There is increasing evidence that conventional cold dark matter (CDM) models lead to conflicts between observations and numerical simulations of dark matter halos on subgalactic scales, which rules out the favored candidates for CDM, namely weakly interacting massive particles (WIMPs). We propose a mechanism of nonthermal production of WIMPs and study its implications on the power spectrum. Our results show that, in this context, WIMPs as candidates for dark matter can work well both on large scales and on subgalactic scales.

We present a novel method of analysis and prove finite time asymptotically self‐similar blowup of the De Gregorio model [13, 14] for some smooth initial data on the real line with compact support. We also prove self‐similar blowup results for the generalized De Gregorio model [41] for the entire range of parameter on ℝ or S1 for Hölder‐continuous initial data with compact support. Our strategy is to reformulate the problem of proving finite time asymptotically self‐similar singularity into the problem of establishing the nonlinear stability of an approximate self‐similar profile with a small residual error using the dynamic rescaling equation. We use the energy method with appropriate singular weight functions to extract the damping effect from the linearized operator around the approximate self‐similar profile and take into account cancellation among various nonlocal terms to establish stability analysis. We remark that our analysis does not rule out the possibility that the original De Gregorio model is well‐posed for smooth initial data on a circle. The method of analysis presented in this paper provides a promising new framework to analyze finite time singularity of nonlinear nonlocal systems of partial differential equations. © 2021 Wiley Periodicals LLC.

Random Testing (RT) is an important and fundamental approach to testing computer software. Adaptive Random Testing (ART) has been proposed to improve the faultdetection capability of RT. ART employs the location information of successful test cases (those that have been executed but not revealed a failure) to enforce an even spread of random test cases across the input domain. Distance-based ART (D-ART) and Restriction-based ART (R-ART) are the first two ART methods, which have considerably improved the fault-detection capability of RT. Both these methods, however, require additional computation to ensure the generation of evenly spread test cases. To reduce the overhead in test case generation, we present in this paper a new ART method using the notion of iterative partitioning. The input domain is divided into equally sized cells by a grid. The grid cells are categorized into three different groups according to their relative locations to successful test cases. In this way, our method can easily identify those grid cells that are far apart from all successful test cases for test case generation. Our method significantly reduces the time complexity, while keeping the high fault-detection capability.

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