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During software evolution, it is advocated that test code should co-evolve with production code. In real development scenarios, test updating may lag behind production code changing, which may cause the project to fail to compile or bring other troubles. Existing techniques based on pre-trained language models can be adopted to repair obsolete tests caused by such unsynchronized code changes, especially syntactic-related ones. However, the lack of target-oriented contextual information affects repair accuracy on large-scale projects. Starting from an obsoleted test, the key challenging task is precisely identifying and constructing Test-Repair-Oriented Contexts (TROCtx) from the whole repository within a limited token size. In this paper, we propose SynBCIATR (Syntactic-Breaking-Change-Induced Automated Test Repair), a novel approach to automatically repair obsolete test cases via precise and concise TROCtx construction. Inspired by developers' programming practices of the task, we design three types of TROCtx: class contexts, usage contexts, and environment contexts. For every type of TROCtx, SynBCIATR automatically collects the changed-token-related code information through static analysis techniques. Then it generates reranking queries to identify the most relevant TROCtxs, which will be taken as the repair-required key context and be input to the Large Language Model for the final test repair. To evaluate the effectiveness of SynBCIATR, we construct a benchmark dataset that contains diverse syntactic breaking changes. The experimental results show that SynBCIATR outperforms baseline approaches both on textual- and intent-matching metrics. With the augmentation of TROCtx constructed by SynBCIATR, hallucinations are reduced by 57.1%.

Facing the drastic climate changes, current strategies for enhancing carbon dioxide stocks need to be thoroughly honed. To address the problem, we first built a carbon sequestration growth model driven by growth rate dependency (GRDM). We abstracted the carbon cycling system into the process of photosynthesis, the humidity fluctuation, and the original storage of carbon in the trees. In the photosynthesis model, we considered various factors, including transition rate of absorption and organic matter production. We also designed an Economic Return Evaluation Model (EREM) to estimate the optimal distribution of trees in the forest based on the utility function. Maximizing the utility brought by the amount of carbon storage, we derived the equation for profit optimization with the constraints of total economic expenses allowed. To assess its performance, we took an object-oriented approach, simulated an ideal forest by placing instances of trees and plotted a time-dependent forest composition graph. After proper normalization of climate and economic data, we also make predictions for 169 worldwide forest-covered countries. Our model further suggests high sensitivity and robustness with a similar trend of overall utility when environmental aridity or proportion of harvested woods are varied. Finally, we apply the model to Georgia temperate deciduous forest, and we evaluate the carbon storage ability to adjust the Red Spruce based on available biological literature research. We recognize that while the model is preliminary in its failure to identify a diverse array of variables, it has encapsulated key features of idealized forests.

Let $G=(V,E)$ be a locally finite connected weighted graph, and $\Omega$ be an unbounded subset of $V$. Using Rothe's method, we study the existence of solutions for the semilinear heat equation $\partial_tu+|u|^{p-1}\cdot u=\Delta u~(p\ge1)$ and the parabolic variational inequality \begin{eqnarray*} \int_{\Omega^\circ} \partial_tu\cdot(v-u)\,d\mu\ge \int_{\Omega^\circ}(\Delta u+f)\cdot(v-u)\,d\mu \qquad\mbox{for any }v\in \mathcal{H}, \end{eqnarray*} where $\mathcal{H}=\{u\in W^{1,2}(V):u=0\mbox{ on }V\backslash\Omega^\circ\}$.

We study a nonlinear wave equation on finite connected weighted graphs. Using Rothe's and energy methods, we prove the existence and uniqueness of solution under certain assumption. For linear wave equation on graphs, Lin and Xie \cite{Lin-Xie} obtained the existence and uniqueness of solution. The main novelty of this paper is that the wave equation we considered has the nonlinear damping term $|u_t|^{p-1}\cdot u_t$ ($p>1$).

Let $G=(V, E)$ be a finite weighted graph, and $\Omega\subseteq V$ be a domain such that $\Omega^\circ\neq\emptyset$. In this paper, we study the following initial boundary problem for the non-homogenous wave equation \begin{equation*} \left\{ \begin{aligned} &\partial_t^2 u(t,x)-\Delta_\Omega u(t,x)=f(t,x),\qquad&&(t,x)\in[0,\infty)\times \Omega^\circ,\\ &u(0,x)=g(x),\qquad&& x\in\Omega^\circ,\\ &\partial_tu(0,x)=h(x),\qquad&& x\in\Omega^\circ,\\ &u(t,x)=0,\qquad&&(t,x)\in[0,\infty)\times\partial \Omega, \end{aligned} \right. \end{equation*} where $\Delta_\Omega$ denotes the Dirichlet Laplacian on $\Omega^\circ$. Using Rothe's method, we prove that the above wave equation has a unique solution.