Sufficient dimension reduction for the conditional mean with a categorical predictor in multivariate regression

Recent sufficient dimension reduction methodologies in multivariate regression do not have direct application to a categorical predictor. For this, we define the multivariate central partial mean subspace and propose two methodologies to estimate it. The first method uses the ordinary least squares. Chi-squared distributed statistics for dimension tests are constructed, and an estimate of the target subspace is consistent and efficient. Moreover, the effects of continuous predictors can be tested without assuming any model. The second method extends Iterative Hessian Transformation to this context. For dimension estimation, permutation tests are used. Simulated and real data examples for illustrating various properties of the proposed methods are presented.     

Robust memory state feedback model predictive control for discrete-time uncertain state delayed systems

In this paper, we propose a memory state feedback model predictive control (MPC) law for a discrete-time uncertain state delayed system with input constraints. The model uncertainty is assumed to be polytopic, and the delay is assumed to be unknown, but with a known upper bound. We derive a sufficient condition for cost monotonicity in terms of LMI, which can be easily solved by an efficient convex optimization algorithm. A delayed state dependent quadratic function with an estimated delay index is considered for incorporating MPC problem formulation. The MPC problem is formulated to minimize the upper bound of infinite horizon cost that satisfies the sufficient conditions. Therefore, a less conservative sufficient conditions in terms of linear matrix inequality (LMI) can be derived to design a more robust MPC algorithm. A numerical example is included to illustrate the effectiveness of the proposed method.     

Bruhat order, smooth Schubert varieties, and hyperplane arrangements

The aim of this article is to link Schubert varieties in the flag manifold with hyperplane arrangements. For a permutation, we construct a certain graphical hyperplane arrangement. We show that the generating function for regions of this arrangement coincides with the Poincaré polynomial of the corresponding Schubert variety if and only if the Schubert variety is smooth. We give an explicit combinatorial formula for the Poincaré polynomial. Our main technical tools are chordal graphs and perfect elimination orderings.     

Ballast Water Treatment Test at Pilot-Scale Using an Underwater Capillary Discharge Device

We demonstrated a pilot-scaled underwater plasma discharge device for the treatment of ballast water (5 ton/h). Phytoplankton and microorganisms in the ballast water were successfully removed using underwater plasma with capillary electrodes. Microorganisms between 10 and 50 μm in the ballast water were eliminated with an efficiency of 99.9% as well as heterotrophic bacteria with an efficiency of 92.7%.     

Triple-band metamaterial absorber based on single resonator

The single resonator generally reveals a single absorption band, and the resonators with different sizes or shapes have to be arranged in order to achieve multi-absorption bands. We propose the triple-band metamaterial absorber by utilizing only single resonator. Meta-atoms are made of the toothed-wheel shape metallic pattern and a continuous metallic plane, separated by a dielectric layer. The first and the third absorption bands are induced by the fundamental and the third-harmonic magnetic resonances, respectively, and the second absorption band is induced by the magnetic resonance relevant to two grooves. In addition, the diffraction peak appears between the second and the third absorption bands, due to the surface currents which are separated between the upper and the lower metallic pattern parts. The proposed structure is scalable to smaller size for the infrared and the visible regimes.     

Efficiency of non-dimensional analysis for absolute nodal coordinate formulation

Nonlinear Dynamics - Absolute nodal coordinate formulation was developed in the mid-1990s. The adoption of the continuum mechanics concept has allowed large displacements and large deformations to...     

Quantitative calculations on the reoxidation behavior of oxide reduction system for pyroprocessing

This paper discusses the development of a separation method for isolation of ¹⁷¹Tm from a half-gram irradiated erbium target in support of stockpile stewardship and astrophysics research. The developed procedure is based on cation exchange separation using alpha-hydroxyisobutyric acid (α-HIBA) as chelating agent. It is able to achieve either a decontamination factor of 1.4(4) × 10⁵ with 68.9(3) % recovery or 95.4(3) % recovery with a decontamination factor of 5.82(7) × 10³ for a mock 500-mg target containing 17.9 mg thulium in a single pass-through at room temperature.     

Development on the reconstruction of photothermal imaging method for subsurface structure

Journal of Visualization - The photothermal imaging technique is a nondestructive inspection technique that visualizes the inside of a metal by utilizing the photothermal effect. Although the...     

Variational boundary integral approach for asymmetric impinging jets of arbitrary two‐dimensional nozzle

We consider asymmetric impinging jets issuing from an arbitrary nozzle. The flow is assumed to be two‐dimensional, inviscid, incompressible, and irrotational. The impinging jet from an arbitrary nozzle has a couple of separated infinite free boundaries, which makes the problem hard to solve. We formulate this problem using the stream function represented with a specific single layer potential. This potential can be extended to the surrounding region of the jet flow, and this extension can be proved to be a bounded function. Using this fact, the formulation yields the boundary integral equations on the entire nozzle and free boundary. In addition, a boundary perturbation produces an extraordinary boundary integral equation for the boundary variation. Based on these variational boundary integral equations, we can provide an efficient algorithm that can treat with the asymmetric impinging jets having arbitrarily shaped nozzles. Particularly, the proposed algorithm uses the infinite computational domain instead of a truncated one. To show the convergence and accuracy of the numerical solution, we compare our solutions with the exact solutions of free jets. Numerical results on diverse impinging jets with nozzles of various shapes are also presented to demonstrate the applicability and reliability of the algorithm.