Soliton dispersion management in nonlinear optical fibers

We consider the concept of quasisoliton propagation in a dispersion management fiber and study the soliton dynamics for soliton dispersion management case, soliton energy control case and guiding center soliton case. We also study the interaction scenario in detail for all the cases.     

Synthesis of broadband and flat parametric gain by idler loss in optical fiber

Besides dispersion engineering, idler-band distributed fiber loss provides a new synthesis freedom to flatten and broaden the gain spectrum for a fiber-optic parametric amplifier. This interesting phenomenon is based on the fact that the power balance between signal and idler is broken by idler loss, which changes the power conversion process in four-wave-mixing. The pump-to-signal conversion efficiency is kept unchanged in spite of the loss.     

Generalized sequential normal compactness in Banach spaces

Normal compactness conditions are important properties of sets, set-valued mappings in variational analysis, which are generalized versions of the classical Lipschitzian property and are essential for the calculus of generalized differentiation theory. In this paper we propose the notion called the generalized sequential normal compactness, and establish its basic properties and calculus in general Banach spaces.     

A newton approach for long term stability studies in power systems

This paper deals with the problem of transient and long term stability of power systems. The issue of assessing both horizons of analysis is particularly focused. This is because the long term stability may be studied by a simplified algebraic model which also captures some dynamic characteristics. Such an approach is called quasi-dynamic model. The idea of analyzing the transient period and migrating to the quasi-dynamic model is addressed in this paper. The theoretical foundation is presented and some tests are carried out in order to validate the approach.     

Three-dimensional rotating flow induced by a shrinking sheet for suction

Series solution of magnetohydrodynamic (MHD) and rotating flow over a porous shrinking sheet is obtained by a homotopy analysis method (HAM). The viscous fluid is electrically conducting in the presence of a uniform applied magnetic field and the induced magnetic field is neglected for small magnetic Reynolds number. Similarity solutions of coupled non-linear ordinary differential equations resulting from the momentum equation are obtained. Convergence of the obtained solutions is ensured by the proper choice of auxiliary parameter. Graphs are sketched and discussed for various emerging parameters on the velocity field. The variations of the wall shear stress f″(0) and ?g′(0) are also tabulated and analyzed.     

Lanczos method for large-scale quaternion singular value decomposition

In many color image processing and recognition applications, one of the most important targets is to compute the optimal low-rank approximations to color images, which can be reconstructed with a small number of dominant singular value decomposition (SVD) triplets of quaternion matrices. All existing methods are designed to compute all SVD triplets of quaternion matrices at first and then to select the necessary dominant ones for reconstruction. This way costs quite a lot of operational flops and CPU times to compute many superfluous SVD triplets. In this paper, we propose a Lanczos-based method of computing partial (several dominant) SVD triplets of the large-scale quaternion matrices. The partial bidiagonalization of large-scale quaternion matrices is derived by using the Lanczos iteration, and the reorthogonalization and thick-restart techniques are also utilized in the implementation. An algorithm is presented to compute the partial quaternion singular value decomposition. Numerical examples, including principal component analysis, color face recognition, video compression and color image completion, illustrate that the performance of the developed Lanczos-based method for low-rank quaternion approximation is better than that of the state-of-the-art methods.

     

Global dynamics and cost-effectiveness analysis of HIV pre-exposure prophylaxis and structured treatment interruptions based on a multi-scale model

Structured treatment interruptions (STI) were proposed to reduce costs and side effects for HIV infected individuals, but whether the possible viral rebound within hosts after treatment interruption would lead to more new infections and additional costs among the population remains unknown. Oral pre-exposure prophylaxis (PrEP) is shown as an effective but expensive strategy to prevent the acquisition of HIV infection. To investigate the effectiveness and cost-effectiveness of STI and PrEP, we develop a multi-scale model linking within-host and between-host dynamics in the presence of drug resistance. Lyapunov functionals are constructed to analyze the global dynamics of the coupled system. We fit this model to the annual AIDS incidence and death data from 1980 to 2014 among men who have sex with men (MSM) in San Francisco and compare the impact of six various intervention scenarios (low, medium, high PrEP coverage with or without STI) on new infections and cost-effectiveness over the next 20 years. We estimate the PrEP efficacy needed to eliminate the disease for different fraction of acquired drug resistance under the above six scenarios. Numerical simulations show that expanding PrEP coverage is very cost-effective, but whether implementing STI is cost-saving depends on the efficacy of second-line drugs. That is to say, STI could always save money, but it may lead to more (less) new infections than continuous therapy and thus less (more) health benefit for high (low) efficacy of second-line drugs. These results provide insights about the long-term effect of STI and PrEP on the disease control and cost-effectiveness.