Invariant Pseudolinearity with Applications

In this paper, we introduce the notion of invariant pseudolinearity for nondifferentiable and nonconvex functions by means of Dini directional derivatives. We present some characterizations of invariant pseudolinear functions. Some characterizations of the solution set of a nonconvex and nondifferentiable, but invariant, pseudolinear program are obtained. The results of this paper extend various results for pseudolinear functions, pseudoinvex functions, and η-pseudolinear functions, and also for pseudoinvex programs, pseudolinear programs, and η-pseudolinear programs.     

Existence theorems for boundary value problems in difference equations

In this research, we study linear difference equations with constant coefficients subject to boundary conditions. Necessary and/or sufficient conditions for the existence of a unique solution will be established. The proofs of the existence and uniqueness theorems are established by means of special types of determinants called Mosaic Vandermonde determinants.     

Superintegrable cases of four-dimensional dynamical systems

Degenerate tri-Hamiltonian structures of the Shivamoggi and generalized Raychaudhuri equations are exhibited. For certain specific values of the parameters, it is shown that hyperchaotic Lü and Qi systems are superintegrable and admit tri-Hamiltonian structures.     

Stimuli-Responsive Macromolecular Architecture by Butler Cyclopolymerizations: Synthesis and Applications

This article reviews the synthesis of polyzwitterions (PZs) (poly-carboxybetaines, -phosphonobetaines, and -sulfobetaines) having multiple pH-responsive centers. The synthesis follows the Butler cyclopolymerization protocol involving a multitude of diallylammonium salts and their copolymerization with SO₂ and maleic acid. The PZs have been transformed into cationic-, anionic-polyelectrolytes, and polyampholytes under the influence of pH. Particular attention is given to the application of these polymers as antiscalants, mild steel corrosion inhibitors, components in constructing Aqueous Two-Phase Systems (ATPSs), and membrane modifiers. The ATPSs could be used to separate various biomolecules, including proteins. Many amphiphilic polymers incorporating a few mol % hydrophobic monomers have shown enhanced viscosities and could be suitable for applications in oil fields. The progress of applying Butler cyclopolymerization in reversible addition-fragmentation chain transfer (RAFT) chemistry has been discussed. Future works are expected to focus on RAFT cyclopolymerization to construct block copolymers.     

Anchor Effect on Pedal Motion Observed in Crystal Phase of an Azobenzene Derivative

Abstract  

Some molecules having a molecular skeleton similar to that of stilbenes and azobenzenes show orientational disorder in the crystals due to pedal motion. Heretofore, the orientational disorder through pedal motion has been observed for the compounds containing only two aromatic rings in the absence of bulky substituent groups. Here we report that the pedal motion can be detected even in the presence of a bulky substituent group to which orientational disorder becomes invisible as a result of anchor effect arising from phenoxyphtalonitrile group. X-ray crystallographic analysis of the compound, C₂₃H₁₈N₄O, reveals the existence of partially overlapped two pedal conformers. The compound crystallizes in the monoclinic space group P2₁/c with a = 12.9429(11) Å, b = 8.5075(5) Å, c = 21.063(2) Å and β = 123.155(6)°. Major pedal conformer is stabilized by weak C–H···O type hydrogen bond and C–H···π type edge-to-face interactions in solid state. Quantum chemical calculations at B3LYP/6-311G+(d,p) level suggest that the stabilization of the compound decreases with increasing deviation from the planar geometry of trans-azobenzene fragment.     

Effects of built-in electric field on donor binding energy in InGaN/ZnSnN2 quantum well structures

In_xGa${}_{1?x}$N/ZnSnN₂ quantum well structures are studied in terms of a binding energy of a donor atom. 1s and $2p_{\pm }$ impurity states are considered. The Schrödinger's and Poisson's equations are solved self-consistently. A hydrogenic type wave function to represent each impurity state is assumed. The calculations include band-bending in the potential energy profile introduced by the built-in electric field existing along the structures. The binding energy and the energy of the transition between the impurity states are represented as a function of the quantum well width, the donor position, and the indium concentration. An external magnetic field up to 10 T is included into the calculations to compute the Zeeman splitting. The maximum value of the transition energy is around 30 meV (nearly 7.3 THz) which occurs in a 15-Å In_0.3Ga_0.7N/ZnSnN₂ quantum well. Being strong, the built-in electric field makes the transition energy drop quickly with the decreasing well width. For the same reason, the energy curves are found to be highly asymmetric function of the donor position around the well center. Compared to the bulk value, the transition energy in the quantum well structures enhances nearly two-fold.     

Systems of quasi-variational relations with applications

In this paper, we introduce a system of quasi-variational relations (in short, SQVR) and present several examples which show that it is a very general and unified model of several problems. We establish the existence of solutions of SQVP, in general, and several other problems, in particular. As an application of our results, we derive maximal element theorems and a collectively fixed point theorem for a family of multivalued maps. As further applications, we study Ky Fan type inequality / inclusion problem for vector valued bifunctions which includes constrained Nash equilibrium problem as a special case. We also present a common fixed point theorem for a family of multivalued maps. The results of this paper improve and generalize several known results on (system of) quasi-equilibrium problems, (system of) quasi-variational inclusions, constrained Nash equilibrium problem, collectively fixed point theorem and KKM type theorems for a family of multivalued maps. Our results also contain several results which appeared in recent literature.     

Effect of C60-SiO2 hybrid nanoparticles on thermophysical and tribological properties of a multigrade engine oil: an experimental study

Journal of Thermal Analysis and Calorimetry - In this study, the thermophysical and tribological properties of a hybrid nanofluid containing fullerene-silica nanoparticles in a multigrade engine...