This paper gives a rigorous and greatly simplified proof of Guttman's theorem for the least upper-bound dimensionality of arbitrary real symmetric matrices S, where the points embedded in a real Euclidean space subtend distances which are strictly monotone with the off-diagonal elements of S. A comparable and more easily proven theorem for the vector model is also introduced. At most n-2 dimensions are required to reproduce the order information for both the distance and vector models and this is true for any choice of real indices, whether they define a metric space or not. If ties exist in the matrices to be analyzed, then greatest lower bounds are specifiable when degenerate solutions are to be avoided. These theorems have relevance to current developments in nonmetric techniques for the monotone analysis of data matrices.

We derive and analyse well-posed boundary conditions for the linear shallow water wave equation. The analysis is based on the energy method and it identifies the number, location and form of the boundary conditions so that the initial boundary value problem is well-posed. A finite-volume method is developed based on the summation-by-parts framework with the boundary conditions implemented weakly using penalties. Stability is proven by deriving a discrete energy estimate analogous to the continuous estimate. The continuous and discrete analysis covers all flow regimes. Numerical experiments are presented verifying the analysis.

In light of inconclusive findings on the effect of political connections, this study explores conditions that affect the effectiveness of political connections on firm performance in democratic systems. First, using a resource dependence rationale, this study stresses the importance of variation in political connections and classifies direct and indirect political connections based on sources of power and the mechanisms for developing connections. Second, this study recognizes that influencing political outcomes is an entire political process in which political power matters. Furthermore, as power is central to the resource dependence rationale unlike exchange in transaction cost economics, this study explores how the effectiveness of political connections is contingent on the dynamics of de jure political power. We find that the effect of direct political connections is susceptible to changes in de jure political power due to its dyadic relationship with de jure power, while indirect political connections are more robust to such changes due to their connections with informal networks holding de facto political power. Further, the positive effects of political connections on firm performance are mediated by operational capability.

Most vibration-based energy harvesters, including piezoelectric harvester system, perform efficiently at only its resonant frequency as linear resonators, usually at very high frequency which are out of the range of frequency of interest. In real life applications, these linear resonators are impractical since real ambient vibrations are simply having varying lower frequencies. Hence, design a tuneable vibration energy harvester at a lower and useful frequency range of interest are essential in allowing promising energy output to meet intended power input at a more practical approach. In this paper, the piezoelectric voltage energy harvester (PVEH) was designed with a flexible fixture with the aim to reduce its first fundamental natural frequency. Two thickness of elastic fixtures were applied to generate power on PVEH. Three experimental techniques were used to measure the vibration characteristics of PVEH. First, the full-field optical technique, amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) measured simultaneously the resonant frequencies and mode shapes. This is followed by the pointwise measurement system, laser Doppler vibrometer (LDV) in which the resonant frequencies were measured by dynamic signal swept-sine analysis. The resonant frequencies and anti-resonant frequencies were also obtained by impedance analysis. The results obtained from experimental measurements were compared with finite element numerical calculation. It is found that the boundary conditions under the elastic fixtures can effectively reduce the resonant frequency of the PVEH with a reasonable voltage output. The fundamental natural frequency of PVEH with the thickness of 0.58-mm elastic fixture is reduced to 37 Hz maintaining at 7.1 volts (1.2 mW), in comparison with the natural frequency on cantilevered PVEH at 78 Hz that produces 7.7 volts (6.5 mW).

The lattice Boltzmann method is employed to simulate the steady flow in a two-dimensional lid-driven semi-elliptical cavity. Reynolds number (Re) and vertical-to-horizontal semi-axis ratio (D) are in the range of 500-5000 and 0.1-4, respectively. The effects of Re and D on the vortex structure and pressure field are investigated, and the evolutionary features of the vortex structure with Re and D are analyzed in detail. Simulation results show that the vortex structure and its evolutionary features significantly depend on Re and D. The steady flow is characterized by one vortex in the semi-elliptical cavity when both Re and D are small. As Re increases, the appearance of the vortex structure becomes more complex. When D is less than 1, increasing D makes the large vortexes more round, and the evolution of the vortexes with D becomes more complex with increasing Re. When D is greater than 1, the steady flow consists of a series of large vortexes which superimpose on each other. As Re and D increase, the number of the large vortexes increases. Additionally, a small vortex in the upper-left corner of the semi-elliptical cavity appears at a large Re and its size increases slowly as Re increases. The highest pressures appear in the upper-right corner and the pressure changes drastically in the upper-right region of the cavity. The total pressure differences in the semi-elliptical cavity with a fixed D decrease with increasing Re. In the region of themain vortex, the pressure contours nearly coincide with the streamlines, especially for the cavity flow with a large Re.

In this work, the hybrid solution reconstruction formulation proposed by Luo et al. [H. Luo, H. Dai, P. F. de Sousa and B. Yin, On the numerical oscillation of the direct-forcing immersed-boundary method for moving boundaries, Computers & Fluids, 56 (2012), pp. 61–76] for the finite-difference discretization on Cartesian meshes is implemented in the finite-element framework of the local domain-free discretization (DFD) method to reduce the numerical oscillations in the simulation of moving-boundary flows. The reconstruction formulation is applied at fluid nodes in the immediate vicinity of the immersed boundary, which combines weightly the local DFD solution with the specific values obtained via an approximation of quadratic polynomial in the normal direction to the wall. The quadratic approximation is associated with the no-slip boundary condition and the local simplified momentum equation. The weighted factor suitable for unstructured triangular and tetrahedral meshes is constructed, which is related to the local mesh intervals near the immersed boundary and the distances from exterior dependent nodes to the boundary. Therefore, the reconstructed solution can account for the smooth movement of the immersed boundary. Several numerical experiments have been conducted for two- and three-dimensional moving-boundary flows. It is shown that the hybrid reconstruction approach can work well in the finite-element context and effectively reduce the numerical oscillations with little additional computational cost, and the spatial accuracy of the original local DFD method can also be preserved.

In this paper, we consider the dependence of eigenvalues of sixth-order boundary value problems on the boundary. We show that the eigenvalues depend not only continuously but also smoothly on boundary points, and that the derivative of the $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}n$th eigenvalue as a function of an endpoint satisfies a first-order differential equation. In addition, we prove that as the length of the interval shrinks to zero all higher eigenvalues of such boundary value problems march off to plus infinity. This is also true for the first (that is, lowest) eigenvalue.

We develop the dimension-reduced hyperbolic moment method for the Boltzmann equation, to improve solution efficiency using a numerical regularized moment method for problems with low-dimensional macroscopic variables and high-dimensional microscopic variables. In the present work, we deduce the globally hyperbolic moment equations for the dimension-reduced Boltzmann equation based on the Hermite expansion and a globally hyperbolic regularization. The numbers of Maxwell boundary condition required for well-posedness are studied. The numerical scheme is then developed and an improved projection algorithm between two different Hermite expansion spaces is developed. By solving several benchmark problems, we validate the method developed and demonstrate the significant efficiency improvement by dimension-reduction.