The noncompact Schauder fixed point theorem in random normed modules

Random normed modules ($RN$ modules) are a random generalization of ordinary normed spaces, which are usually endowed with the two kinds of topologies -- the $(\varepsilon,\lambda)$-topology and the locally $L^0$-convex topology. The purpose of this paper is to give a noncompact generalization of the classical Schauder fixed point theorem for the development and financial applications of $RN$ modules. Motivated by the randomized version of the classical Bolzano-Weierstrauss theorem, we first introduce the two notions of a random sequentially compact set and a random sequentially continuous mapping under the $(\varepsilon,\lambda)$-topology and further establish their corresponding characterizations under the locally $L^0$-convex topology so that we can treat the fixed point problems under the two kinds of topologies in an unified way. Then we prove our desired Schauder fixed point theorem that in a $\sigma$-stable $RN$ module every continuous (under either topology) $\sigma$-stable mapping $T$ from a random sequentially compact closed $L^0$-convex subset $G$ to $G$ has a fixed point. The whole idea to prove the fixed point theorem is to find an approximate fixed point of $T$, but, since $G$ is not compact in general, realizing such an idea in the random setting forces us to construct the corresponding Schauder projection in a subtle way and carry out countably many decompositions for $T$ so that we can first obtain an approximate fixed point for each decomposition and eventually one for $T$ by the countable concatenation skill. Besides, the new fixed point theorem not only includes as a special case Bharucha-Reid and Mukherjea's famous random version of the classical Schauder fixed point theorem but also implies the corresponding Krasnoselskii fixed point theorem in $RN$ modules.Comment: 37 page

Strategic Preys Make Acute Predators: Enhancing Camouflaged Object Detectors by Generating Camouflaged Objects

Camouflaged object detection (COD) is the challenging task of identifying camouflaged objects visually blended into surroundings. Albeit achieving remarkable success, existing COD detectors still struggle to obtain precise results in some challenging cases. To handle this problem, we draw inspiration from the prey-vs-predator game that leads preys to develop better camouflage and predators to acquire more acute vision systems and develop algorithms from both the prey side and the predator side. On the prey side, we propose an adversarial training framework, Camouflageator, which introduces an auxiliary generator to generate more camouflaged objects that are harder for a COD method to detect. Camouflageator trains the generator and detector in an adversarial way such that the enhanced auxiliary generator helps produce a stronger detector. On the predator side, we introduce a novel COD method, called Internal Coherence and Edge Guidance (ICEG), which introduces a camouflaged feature coherence module to excavate the internal coherence of camouflaged objects, striving to obtain more complete segmentation results. Additionally, ICEG proposes a novel edge-guided separated calibration module to remove false predictions to avoid obtaining ambiguous boundaries. Extensive experiments show that ICEG outperforms existing COD detectors and Camouflageator is flexible to improve various COD detectors, including ICEG, which brings state-of-the-art COD performance.Comment: Accepted at ICLR 202

Study of the Forming Characteristics of Small-Caliber Ammunition with Circumferential MEFP

To study the influence of the structural parameters of the ammunition liner of small-caliber ammunition on the forming characteristics of the projectile, an integrated circumferential multiple explosively formed projectile (MEFP) warhead with an integrated shell and the liner was initially designed, and the wall thickness of the liner is variable. LS-DYNA finite-element software is used to simulate the integral circumferential MEFP of the preliminary design, based on the numerical simulation results, the influence of the thickness at the center of the liner, and the curvature radius of the liner on the shape and velocity of the formed projectile. The numerical simulation results show that when the thickness of the center of the liner is constant and the curvature radius increases gradually, the velocity of the formed projectile decreases and the length: Diameter ratio of formed projectile decreases gradually. When the curvature radius of the liner remains unchanged, the velocity of the formed projectile decreases with the increase of the thickness of the center of the liner, and the shape of the formed projectile does not change significantly. The results show that when the design of integrating the shell and the liner was adopted for the integral circumferential MEFP warhead, the shape of the formed projectile is greatly affected by the curvature radius of the liner (curvature radius of inner and outer walls of the liner), but less by the thickness of the center of the liner. The velocity of the formed projectile is affected by the curvature radius of the inner and outer walls of the liner and the thickness of the center of the liner. Moreover, the influence of the thickness of the center of the liner on the velocity of the formed projectile is greater than that of the curvature radius of the outer wall of the liner

Low-Cost Metamaterial Antennas: Forward-Looking Imaging Experiment and Analysis

A phase error correction method is proposed to compensate for the phase error in super-resolution correlated imaging based on metamaterial antennas. The varying carrier frequencies of a metamaterial antenna can generate the random radiation field for super-resolution correlation imaging, but the variation of the signal carrier frequency leads to large phase errors in the imaging results. In this proposed method, the sampling matrix in the super-resolution correlated imaging algorithm is used to compensate for the phase errors. Each element of the matrix is multiplied by a compensation phase corresponding to the phase error, and the error is subtly removed from the algorithm. In the experiment, the antenna pattern at each frequency of the metamaterial antenna is measured and recorded. In addition, an external field experiment is also carried out, and the collected data are imaged with the improved algorithm. Experimental results show that this technology can effectively solve the effect of phase errors on imaging results caused by signal carrier frequency changes

Development of SiC Nanoparticles and Second Phases Synergistically Reinforced Mg-Based Composites Processed by Multi-Pass Forging with Varying Temperatures

In this study, SiC nanoparticles were added into matrix alloy through a combination of semisolid stirring and ultrasonic vibration while dynamic precipitation of second phases was obtained through multi-pass forging with varying temperatures. During single-pass forging of the present composite, as the deformation temperature increased, the extent of recrystallization increased, and grains were refined due to the inhibition effect of the increasing amount of dispersed SiC nanoparticles. A small amount of twins within the SiC nanoparticle dense zone could be found while the precipitated phases of Mg17Al12 in long strips and deformation bands with high density dislocations were formed in the particle sparse zone after single-pass forging at 350 °C. This indicated that the particle sparse zone was mainly deformed by dislocation slip while the nanoparticle dense zone may have been deformed by twinning. The yield strength and ultimate tensile strength of the composites were gradually enhanced through increasing the single-pass forging temperature from 300 °C to 400 °C, which demonstrated that initial high forging temperature contributed to the improvement of the mechanical properties. During multi-pass forging with varying temperatures, the grain size of the composite was gradually decreased while the grain size distribution tended to be uniform with reducing the deformation temperature and extending the forging passes. In addition, the amount of precipitated second phases was significantly increased compared with that after multi-pass forging under a constant temperature. The improvement in the yield strength of the developed composite was related to grain refinement strengthening and Orowan strengthening resulting from synergistical effect of the externally applied SiC nanoparticles and internally precipitated second phases