Two questions on stable equivalences of Morita type

It is well-known that derived equivalences preserve tensor products and trivial extensions. We disprove both constructions for stable equivalences of Morita type.Comment: 9 page

Connecting Software Metrics across Versions to Predict Defects

Accurate software defect prediction could help software practitioners allocate test resources to defect-prone modules effectively and efficiently. In the last decades, much effort has been devoted to build accurate defect prediction models, including developing quality defect predictors and modeling techniques. However, current widely used defect predictors such as code metrics and process metrics could not well describe how software modules change over the project evolution, which we believe is important for defect prediction. In order to deal with this problem, in this paper, we propose to use the Historical Version Sequence of Metrics (HVSM) in continuous software versions as defect predictors. Furthermore, we leverage Recurrent Neural Network (RNN), a popular modeling technique, to take HVSM as the input to build software prediction models. The experimental results show that, in most cases, the proposed HVSM-based RNN model has a significantly better effort-aware ranking effectiveness than the commonly used baseline models

Higman ideal, stable Hochschild homology and Auslander-Reiten conjecture

Let A and B be two finite dimensional algebras over an algebraically closed field, related to each other by a stable equivalence of Morita type. We prove that A and B have the same number of isomorphism classes of simple modules if and only if their 0-degree Hochschild Homology groups HH 0(A) and HH 0(B) have the same dimension. The first of these two equivalent conditions is claimed by the Auslander-Reiten conjecture. For symmetric algebras we will show that the Auslander-Reiten conjecture is equivalent to other dimension equalities, involving the centers and the projective centers of A and B. This motivates our detailed study of the projective center, which now appears to contain the main obstruction to proving the Auslander-Reiten conjecture for symmetric algebras. As a by-product, we get several new invariants of stable equivalences of Morita typ

Traveling wavefronts of a prey–predator diffusion system with stage-structure and harvesting

AbstractFrom a biological point of view, we consider a prey–predator-type free diffusion fishery model with stage-structure and harvesting. First, we study the stability of the nonnegative constant equilibria. In particular, the effect of harvesting on the stability of equilibria is discussed and supported with numerical simulation. Then, employing the upper and lower solution method, we show that when the wave speed is large enough there exists a traveling wavefront connecting the zero solution to the positive equilibrium of the system. Numerical simulation is also carried out to illustrate the main result