The Degree Preserving Spanning Tree Problem: Valid Inequalities and Branch-and-cut method

Given a connected undirected graph G, the Degree Preserving Spanning Tree Problem (DPSTP) consists in finding a spanning tree T of G that maximizes the number of vertices that have the same degree in T and in G. In this paper, we introduce Integer Programming formulations, valid inequalities and a Branch-and-cut algorithm for the DPSTP. Reinforced with new valid inequalities, the upper bounds provided by the formulation behind our Branch-and-cut method dominate previous DPSTP bounds in the literature.     

Optimal feedback gains of a delayed proportional-derivative (PD) control for balancing an inverted pendulum

In the dynamics analysis and synthesis of a con-trolled system, it is important to know for what feedback gains can the controlled system decay to the demanded steady state as fast as possible. This article presents a sys-tematic method for finding the optimal feedback gains by taking the stability of an inverted pendulum system with a delayed proportional-derivative controller as an example. First, the condition for the existence and uniqueness of the stable region in the gain plane is obtained by using the D-subdivision method and the method of stability switch. Then the same procedure is used repeatedly to shrink the stable region by decreasing the real part of the rightmost charac-teristic root. Finally, the optimal feedback gains within the stable region that minimizes the real part of the rightmost root are expressed by an explicit formula. With the optimal feedback gains, the controlled inverted pendulum decays to its trivial equilibrium at the fastest speed when the initial val-ues around the origin are fixed. The main results are checked by numerical simulation.     

Optimal time delays in a class of reaction-diffusion equations

ABSTRACT

A class of semilinear parabolic reaction diffusion equations with multiple time delays is considered. These time delays and corresponding weights are to be optimized such that the associated solution of the delay equation is the best approximation of a desired state function. The differentiability of the mapping is proved that associates the solution of the delay equation to the vector of weights and delays. Based on an adjoint calculus, first-order necessary optimality conditions are derived. Numerical test examples show the applicability of the concept of optimizing time delays.     

An analysis of peak overpressures in vented gaseous explosions

Experimental data from vented explosion tests using stoichiometric methane–air and 18% hydrogen–air mixtures in a 63.7 m³ chamber with a 2.7 or 5.4 m² vent are presented. Results from experiments conducted using stoichiometric propane–air in 2.42 m³ vessel with a 0.26 m² vent are also reported. The tests were focused on the effect of fuel, enclosure size, ignition location, vent size, and obstacles on the pressure development of a propagating flame in a vented enclosure. The dependence of the maximum pressure generated on the experimental parameters was analyzed. It was found that the pressure maxima may be caused by pressure transients controlled by the interplay of the maximum-flame area, the burning velocity, and the overpressure generated by an external explosion. A simple model was proposed to estimate the maximum pressure for each of the main pressure transients. The model was found to agree with the experimental data within the experimental uncertainty.     

Dependence of electronic and optical properties of multilayer SiC and GeC on stacking sequence and external electric field

The electronic and optical properties of different stacked multilayer SiC and GeC are investigated with and without external electric field (EEF). The band gaps of multilayer SiC and GeC are found smaller than that of monolayer SiC and GeC due to the interlayer coupling effect. When EEF is applied, the direct band gaps (ΔK–M) of multilayer SiC and direct band gaps (ΔK–K) of multilayer GeC all turn to indirect band gaps (ΔK–G) as the band at the G point drops dramatically toward zero. The imaginary part ε₂(ω)s of multilayer SiC and GeC show that new absorption peaks between 2–5 eV appear when the polarized direction is perpendicular to the layer plane, and new absorption peaks in infrared region appear as the EEF is higher than a certain point when the polarized direction is parallel to the layer plane. Our calculations reveal that different stacking sequences and EEF can provide a wide tunable band structures and optical properties for multilayer SiC and GeC.     

