The truncated singular value decomposition has been widely used in many areas of science including engineering, and statistics, etc. In this paper, the original truncated complex singular value decomposition problem is formulated as a Riemannian optimization problem on a product of two complex Stiefel manifolds, a practical algorithm based on the generic Riemannian trust-region method of Absil et al. is presented to solve the underlying problem, which enjoys the global convergence and local superlinear convergence rate. Numerical experiments are provided to illustrate the efficiency of the proposed method. Comparisons with some classical Riemannian gradient-type methods, the existing Riemannian version of limited-memory BFGS algorithms in the MATLAB toolbox Manopt and the Riemannian manifold optimization library ROPTLIB, and some latest infeasible methods for solving manifold optimization problems, are also provided to show the merits of the proposed approach.

The study prepares glass fiber reinforced composites through Vacuum Assisted Resin Infusion (VARI) process, selects glass fibers of different specifications, and studies the effects of lay-up mode, thickness, simulated normal incident angle, and temperature of fiber composites s on their ballistic performance. Results show that with slimmer fiber monofilament, reinforced materials perform better in ballistics; the lay-up mode has limited influence on ballistic performance; the relationship between thickness and ballistic performance is positively linear; and the relationship between normal incident angle and ballistic performance is parabolic. Compared with room temperature conditions, the ballistic performance of composites does not decrease and even increases slightly under low temperatures. Yet, the performance decreases sharply at high temperatures.

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The purification of indoor pathogenic microorganisms has become a topic of concern. The use of nonwoven media air filters causes high resistance, and the problem of noise limited their application under high air volume. Thus, we propose a micro-electrostatic filter, which has improved performance compared to an electrostatic filter, with a new type of cylindrical structure to tackle indoor pathogenic microbial aerosol pollution. Through simulation, it is found that the filtration performance of a cylindrical structure is better than that of a plate structure under all simulation conditions. For particles larger than 1 μm, the shortest theoretical length of the dust collecting plate required for the cylindrical structure is 34% shorter than that for the plate structure. For 0.1 μm particles, the filtration efficiency of the cylindrical structure is nearly 20~30% (the maximum value is 29.76%) higher than that of the plate structure, while the air velocity is 1.5 m/s~2.5 m/s. The resistance of the cylindrical micro-electrostatic filter is only half of that of the combined plate type micro-electrostatic filter, indicating that the cartridge structure has enormous energy-saving potential. The introduction of the quality factor further proves that the integrated filtration performance of the cartridge micro-electrostatic filter is better. The application of cylindrical micro-electrostatic filters in HVAC systems can help improve indoor air quality and reduce health risks.