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In the current software development environment, third-party libraries play a crucial role. They provide developers with rich functionality and convenient solutions, speeding up the pace and efficiency of software development. However, with the widespread use of third-party libraries, associated security risks and potential vulnerabilities are increasingly apparent. Malicious attackers can exploit these vulnerabilities to infiltrate systems, execute unauthorized operations, or steal sensitive information, posing a severe threat to software security. Research on third-party libraries in software becomes paramount to address this growing security challenge. Numerous research findings exist regarding third-party libraries' usage, ecosystem, detection, and fortification defenses. Understanding the usage and ecosystem of third-party libraries helps developers comprehend the potential risks they bring and select trustworthy libraries. Third-party library detection tools aid developers in automatically discovering third-party libraries in software, facilitating their management. In addition to detection, fortification defenses are also indispensable. This article profoundly investigates and analyzes this literature, summarizing current research achievements and future development directions. It aims to provide practical and valuable insights for developers and researchers, jointly promoting the healthy development of software ecosystems and better-protecting software from security threats., Comment: 21 pages, 3 figures, one table

The research explores a high irregularity, commonly referred to as intermittency, of the solution to the non-stationary parabolic Anderson problem: \begin{equation*} \frac{\partial u}{\partial t} = \varkappa \mathcal{L}u(t,x) + \xi_{t}(x)u(t,x) \end{equation*} with the initial condition \(u(0,x) \equiv 1\), where \((t,x) \in [0,\infty)\times \mathbb{Z}^d\). Here, \(\varkappa \mathcal{L}\) denotes a non-local Laplacian, and \(\xi_{t}(x)\) is a correlated white noise potential. The observed irregularity is intricately linked to the upper part of the spectrum of the multiparticle Schr\"{o}dinger equations for the moment functions \(m_p(t,x_1,x_2,\cdots,x_p) = \langle u(t,x_1)u(t,x_2)\cdots u(t,x_p)\rangle\). In the first half of the paper, a weak form of intermittency is expressed through moment functions of order $p\geq 3$ and established for a wide class of operators $\varkappa \mathcal{L}$ with a positive-definite correlator $B=B(x))$ of the white noise. In the second half of the paper, the strong intermittency is studied. It relates to the existence of a positive eigenvalue for the lattice Schr\"odinger type operator with the potential $B$. This operator is associated with the second moment $m_2$. Now $B$ is not necessarily positive-definite, but $\sum B(x)\geq 0$.

We study the non-stationary Anderson parabolic problem on the lattice $Z^d$, i.e., the equation \begin{equation}\label{andersonmodel} \begin{aligned} \frac{\partial u}{\partial t} &=\varkappa \mathcal{A}u(t,x)+\xi_{t}(x)u(t,x) u(0,x) &\equiv 1, \, (t,x) \in [0,\infty)\times Z^d. \end{aligned} \end{equation} Here $\mathcal{A}$ is non-local Laplacian, $\xi_t (x), \ t \geq 0, \ x \in Z^d$ is the family of the correlated white noises and $\varkappa >0$ is the diffusion coefficient. The changes of $\varkappa$ (large versus small) are responsible for the qualitative phase transition in the model. At the first step the analysis of the model is reduced to the solution of the stochastic differential equation(SDE) (in the standard It\^{o}'s form) on the weighted Hilbert space $l^2(Z^d,\mu)$ with appropriate measure $\mu$. The equations of first two moments of the solution $u(t,x)$ are derived and studied using the spectral analysis of the corresponding Schr\"{o}dinger operators with special class of the positive definite potentials. The analysis reveals several bifurcations depending on the properties of the kernel of $\mathcal{A}$ and the correlation function in the potential.

Investigations on II-Sn-N2 (II = Mg, Ca) have been started very recently compared to the intense research of the Zn-IV-N2 (IV = Si, Ge, Sn). In this work, we perform a comprehensive study of cation disorder in stoichiometric MgSnN2 and crystal structure characteristic, doping behavior of off-stoichiometric Mg1+xSn1-xN2 (x = -0.8, -0.6, -0.5, -0.4, -0.2, 0.2, 0.4, 0.5, 0.6, 0.8) by using the cluster expansion method and first principles calculations. It is found that cation disorder in stoichiometric MgSnN2 induces a band gap reduction because of a violation of the octet rule. Moreover, the local disorder, namely forming (4,0) or (0,4) tetrahedra, would lead to an appreciable band gap reduction and hinder the enhancement of the optical absorption. An off-stoichiometric Mg/Sn ratio can strongly affect the morphology of Mg1+xSn1-xN2 samples due to the higher ionicity of the Mg-N bonds in comparison with Zn-N bonds. Furthermore, Mg1+xSn1-xN2 compounds show an ambipolar self-doping behavior, i.e., Mg-rich Mg1+xSn1-xN2 show p-type doping while Sn-rich ones exhibit n-type doping owing to the formation of acceptor-type antisite defect MgSn or donor-type antisite defect SnMg, respectively.