Ratio-conjugation tool and its application in linear optimization models†

The ratio-conjugation-tool (RC) is constructed systematically, and its applicability for analysis of economic models is demonstrated. One of the main results establishes a general formula for RC of aggregative function. This tool is applied to the analysis of linear economic dynamics models of Neumann–Gale type which can be solved by a dynamic programming method: for each direct problem we construct the corresponding dual RC-problem. Moreover, we consider three examples of the most important economic dynamics models and look at these now from a unified general position.     

On the Rayleigh-Plateau instability

In this paper,we study the surface instability of a cylindrical pore in the absence of stress. This instability is called the Rayleigh-Plateau instabilty. We consider the model developed by Spencer et ...     

Indirect Differential Pulse Voltammetric Determination of Aluminum Biological Samples in the Presence of 3, 4-Dihydroxyphenylalanine

ABSTRACT

Indirect differential pulse voltammetric (DPV) determination of aluminum in the presence of 3, 4-dihydroxyphenylalanine (L-dopa) with glass carbon electrode as working electrode has been described. The method relies on the decrease of DPV anodic peak current of L-dopa with the addition of Al^III The decreasing value of the peak current is linear with the increase of Al^III concentration. Under the optimum experimental conditions (pH 4.8, 6×10^?4 M L-dopa, 0.06M NaAc - HAc ¹buffer solution), the linear ranges are 4.0×10^?7 - 5.2×10^?6 M and 7.2×10^?6 - 4.5×10^?5 M. The relative standard deviation for 8×10^?6 M aluminum is 1.0% (n = 8) and the detection limit is 3.5×10^?7 M. A number of foreign species for interference have been studied. The method has been applied to determine aluminum in drinking water, synthetic renal dialysate and urine samples.     

Lack of anomalous diffusion in linear translationally-invariant systems determined by only one initial condition

It is shown that as far as the linear diffusion equation meets both time- and space-translational invariance, the time dependence of a moment of degree α is a polynomial of degree at most equal to α, while all connected moments are at most linear functions of time. As a special case, the variance is an at most linear function of time.     

A numerical analysis of a class of generalized Boussinesq‐type equations using continuous/discontinuous FEM

An improved class of Boussinesq systems of an arbitrary order using a wave surface elevation and velocity potential formulation is derived. Dissipative effects and wave generation due to a time‐dependent varying seabed are included. Thus, high‐order source functions are considered. For the reduction of the system order and maintenance of some dispersive characteristics of the higher‐order models, an extra O(μ²ⁿ⁺²) term (n ∈ ?) is included in the velocity potential expansion. We introduce a nonlocal continuous/discontinuous Galerkin FEM with inner penalty terms to calculate the numerical solutions of the improved fourth‐order models. The discretization of the spatial variables is made using continuous P₂ Lagrange elements. A predictor‐corrector scheme with an initialization given by an explicit Runge–Kutta method is also used for the time‐variable integration. Moreover, a CFL‐type condition is deduced for the linear problem with a constant bathymetry. To demonstrate the applicability of the model, we considered several test cases. Improved stability is achieved. Copyright © 2011 John Wiley & Sons, Ltd.     

Silicon‐containing trifunctional and tetrafunctional cyanate esters: Synthesis,cure kinetics,and network properties

The synthesis and physical properties of new silicon‐containing polyfunctional cyanate ester monomers methyl[tris(4‐cyanatophenyl)]silane and tetrakis(4‐cyanatophenyl)silane, as well as polycyanurate networks formed from these monomers are reported. The higher crosslinking functionality compared to di(cyanate ester) monomers enables much higher ultimate glass transition temperatures to be obtained as a result of thermal cyclotrimerization. The ability to reach complete conversion is greatly enhanced by cocure of the new monomers with di(cyanate ester) monomers such as 1,1‐bis(4‐cyanatophenyl)ethane. The presence of silicon in these polycyanurate networks imparts improved resistance to rapid oxidation at elevated temperatures, resulting in char yields as high as 70% under nitrogen and 56% in air in the best‐performing networks. The water uptake in the silicon‐containing networks examined is 4–6 wt % after 96 h of immersion at 85 °C, considerably higher than both carbon‐containing and/or di(cyanate ester) analogs. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 767–779     

Immersed boundary method for unsteady kinetic model equations

Predicting unsteady flows and aerodynamic forces for large displacement motion of microstructures requires transient solution of Boltzmann equation with moving boundaries. For the inclusion of moving complex boundaries for these problems, three immersed boundary method flux formulations (interpolation, relaxation, and interrelaxation) are presented. These formulations are implemented in a 2‐D finite volume method solver for ellipsoidal‐statistical (ES)‐Bhatnagar‐Gross‐Krook (BGK) equations using unstructured meshes. For the verification, a transient analytical solution for free molecular 1‐D flow is derived, and results are compared with the immersed boundary (IB)‐ES‐BGK methods. In 2‐D, methods are verified with the conformal, non‐moving finite volume method, and it is shown that the interrelaxation flux formulation gives an error less than the interpolation and relaxation methods for a given mesh size. Furthermore, formulations applied to a thermally induced flow for a heated beam near a cold substrate show that interrelaxation formulation gives more accurate solution in terms of heat flux. As a 2‐D unsteady application, IB/ES‐BGK methods are used to determine flow properties and damping forces for impulsive motion of microbeam due to high inertial forces. IB/ES‐BGK methods are compared with Navier–Stokes solution at low Knudsen numbers, and it is shown that velocity slip in the transitional rarefied regime reduces the unsteady damping force. Copyright © 2015 John Wiley & Sons, Ltd.     

Cantor-type cylindrical-coordinate method for differential equations with local fractional derivatives

In this Letter, we propose to use the Cantor-type cylindrical-coordinate method in order to investigate a family of local fractional differential operators on Cantor sets. Some testing examples are given to illustrate the capability of the proposed method for the heat-conduction equation on a Cantor set and the damped wave equation in fractal strings. It is seen to be a powerful tool to convert differential equations on Cantor sets from Cantorian-coordinate systems to Cantor-type cylindrical-coordinate systems.     

Resonant control of solitons

It is shown that the effect of “scattering on resonance” can be used to control envelope solitons in the driven nonlinear Schrödinger equation. The control occurs by the frequency modulated driving with multiple crossing of the resonant frequency of the soliton.