3-Tetrahydrofurfuryloxy-2-Hydroxypropyl Methacrylate: Synthesis,Characterization, Homopolymerization,and Copolymerization

Abstract

3-Tetrahydrofurfuryloxy-2-hydroxypropyl methacrylate monomer was prepared from methacrylic acid, tetrahydrofurfuryl alchol, and epichlorhydrin. Homopolymerization and copolymerization with (2-phenyl-1,3-dioxolane-4-yl)methyl methacrylate and N-vinyl pyrrolidone monomers were carried out in 1,4-dioxane solution at 60°C using benzoyl peroxide as initiator. Infrared, proton and carbon-13 nuclear magnetic resonance techniques were used in characterizations of the monomer, the homopolymer and the copolymers were determined by DSC technique. The copolymer compositions were estimated from 1H-NMR spectra. The reactivity ratios in copolymerization of 3-tetrahydrofurfuryloxy-2-hydroxypropyl methacrylate and (2-phenyl-1,3-dioxolane-4-yl) methyl methacrylate were calculated by both Kelen-Tüdos and Fineman-Ross methods.     

Decoupling and reduction in Chern–Simons modified gravity

We show that for four-dimensional spacetimes with a non-null hypersurface orthogonal Killing vector and for a Chern–Simons (CS) background (non-dynamical) scalar field, which is constant along the Killing vector, the source-free equations of CS modified gravity decouple into their Einstein and Cotton constituents. Thus, the model supports only general relativity solutions. We also show that, when the cosmological constant vanishes and the gradient of the CS scalar field is parallel to the non-null hypersurface orthogonal Killing vector of constant length, CS modified gravity reduces to topologically massive gravity in three dimensions. Meanwhile, with the cosmological constant such a reduction requires an appropriate source term for CS modified gravity.     

Approximate solution of the system of nonlinear integral equation by Newton-Kantorovich method

The Newton-Kantorovich method is developed for solving the system of nonlinear integral equations. The existence and uniqueness of the solution are proved, and the rate of convergence of the approximate solution is established. Finally, numerical examples are provided to show the validity and the efficiency of the method presented.     

Regularized Green’s function and group of reflections in a cavity with triangular cross section

For a certain class of triangles (with angles proportional to π/N, N ≥ 3) we formulate the image method by making use of the group G _N generated by reflections with respect to three lines which form the triangle under consideration. A regularized Green’s function (which is employed in Casimir energy calculations) is obtained by classification of subgroups of G _N and corresponding fixed points in the triangle.     

Stationary spinning strings and symmetries of classical spacetimes

We explore the symmetries of classical stationary spacetimes in terms of the dynamics of a spinning string described by a worldsheet supersymmetric action. We show that for stationary configurations of the string, the action reduces to that for a pseudo-classical spinning point particle in an effective space, which is a conformally scaled quotient space of the original spacetime. As an example, we consider the stationary spinning string in the Kerr–Newman spacetime, whose motion is equivalent to that of the spinning point particle in the three-dimensional effective space. We present the Killing tensor as well as the spin-valued Killing vector of this space. However, the nongeneric supersymmetry corresponding to the Killing–Yano tensor of the Kerr–Newman spacetime is lost in the effective space.     

Uniqueness of rotating charged black holes in five-dimensional minimal gauged supergravity

We study a five-dimensional spacetime admitting, in the presence of torsion, a non-degenerate conformal Killing–Yano 2-form which is closed with respect to both the usual exterior differentiation and the exterior differentiation with torsion. Furthermore, assuming that the torsion is closed and co-closed with respect to the exterior differentiation with torsion, we prove that such a spacetime is the only spacetime given by the Chong–Cvetič–Lü–Pope solution for stationary, rotating charged black holes with two independent angular momenta in five-dimensional minimal gauged supergravity.     

Stationary Electromagnetic Fields of a Slowly Rotating Magnetized Neutron Star in General Relativity

Following the general formalism presented by Rezzolla, Ahmedov and Miller, ⁽¹⁾ we here derive analytic solutions of the electromagnetic fields equations in the internal and external background spacetime of a slowly rotating highly conducting magnetized neutron star. The star is assumed to be isolated and in vacuum, with a dipolar magnetic field not aligned with the axis of rotation. Our results indicate that the electromagnetic fields of a slowly rotating neutron star are modified by general relativistic effects arising from both the monopolar and the dipolar parts of the gravitational field. The results presented here differ from the ones discussed by Rezzolla, Ahmedov and Miller ⁽¹⁾ mainly in that we here consider the interior magnetic field to be dipolar with the same radial dependence as the external one. While this assumption might not be a realistic one, it should be seen as the application of our formalism to a case often discussed in the literature.     

General Relativistic Thermoelectric Effects in Superconductors

We discuss the general-relativisticcontributions which occur in the electromagneticproperties of a superconductor with a heat flow. Theappearance of a general-relativistic contribution to themagnetic flux through a superconducting thermoelectricbimetallic circuit is shown. The response of theJosephson junctions to a heat flow is investigated inthe general-relativistic framework. Somegravitothermoelectric effects which are observable in thesuperconducting state in the Earth's gravitational fieldare considered.     

Particle motion and electromagnetic fields of rotating compact gravitating objects with gravitomagnetic charge

The exact solution for the electromagnetic field occuring when the Kerr–Taub–NUT compact object is immersed (i) in an originally uniform magnetic field aligned along the axis of axial symmetry (ii) in dipolar magnetic field generated by current loop has been investigated. Effective potential of motion of charged test particle around Kerr–Taub–NUT gravitational source immersed in magnetic field with different values of external magnetic field and NUT parameter has been also investigated. In both cases presence of NUT parameter and magnetic field shifts stable circular orbits in the direction of the central gravitating object. Finally we find analytical solutions of Maxwell equations in the external background spacetime of a slowly rotating magnetized NUT star. The star is considered isolated and in vacuum, with monopolar configuration model for the stellar magnetic field.     

Vibrational spectra of an LiNO3–(CH3)2SO2 system

Raman and IR absorption spectra were studied and molecular relaxation characteristics of vibrations of the anion and solvent were calculated for an xLiNO₃–(1 – x)(CH₃)₂SO₂ system (x = 0.1, 0.2, 0.3, 0.4 M). It was found that it is impossible to increase the concentration of free ions involved in charge transfer in such a system by either increasing the temperature or changing the concentration composition in the studied range of x.