Time reversal acoustic communication receivers: DSP implementation and fast channel estimation

A communication system is implemented on digital signal processors (DSPs) for the underwater acoustic environment. The implemented receiver uses time reversal multi-channel combining followed by a single-channel decision feedback equalizer. Periodic channel estimation is employed to track the channel fluctuations. These techniques are used to mitigate time-varying inter-symbol interference, which is the main challenge in the underwater acoustic channel at operating frequencies greater than 10 kHz. Various optimization tasks are performed to reduce the receiver computational complexity. A fast implementation of the matching pursuit algorithm is tested on the DSP platform. Its performance, in terms of accuracy and run-time, is compared with that of the basic matching pursuit algorithm. Experimental results of the transmission and demodulation of binary phase-shift keying signals at three different symbol rates were obtained in the local Delaware Bay. The low bit error rates demonstrate the effectiveness of our implementation.     

A model of product line design and introduction sequence with reservation utility

Cannibalization is a major concern for a firm when designing a product line. In addition, external options from outside the firm’s product line may also play a significant role. In this paper, we investigate the impact of external options, represented by reservation utility, on product line design and introduction sequence. We find that: (a) heterogeneous reservation utility defines the relative attractiveness of segments and corresponding product line; (b) reservation utility makes it more favorable to introduce products sequentially rather than simultaneously; (c) aggregating segments is an effective way to mitigate cannibalization when it becomes too difficult to manage with different values of reservation utility across multiple segments; and (d) introducing products in a non-monotone order of quality can improve profit from simultaneous introduction when the value of reservation utility of a middle segment is particularly high.     

Nonreciprocal devices in integrated optics

This article reviews the solutions that have been studied for the implementation of nonreciprocal devices in integrated optics. These components, either isolators or circulators, use the nonreciprocal interaction between light and a magnetic medium. The only two isolators that have been experimented on to date are described in detail with their advantages and drawbacks, and some solutions are proposed to overcome the difficulties encountered.     

D-admissible hybrid control of a class of singular systems

This paper mainly studies the problem of designing a hybrid state feedback D-admissible controller for a class of linear and nonlinear singular systems. Based on the relationship between singular discrete systems and singular delta operator systems, several necessary and sufficient conditions for a linear singular delta operator system to be D-admissible (i.e. regular, causal and all finite poles lie in a prescribed circular region) with different representations are derived. Then, the existence conditions and explicit expressions of a desirable D-admissible controller are given by means of matrix inequalities and strict linear matrix inequalities, respectively. We further extend the obtained results to singular delta operator systems with Lipschitz nonlinear perturbations, and the design methods of hybrid controller are presented for the nonlinear case as well. Finally, numerical examples as well as simulations are provided to illustrate the effectiveness of the theoretical outcomes obtained in the paper.     

Synthesis and Characterization of Iron Nanowires

The iron nanowires can be fabricated via the process in which sodium borohydride reduces iron salts in external magnetic field. The iron nanowires are found to be covered by passivated layers of iron oxide which prevent the oxidation of iron nanowires. In this process, the boron will include in iron nanowires. The average length and diameter of iron nanowires is around 1.2 micrometers and 60 nanometers, respectively. According to ICP results, the contents of B and Fe are about 1.98 wt% and 87.04 wt%, respectively, in iron nanowires. A wide variety of equipment is used to investigate the morphological, microchemical, and structural characteristics of the newly synthesized iron nanowires ––– e.g., XRD, FE‐SEM, HR‐TEM, VSM and XANES. XANES analysis indicates the boron in iron nanowires exists in the form of B₂O₃. The saturation magnetization and the coercive force of iron nanowires are 157.93 emu/g and 9.74 Oe, respectively. In‐situ images of synthesized iron nanowires during reduction process in magnetic field are observed by NSRRC transmission X‐ray microscope. Thus, this study develop a novel process to produce iron nanowires with large quantitates and can control its length and diameter by various the concentration of precursors for various applications.