Compact Difference Schemes for the Multidimensional Klein–Gordon Equation

Differential Equations - Stable compact difference schemes of $$4+2$$ and $$4+4 $$ approximation orders are considered and studied on standard stencils for the multidimensional Klein–Gordon...     

Selection of crude Solidago virgaurea L. ssp. extracts based on two fast and efficient chromatographic methods (high-performance thin-layer chromatography or high-performance liquid chromatography) for the quantification of total saponins

JPC – Journal of Planar Chromatography – Modern TLC - A previous study on Solidago virgaurea extracts showed an inhibiting activity of Candida albicans yeast—hyphal transition due...     

Analysis of expanded mixed finite element methods for the generalized forchheimer flows of slightly compressible fluids

The nonlinear Forchheimer equations are used to describe the dynamics of fluid flows in porous media when Darcy's law is not applicable. In this article, we consider the generalized Forchheimer flows for slightly compressible fluids, and then study the expanded mixed finite element method applied to the initial boundary value problem for the resulting degenerate parabolic equation for pressure. The bounds for the solutions, time derivative, and gradient of solutions are established. Utilizing the monotonicity properties of Forchheimer equation and boundedness of solutions, a priori error estimates for solution are obtained in ‐norm, ‐norm as well as for its gradient in ‐norm for all . Optimal ‐error estimates are shown for solutions under some additional regularity assumptions. Numerical results using the lowest order Raviart–Thomas mixed element confirm the theoretical analysis regarding convergence rates. Published 2015. Numer Methods Partial Differential Eq 32: 60–85, 2016     

The second law, Maxwell's demon, and work derivable from quantum heat engines

With a class of quantum heat engines which consists of two-energy-eigenstate systems undergoing, respectively, quantum adiabatic processes and energy exchanges with heat baths at different stages of a cycle, we are able to clarify some important aspects of the second law of thermodynamics. The quantum heat engines also offer a practical way, as an alternative to Szilard's engine, to physically realize Maxwell's demon. While respecting the second law on the average, they are also capable of extracting more work from the heat baths than is otherwise possible in thermal equilibrium.     

Active Q switching of a fiber laser with a microsphere resonator

We propose and demonstrate an active Q-switched fiber laser using a high-Q microsphere resonator as the Q-switching element. The laser cavity consists of an Er-doped fiber as the gain medium, a glass microsphere reflector (coupled through a fiber taper) at one end of the cavity, and a fiber Bragg grating reflector at the other end. The reflectivity of the microsphere is modulated by changing the gap between the microsphere and the fiber taper. Active Q switching is realized by oscillating the microsphere in and out of contact with the taper. Using this novel technique, we have obtained giant pulses (maximum peak power approximately 102 W, duration approximately 160 ns) at a low pump-power threshold (approximately 3 mW).     

The radiation of polarized matter in a wave-guide of general cross-section with many dielectrics II

The second part of the work deals with the boundary conditions and derives the relations for unknown boundary functions. They are obtained as a system of integral equations.     

Combined Optimal Stopping and Singular Stochastic Control

In this article, a simple of combined singular stochastic control and optimal stopping in the jump-diffusion model is formulated and solved. We give sufficient conditions for the existence of an optimal strategy which has the same form as in continuous case given by Davis and Zervos [3 Davis , M.H.A. , and Zervos , M. 1994. A problem of singular stochastic control with discretionary stopping. Annals of Applied Probility 4(1):226–240. [Google Scholar]] and also Karatzas et al. [5 Karatzas , I. , Ocone , D. , Wang , H. , and Zervos , M. 2000 . Finite-fuel singular control with discretionary stopping . Stochastics and Stochastics Reports 71 : 1 – 50 .[Taylor & Francis Online] , [Google Scholar]]. This result is applied to solve explicitly an example of such problem.