves and its interaction with characteristic shocks in polyatomic gas

We present Lie symmetry analysis for investigating the shock‐wave structure of hyperbolic differential equations of polyatomic gases. With the application of symmetry analysis, we derive particular exact group invariant solutions for the governing system of partial differential equations (PDEs). In the next step, the evolutionary behavior of weak shock along with the characteristic shock and their interaction is investigated. Finally, the amplitudes of reflected wave, transmitted wave, and the jump in shock acceleration influenced by the incident wave after interaction are evaluated for the considered system of equations.     

Calculations of Isoelectronic Series of He Using Noninteger n‐Slater Type Orbitals in Single and Double Zeta Approximations

Using integer and noninteger n-Slater type orbitals in single- and double-zeta approximations, the Hartree-Fock-Roothaan calculations were performed for the ground states of first ten cationic members of the isoelectronic series of He atom. All the noninteger parameters and orbital exponents were fully optimized. In the case of noninteger n-Slater type orbitals in double zeta basis sets, the results of calculations obtained are more close to the numerical Hatree-Fock values and the average deviations of our ground state energies do not exceed 2×10^－6 hartrees of their numerical results.     

Development of an HPLC method for determination of pentachloronitrobenzene, hexachlorobenzene and their possible metabolites

Background

Pentachloronitrobenzene (PCNB) and hexachlorobenzene (HCB) are highly toxic and widespread in every environmental compartment. Some of metabolic products such as amino/nitro containing chlorinated aromatic compounds can be determined by gas chromatography coupled with electron capture detector (GC-ECD). However, it is difficult to identify some of chlorophenolic and chloroquinolic intermediates produced from PCNB and HCB by the above mentioned technique. Therefore, for analysis of these compounds and their metabolites, we have developed a high performance liquid chromatography (HPLC) based method.

Results

The extraction of PCNB and HCB from soil and minimal salt medium was carried out with ethyl acetate and hexane respectively with good recoveries (98% for PCNB and 97% for HCB). The validation of the proposed extraction and HPLC method was done by analysis of PCNB and HCB biodegradation and their metabolites identification from anaerobic enriched soil samples.

Conclusion

A rapid, sensitive and simple HPLC based analytical method was developed for the analysis of PCNB, HCB and their possible intermediates.     

Decay rates of solutions to thermoviscoelastic plates with memory

We consider the thermoelastic plate under the presence of along range memory. We find uniform rates of decay (in time)of the energy, provided that suitable assumptions on the relaxationfunctions are given. Namely, if the relaxation decays exponentiallythen the first order energy also decays exponentially. Whenthe relaxation g satisfies -c₁g(t)^1+1/_p g'(t) -c_og(t)^1+1/_p; and g,g^1-1/_p L¹ (R) withp > 2 then the energy decays as 1/(1+t)^p. A new Liapunov functionalis built for this problem.     

Co-Jacobian for Lipschitzian Maps

The notion of co-Jacobian is introduced for locally Lipschitz functions acting between arbitrary normed spaces. The main results of this paper provide a characterization, calculus rules, a mean value theorem, as well as the computation of the co-Jacobian of piecewise smooth functions. Comparisons with known differentiability notions and Mordukhovich’s co-derivatives are derived.