Nonextensive effects on QCD chiral phase diagram and baryon-number fluctuations within Polyakov-Nambu-Jona-Lasinio model

In this paper, a version of the Polyakov-Nambu-Jona-Lasinio (PNJL) model based on nonextensive statistical mechanics is presented. This new statistics summarizes all possible factors that violate the assumptions of the Boltzmann-Gibbs (BG) statistics to a dimensionless nonextensivity parameter $q$, and when $q$ tends to 1, it returns to the BG case. Within the nonextensive PNJL model, we found that as $q$ increases, the location of the critical end point (CEP) exhibits non-monotonic behavior. That is, for $q<1.15$, CEP moves in the direction of lower temperature and larger quark chemical potential. But for $q>1.15$, CEP turns to move in the direction of lower temperature and lower quark chemical potential. In addition, we studied the moments of the net-baryon number distribution, that is, the variance ($\sigma^{2}$), skewness (S), and kurtosis ($\kappa$). Our results are generally consistent with the latest experimental data, especially for $\sqrt{S_{NN}}>19.6\ \mathrm{GeV}$, when $q$ is set to $1.07$

Nonsurjective zero product preservers between matrices over an arbitrary field

In this paper, we give concrete descriptions of additive or linear disjointness preservers between matrix algebras over an arbitrary field $\mathbb{F}$ of different sizes. In particular, we show that a linear map $\Phi: M_n(\mathbb{F}) \rightarrow M_r(\mathbb{F})$ preserving zero products carries the form $$\Phi(A)= S\begin{pmatrix} R\otimes A & 0 \cr 0 & \Phi_0(A)\end{pmatrix} S^{-1},$$ for some invertible matrices $R$ in $M_k(\mathbb{F})$, $S$ in $M_r(\mathbb{F})$ and a zero product preserving linear map $\Phi_0: M_n(\mathbb{F}) \rightarrow M_{r-nk}(\mathbb{F})$ with range consisting of nilpotent matrices. Here, either $R$ or $\Phi_0$ can be vacuous. The structure of $\Phi_0$ could be quite arbitrary. We classify $\Phi_0$ with some additional assumption. When $\Phi(I_n)$ has a zero nilpotent part, especially when $\Phi(I_n)$ is diagonalizable, we have $\Phi_0(X)\Phi_0(Y) = 0$ for all $X, Y$ in $M_n(\mathbb{F})$, and we give more information about $\Phi_0$ in this case. Similar results for double zero product preservers and orthogonality preservers are obtained.Comment: 29 page

DNA Repair Pathways in Cancer Therapy and Resistance

DNA repair pathways are triggered to maintain genetic stability and integrity when mammalian cells are exposed to endogenous or exogenous DNA-damaging agents. The deregulation of DNA repair pathways is associated with the initiation and progression of cancer. As the primary anti-cancer therapies, ionizing radiation and chemotherapeutic agents induce cell death by directly or indirectly causing DNA damage, dysregulation of the DNA damage response may contribute to hypersensitivity or resistance of cancer cells to genotoxic agents and targeting DNA repair pathway can increase the tumor sensitivity to cancer therapies. Therefore, targeting DNA repair pathways may be a potential therapeutic approach for cancer treatment. A better understanding of the biology and the regulatory mechanisms of DNA repair pathways has the potential to facilitate the development of inhibitors of nuclear and mitochondria DNA repair pathways for enhancing anticancer effect of DNA damage-based therapy