Abstract:
Thermogravimetry was used for the evaluation of the thermo-oxidative stability of waterborne polyurethanes (wbPUR) containing catalysts of different selectivity. From Arrhenius plots, activation energies of between 50 and 120 kJ mol-1 for wbPUR were determined, depending on the temperature interval, selectivity of the catalyst and degree of degradation. Waterborne polyurethanes without catalyst showed lower thermal stability than waterborne polyurethanes with catalysts of different selectivity. Non-isothermal thermogravimetry indicated the presence of different degradation processes and enabled the kinetics parameters at higher degrees of degradation to be evaluated.

Abstract:
In this study, we investigate the influence of viscous heating parameter on the steady flow of a reactive variable viscous fluid in a cylindrical pipe with an isothermal wall under reasonable assumption. Numerical solutions are constructed for the governing non linear boundary value problem using shooting technique together with Runge-Kutta method and important properties of the temperature field and thermal are critically discussed. Necessary and sufficient conditions for existence and uniqueness were provided for the problem to have physical implications.

Abstract:
Cylindrical algebraic decomposition (CAD) is an important tool for the study of real algebraic geometry with many applications both within mathematics and elsewhere. It is known to have doubly exponential complexity in the number of variables in the worst case, but the actual computation time can vary greatly. It is possible to offer different formulations for a given problem leading to great differences in tractability. In this paper we suggest a new measure for CAD complexity which takes into account the real geometry of the problem. This leads to new heuristics for choosing: the variable ordering for a CAD problem, a designated equational constraint, and formulations for truth-table invariant CADs (TTICADs). We then consider the possibility of using Groebner bases to precondition TTICAD and when such formulations constitute the creation of a new problem.

Abstract:
In this study a more precise formulation of electrical capacitance for a cylindrical capacitive sensor is reported. By using different theoretical models such as Coulomb law, Gauss law and Laplace equation the electrical capacitance is calculated. Based on the given models the relation between the capacitance and the geometrical parameters (e.g., cylindrical length) is formulated and by using suitable software capacitance variation is computed and compared for different methods. In Coulomb method, the electrical potential is first solved numerically by using Mathematica and then the electrical capacitance is computed. It is found that the active capacitor length is crucial parameter in the calculations and therefore variation of this parameter is considered in our calculations. It is noted that the capacitance value is very sensitive to the length according to the method and it is deviated sharply for small length (about 20 cm) from the Gauss approximation. By comparing obtained results one recognizes that there is a pronounced error difference using approximated laws in short capacitor length range while for long length a negligible difference is noted between the tested models.

Abstract:
The coherent phenomena in mesoscopic cylindrical normal metal (N) - superconductor (S) structures have been investigated theoretically. The magnetic moment (persistent current) of such a structure has been calculated numerically and (approximately) analytically. It is shown that the current in the N layer corresponding to the free-energy minimum is always diamagnetic. As the field increases, the magnetic moment (current) exhibits jumps at certain values of the trapped magnetic flux and the NS structure changes to a state with smaller absolute value of the diamagnetic moment. This occurs when the persistent current is unable to screen the external field. The magnetic moment increase stepwise and the system changes into a new stable state. The magnetic field penetrates into a larger volume of the N layer. The state has smaller absolute value of the diamagnetic moment. Experimentally, this is interpreted as the presence of a paramagnetic addition in the system (paramagnetic reentrant effect). The results obtained are in qualitative agreement with the experiments conducted by P. Visani et al. [Phys. Rev. Lett. 65, 1514 (1990)].

Abstract:
Although the spectral lines of hydrogen contain valuable information on the physical properties of a variety of astrophysical plasmas, including the upper solar chromosphere, relatively little is known about their scattering polarization signals whose modification via the Hanle effect may be exploited for magnetic field diagnostics. Here we report on a basic theoretical investigation of the linear polarization produced by scattering processes and the Hanle effect in Ly-a, Ly-b and H-a taking into account multilevel radiative transfer effects in an isothermal stellar atmosphere model, the fine-structure of the hydrogen levels, as well as the impact of collisions with electrons and protons. The main aim of this first paper is to elucidate the physical mechanisms that control the linear polarization in the three lines, as well as its sensitivity to the perturbers density and to the strength and structure of micro-structured and deterministic magnetic fields. To this end, we apply an efficient radiative transfer code we have developed for performing numerical simulations of the Hanle effect in multilevel systems with overlapping line transitions. For low density plasmas such as that of the upper solar chromosphere collisional depolarization is caused mainly by collisional transitions between the fine-structure levels of n=3, so that it is virtually insignificant for Ly-a but important for Ly-b and H-a. We show the impact of the Hanle effect on the three lines taking into account the radiative transfer coupling between the different hydrogen line transitions. For example, we demonstrate that the linear polarization profile of the H-a line is sensitive to the presence of magnetic field gradients in the line core formation region and that in solar-like chromospheres selective absorption of polarization components does not play any significant role on the emergent scattering polarization.

Abstract:
In this note we will propose a method on how to determine the nth numeric palindrome based on the result in [1] though maybe there are other methods available on finding it.

Abstract:
Using cylindrical harmonics and Fourier series, a new integral equation formulation is derived for perfectly conducting 2D scattering problems. This new integral equation is based on the fact that, all of the electric and magnetic field components are zero inside a perfect electric conductor. The incident and scattered fields are expressed in the cylindrical coordinate system with respect to a common origin inside the scatterer, using the addition theorem for Bessel and Hankel functions. The resulting electric or magnetic field is set equal to zero for all the points inside the largest cylinder that is contained in and tangent to the surface of the scatterer. As a result the field point variables are eliminated from the integral equation and only the source points are present in this formulation. Therefore the size of the problem is reduced considerably. A dramatic improvement in the computation speed is seen compared to the classical method of moments. TE and TM scattering problems are considered and the integral equation formulation is derived and solved for both cases.

Abstract:
Taking advantage of the flexibility of the variational method with coordinate transformations, we derive a self-consistent set of equations of motion from a discretized Lagrangian to study kinetic plasmas using a Fourier decomposed cylindrical coordinate system. The phase-space distribution function was reduced to a collection of finite-sized macro-particles of arbitrary shape moving on a virtual Cartesian grid. However, the discretization of field quantities was performed in cylindrical coordinates and decomposed into a truncated Fourier series in angle. A straightforward finite element interpolation scheme is used to transform between the two grids. The equations of motion were then obtained by demanding the action be stationary. The primary advantage of the variational approach is preservation of Lagrangian symmetries. In the present case, this leads to exact energy conservation, thus avoiding possible difficulties with grid heating.

Abstract:
Cylindrical algebraic decompositions (CADs) are a key tool for solving problems in real algebraic geometry and beyond. We recently presented a new CAD algorithm combining two advances: truth-table invariance, making the CAD invariant with respect to the truth of logical formulae rather than the signs of polynomials; and CAD construction by regular chains technology, where first a complex decomposition is constructed by refining a tree incrementally by constraint. We here consider how best to formulate problems for input to this algorithm. We focus on a choice (not relevant for other CAD algorithms) about the order in which constraints are presented. We develop new heuristics to help make this choice and thus allow the best use of the algorithm in practice. We also consider other choices of problem formulation for CAD, as discussed in CICM 2013, revisiting these in the context of the new algorithm.