Synthesis and polymerization of new di‐octadecyl ester derivatives of α‐hydroxymethyl acrylate: A structure‐property correlation for their copolymers with methyl methacrylate

New ether dimer (ED‐Od) and diester (ODE) derivatives of α‐hydroxymethylacrylate, each having two octadecyl side chains, were synthesized and (co)polymerized to evaluate the effects of differences in the structures of the monomers on final (co)polymer properties, particularly glass transition temperature. The free radical polymerizations of both monomers yielded high‐molecular weight polymers. Cyclopolymer formation of ED‐Od was confirmed by ¹³C NMR analysis and the cyclization efficiency (0.95 or greater) was found to be as high as the cyclization efficiencies of the cyclopolymerizations of ether dimers of various alkyl α‐hydroxymethylacrylates synthesized previously. Copolymers of both ED‐Od and ODE with methyl methacrylate (MMA) showed significant T_g decreases over PMMA due to octadecyl side groups causing “internal” plasticization. Comparison of the T_g's of the copolymers of octadecyl methacrylate, ED‐Od and ODE with MMA revealed that the impacts of these monomers on depression of T_g's are identical. That is, the magnitude of decrease in T_g's was quantitatively related to the number of the octadecyl side groups in the copolymers rather than their placement on the same or randomly incorporated repeat units. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 7785–7793, 2008     

On positive solutions for a nonlinear boundary value problem with impulse

In this paper we study nonlinear second order differential equations subject to separated linear boundary conditions and to linear impulse conditions. Sign properties of an associated Green’s function are investigated and existence results for positive solutions of the nonlinear boundary value problem with impulse are established. Upper and lower bounds for positive solutions are also given.     

Approximate construction of the set of trajectories of the control system described by a Volterra integral equation

In this paper the set of trajectories of the control system is investigated. It is assumed that the behavior of the control system is described by a Volterra integral equation which is nonlinear with respect to the state vector and is affine with respect to the control vector, and the control functions have an integral constraint. An approximation of the set of trajectories by the set which consists of a finite number of trajectories is given. The Hausdorff distance between the set of trajectories of the system and the set, consisting of a finite number of trajectories is evaluated.     

An algorithm for approximating piecewise linear concave functions from sample gradients

An effective algorithm for solving stochastic resource allocation problems is to build piecewise linear, concave approximations of the recourse function based on sample gradient information. Algorithms based on this approach are proving useful in application areas such as the newsvendor problem, physical distribution and fleet management. These algorithms require the adaptive estimation of the approximations of the recourse function that maintain concavity at every iteration. In this paper, we prove convergence for a particular version of an algorithm that produces approximations from stochastic gradient information while maintaining concavity.     

Comparison of flow structures in the downstream region of a cylinder and sphere

An experimental investigation of flow structures downstream of a circular cylinder and sphere immersed in a free-stream flow is performed for Re = 5000 and 10,000 using qualitative and quantitative flow visualization techniques. The obtained results are presented in terms of time-averaged velocity vectors, patterns of streamlines, vorticity, Reynolds stress correlations and turbulent kinetic energy distributions. Flow data reveal that the size of wake flow region, the location of singular and double points, the peak values of turbulence quantities, such as Reynolds stress correlations, vorticity fluctuations and turbulent kinetic energy vary as a function of models’ geometry and Reynolds Numbers. The concentration of small scale vortices is more dominant in the wake of the sphere than that of the cylinder. The maximum value of turbulent kinetic energy (TKE) occurs close to the saddle point for the cylinder case while two maximum values of TKE occur along shear layers for the sphere one because of the 3-D flow behavior.     

Direct generation of 81 nJ pulses and external compression to a subpicosecond regime with a 4.9 MHz chirped-pulse multipass-cavity Cr⁴⁺:forsterite oscillator

We report direct generation of 81 nJ chirped pulses from a room-temperature, Kerr lens mode-locked Cr??:forsterite oscillator operating at 1258 nm. To increase the pulse energy, the pulse repetition rate of the short x-type resonator was lowered from 143 to 4.9 MHz by the addition of a q-preserving multipass cavity, which provided an additional effective optical path length of 59.4 m. The duration of the chirped pulses was around 5.5 ps with a spectral width of 21 nm. The pulses were externally compressed to 607 fs by using a diffraction grating pair. To our knowledge, this is the highest reported pulse energy directly generated from a room-temperature mode-locked Cr??:forsterite laser.     

Removal of methylene blue dye from aqueous solution by semi‐interpenetrating polymer network hybrid hydrogel: Optimization through Taguchi method

In this study, sodium humate/poly(acrylamide‐co‐methacrylic acid)/kaolin semi‐interpenetrating polymer network hybrid hydrogel was synthesized as an effective adsorbent for the removal of methylene blue. The morphological and structural properties, and swelling behavior in distilled water and various environments of hybrid hydrogel were investigated with different analyses and tests. The equilibrium swelling percent of hybrid hydrogel reached to 37,000% in 240 min. The parameters (agitation time, concentration, dose, temperature, and pH) affecting adsorption process for methylene blue were optimized using Taguchi method. The data obtained in optimum conditions were well fitted to Langmuir adsorption isotherm and maximum adsorption capacity was determined as 833. 33 mg/g. In the light of the results, the utilization of hybrid hydrogel with high swelling capacity is foreseen as a favored adsorbent in several separation processes. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 1070–1078     

Indices defect theory of singular Hahn-Sturm-Liouville operators

In this article, we extend the results concerning the deficiency index problem to singular Hahn-Sturm-Liouville difference operators. We establish some criteria under which the singular Hahn-Sturm-Liouville equation is of limit-point case at infinity.     

On solutions of the fifth-order dispersive equations with porous medium type non-linearity

In this work, we focus on obtaining the exact solutions of the fifth-order semi-linear and non-linear dispersive partial differential equations, which have the second-order diffusion-like (porous-type) non-linearity. The proposed equations were not studied in the literature in the sense of the exact solutions. We reveal solutions of the proposed equations using the classical Riccati equations method. The obtained exact solutions, which can play a key role to simulate non-linear waves in the medium with dispersion and diffusion, are illustrated and discussed in details.     

Standard forms of the eigenvalue problems associated with gyroscopic systems

The eigenvalue problem arising in the free vibration and stability analysis of gyroscopic systems is associated with a λ-matrix in which λ as well as its square appears. The characteristic polynomial of a non-dissipative gyroscopic system however, is a function of λ², and an equivalent standard eigenvalue formulation involving only λ² as an eigenvalue, therefore, seems to be a more appropriate representation of the physical system. Such forms and the related transformations are discussed herein. Similarly, when the loading parameter also appears explicitly in the λ-matrix, an equivalent double-eigenvalue problem involving λ² and the loading parameter as eigenvalues is generated. The extremum properties of the Rayleigh Quotient leads to a convenient proof of an upper bound theorem on λ². The use of left and right eigenvectors and the new double-eigenvalue formulation allows for the establishment of a flutter condition similar to one obtained for circulatory systems earlier. An example illustrating some of the concepts is presented.