Optimal synthesis in an infinite-dimensional space

For a class of optimal control problems and Hamiltonian systems generated by these problems in the space l ₂, we prove the existence of extremals with a countable number of switchings on a finite time interval. The optimal synthesis that we construct in the space l ₂ forms a fiber bundle with piecewise smooth two-dimensional fibers consisting of extremals with a countable number of switchings over an infinite-dimensional basis of singular extremals.     

Investigation of structural changes related to temperature: An understanding of H-bond based proton transfer in 4(5)-vinylimidazole and acrylic acid copolymer membrane

An attempt to understand how proton transfer proceeds in poly (acrylic acid-co-4(5)-vinylimidazole) has been carried out based on the temperature dependent characterization techniques, i.e., Fourier transform infrared spectroscopy (FTIR), wide angle X-ray diffraction (WAXD), Raman spectroscopy, including the atomic distance calculations. Systematical studies are achieved from a series of poly (acrylic acid-co-4(5)-vinylimidazole) with different acrylic acid content. When the copolymer is almost an ideal in equimolar ratio of an alternating structure, the hydrogen bond between carboxylic acid and imidazole is maintained and initiates the proton conductivity even at 120 °C. Whereas when the copolymer is carboxylic acid rich, the dehydration to form anhydride proceeds resulting in the decrease in proton conductivity at high temperature. The radial distribution function (RDF) calculated from the WAXD pattern shows that the inter-atomic distances reflect how the increase in temperature induces a favorable packing structure under the hydrogen bond network and the chain mobility to enhance the proton transfer at high temperature, especially in the case of the copolymer with an ideal alternating structure.     

Preparation of 4(5)-vinylimidazole-co-acrylic acid copolymer and thermal performances related to applicability as PEM fuel cells

A series of acrylic acid and 4(5)-vinylimidazole copolymers for a non-hydrous proton transferring membrane used in polymer electrolyte membrane for fuel cell (PEMFC) are reported. The feed ratio of each monomer results in the variation of copolymer as evaluated by Fourier transform infrared spectroscopy (FTIR), and nuclear magnetic resonance spectroscopy (¹H-NMR). Differential scanning calorimeter and thermal gravimetric analyzer confirm the thermal properties of copolymer films with T_g at 105-177 °C and T_d above 230 °C. The simultaneous analysis of wide angle X-ray diffraction (WAXD) and differential scanning calorimetry (DSC) suggests the thermal performance about the decrease in domain size as a consequence of the loss of moisture content in the membrane and the increase in domain size as a consequence of chain mobility after T_g. The proton conductivities under anhydrous condition of the copolymer membranes are in the range of 10⁻² S/cm even up to 120 °C.     

Clock synchronization in symmetric stochastic networks

We consider a stochastic model of clock synchronization in a wireless network of $N$ sensors interacting with one dedicated accurate time server. For large $N$ we find an estimate of the final time sychronization error for global and relative synchronization. The main results concern the behavior of the network on different timescales $t_{N}\rightarrow \infty $ , $N\rightarrow \infty $ . We discuss the existence of phase transitions and find the exact timescales for which an effective clock synchronization of the system takes place.     

Synthesis of lactic acid–Zr(IV) phosphate nanocomposite ion exchanger for green remediation

Lactic acid–Zr(IV) phosphate nanocomposite (LA/ZPNC) ion exchanger was synthesised by sol-gel method. The nanocomposite ion exchanger was characterized by different techniques such as Fourier transform infrared spectroscopy (FTIR), transmission electron microscopy (TEM), scanning electron microscopy (SEM), energy X-ray diffraction (XRD) and thermogravimetric analysis (TGA/DTA/DSC). LA/ZPNC was employed for different physicochemical properties such as ion exchange capacity, elution behaviour, effect of eluent concentration, pH titration and thermal stability. The ion exchange capacity of LA/ZPNC was higher as compared to their inorganic counterpart. pH results indicate the bifunctional nature of nanocomposite. A degradation efficiency of 89.47 % was attained in 4 h of illumination. The distribution coefficient (K _d) studies of LA/ZPNC ion exchanger were investigated for eight different metal ions and found more selective for Al³⁺ with higher K _d value. It was explored for photocatalytic study of methylene blue under solar illumination.     

Copper(II)chloride-mediated cyclization reaction of N-alkoxy-ortho-alkynylbenzamides

A regioselective intramolecular cyclization/halogenation reaction of N-alkoxy-o-alkynylbenzamides with CuCl(2)/NCS was developed. The corresponding 3-(chloromethylene)isobenzofuran-1-ones were exclusively obtained via 5-exo-dig cyclization in moderate to excellent yields within 0.5-1 h. This approach has been successfully used to synthesize a biaryl compound by the Suzuki-Miyaura reaction.     

Optimal control problems for wave equations

The problem on minimizing a quadratic functional on trajectories of the wave equation is considered. We assume that the density of external forces is a control function. A control problem for a partial differential equation is reduced to a control problem for a countable system of ordinary differential equations by use of the Fourier method. The controllability problem for this countable system is considered. Conditions of the noncontrollability for some wave equations were obtained.