A Scattering Problem for a Local Perturbation of an Open Periodic Waveguide

In this paper we consider the propagation of waves in an open waveguide in R^2 where the index of refraction is a local perturbation of a function which is periodic along the axis of the waveguide and equal to one outside a strip of finite width. Motivated by the limiting absorption principle (proven in an ealier paper by the author for the case of an open waveguide in the half space) we formulate a radiation condition which allows the existence of propagating modes and prove uniqueness, existence, and stability of a solution. In the last part we investigate the decay properties of the radiating part in the direction of periodicity and orthogonal to it.

Gas transportation system development in Mongolia under gas prices uncertainty

The paper analyses the stability of a solution to a problem of gas transportation system development in terms of gas import prices. The object of the study is a future gas transportation system in Mongolia. The employed tools are based on an original optimization problem, which is aimed to support decision-making process when choosing capacity, location, and time for investments in gas infrastructure. Different scenarios of gas import prices are considered for Mongolia. A stable solution is defined as the solution that is included in the optimal plans for every scenario. A multi-criteria approach is proposed to expanding the area of stable solutions. In conclusion, the priority areas of gas transportation system development in Mongolia are highlighted.

Ill-posed Boundary-value Problem for a System of Partial Differential Equations with Two Degenerate Lines

This paper is devoted to the investigation of ill-posed boundary-value problem for system of parabolic type equations with changing time direction with two degenerate lines. The problem under consideration is ill-posed in the sense of J. Hadamard, namely, there is no continuous dependence of the solution on the initial data. Such equations have many different applications, for example, describe the processes of heat propagation in inhomogeneous media, the interaction of filtration flows, mass transfer near the surface of an aircraft, and the description of complex viscous fluid flows. As possible applications should also indicate the task of calculating heat exchangers, in which the counter flow principle is used. Theorems on the uniqueness and conditional stability of a solution on a set of well-posedness are proved. We construct a sequence of approximate (regularized) solutions that are stable on the set of well-posedness

One-Pot Processing of Regenerated Cellulose Nanoparticles/Waterborne Polyurethane Nanocomposite for Eco-friendly Polyurethane Matrix

Regenerated cellulose nanoparticles (RCNs) reinforced waterborne polyurethanes (WPU) were developed to improve mechanical properties as well as biodegradability by using a facile, eco-friendly approach, and introducing much stronger chemical bonding than common physical bonding between RCNs and WPU. Firstly, RCNs which have an effect on improving the solubility and stability of a solution, thereby resulting in lower crystallinity, were fabricated by using a NaOH/urea solution. In addition, the stronger chemical bond between RCNs and WPU was here introduced by regarding at which stage in particular added RCNs worked best on strengthening their bond in the process of WPU synthesis. The chemical structure, mechanical, particle size and distribution, viscosity, and thermal properties of the resultant RCNs/WPU nanocomposites were investigated by Fourier transform infrared analysis (FTIR), Zeta-potential analysis, viscometer, thermogravimetric analysis (TGA), Instron, and dynamic mechanical analysis (DMA). The results of all characterizations indicated that the RCNs/WPU-DMF associated with the addition of RCNs in DMF-dispersed step resulted in more effectively crosslinked between WPU and nano-fillers of nanocellulose particles in the dispersion than Acetone and Water-dispersed steps, thereby attributing to novel interactions formed between RCNs and WPU.

Identification of a kernel in an evolutionary integral equation occurring in subdiffusion

An inverse problem to determine a kernel in an evolutionary integral equation occurring in modeling of subdiffusion is considered. The existence, uniqueness and stability of a solution of the inverse problem are proved in an abstract setting. The results are global in time.