On a class of inverse quadratic eigenvalue problem

AbstractIn this paper, we first give the representation of the general solution of the following inverse monic quadratic eigenvalue problem (IMQEP): given matrices Λ=diag{λ1,…,λp}∈Cp×p, λi≠λj for i≠j, i,j=1,…,p, X=[x1,…,xp]∈Cn×p, rank(X)=p, and both Λ and X are closed under complex conjugation in the sense that λ2j=λ̄2j−1∈C, x2j=x̄2j−1∈Cn for j=1,…,l, and λk∈R, xk∈Rn for k=2l+1,…,p, find real-valued symmetric matrices D and K such that XΛ2+DXΛ+KX=0. Then we consider a best approximation problem: given D̃,K̃∈Rn×n, find (Dˆ,Kˆ)∈SDK such that ‖(Dˆ,Kˆ)−(D̃,K̃)‖W=min(D,K)∈SDK‖(D,K)−(D̃,K̃)‖W, where ‖⋅‖W is a weighted Frobenius norm and SDK is the solution set of IMQEP. We show that the best approximation solution (Dˆ,Kˆ) is unique and derive an explicit formula for it

Solutions to an inverse monic quadratic eigenvalue problem

AbstractGiven n+1 pairs of complex numbers and vectors (closed under complex conjugation), the inverse quadratic eigenvalue problem is to construct real symmetric or anti-symmetric matrix C and real symmetric matrix K of size n×n so that the quadratic pencil Q(λ)=λ2In+λC+K has the given n+1 pairs as eigenpairs. Necessary and sufficient conditions under which this quadratic inverse eigenvalue problem is solvable are obtained. Numerical algorithms for solving the problem are developed. Numerical examples illustrating these solutions are presented

Maintenance of xylem hydraulic function during winter in the woody bamboo Phyllostachys propinqua McClure

Background Frost is a common environmental stress for temperate plants. Xylem embolism occurs in many overwintering plants due to freeze-thaw cycles, so coping with freeze-thaw-induced embolisms is essential for the survival of temperate plants. Methods This study was conducted on Phyllostachys propinqua McClure, a woody bamboo species that was grown under natural frost conditions to explore its responses to winter embolisms. From autumn to the following spring, the following measurements were recorded: predawn branch and leaf embolism, branch and leaf relative water content (RWC), root pressure and soil temperature, xylem sap osmotic potential, branch and leaf electrolyte leakage (EL), branch nonstructural carbohydrate (NSC) content and leaf net photosynthetic rate. Results P. propinqua had a mean vessel diameter of 68.95 ±1.27 µm but did not suffer severe winter embolism, peaking around  60% in winter (January), with a distinct reduction in March when root pressure returned. Leaves had a more severe winter embolism, up to 90%. Leaf RWC was much lower in winter, and leaf EL was significantly higher than branch EL in all seasons. Root pressure remained until November when soil temperature reached 9 °C, then appeared again in March when soil temperatures increased from −6 °C (January) to 11 °C. Xylem sap osmotic potential decreased from autumn to winter, reaching a minimum in March, and then increasing again. Soluble sugar (SS) concentration increased throughout the winter, peaked in March, and then decreased. Conclusions These results suggest that (1) there is a hydraulic segmentation between the stem and leaf, which could prevent stem water loss and further embolization in winter; (2) maintenance of root pressure in early winter played an important role in reducing the effect of freeze-thaw cycles on the winter embolism; (3) the physiological process that resulted in a decrease in xylem sap osmotic potential and tissue water content, and an accumulation of SS associated with cold acclimation also aided in reducing the extent of freeze-thaw-induced embolism. All these strategies could be helpful for the maintenance of xylem hydraulic function of this bamboo species during winter

Removal Effect of Nitrifying Bacteria on Ammonia Nitrogen in Water

[Objectives] To investigate the removal effect of nitrifying bacteria on ammonia nitrogen in water. [Methods] In this experiment, the treated water (referred to as raw water hereinafter) from the Changping Town Qiaoli Water Treatment Project in Dongguan City of Guangdong Province was used as the experimental water body, and the nitrifying bacteria liquid used in the project was taken as the experimental material, to explore the removal effect of the nitrifying bacteria liquid on the ammonia nitrogen in the water body. [Results] Under the condition that other variables remain unchanged, the more the amount of nitrifying bacteria liquid added, the higher the removal efficiency of nitrifying bacteria liquid; under the same conditions, the removal effect of ammonia nitrogen in a stirred water body is better than that in an unstirred water body; the removal effect of ammonia nitrogen in a water body with bio-media/carriers is better than that without bio-media/carriers. [Conclusions] Nitrifying bacteria have a better removal effect on the ammonia nitrogen in the water body

Removal Effect of Nitrifying Bacteria on Ammonia Nitrogen in Water

[Objectives] To investigate the removal effect of nitrifying bacteria on ammonia nitrogen in water. [Methods] In this experiment, the treated water (referred to as raw water hereinafter) from the Changping Town Qiaoli Water Treatment Project in Dongguan City of Guangdong Province was used as the experimental water body, and the nitrifying bacteria liquid used in the project was taken as the experimental material, to explore the removal effect of the nitrifying bacteria liquid on the ammonia nitrogen in the water body. [Results] Under the condition that other variables remain unchanged, the more the amount of nitrifying bacteria liquid added, the higher the removal efficiency of nitrifying bacteria liquid; under the same conditions, the removal effect of ammonia nitrogen in a stirred water body is better than that in an unstirred water body; the removal effect of ammonia nitrogen in a water body with bio-media/carriers is better than that without bio-media/carriers. [Conclusions] Nitrifying bacteria have a better removal effect on the ammonia nitrogen in the water body

The Regulatory Mechanisms and Therapeutic Potential of MicroRNAs: From Chronic Pain to Morphine Tolerance

Chronic pain, including cancer-related pain, is a pain condition often caused by inflammation or dysfunctional nerves. Chronic pain treatment poses a significant health care challenge, where opioids especially morphine are widely used and patients often develop tolerance over time with aggravated pain. microRNA (miRNA) is known to play important roles in regulating gene expressions in the nervous system to affect neuronal network plasticity related to algogenesis and the developing of morphine tolerance. In this article, we reviewed studies conducted in rodent animal models investigating the mechanisms of miRNAs regulation in chronic pain with different phenotypes and morphine tolerance. In addition, the potential of targeting miRNAs for chronic pain and morphine tolerance treatment is also reviewed. Finally, we point out the directions of the future research in chronic pain and morphine tolerance

Blowing Ultrathin 2D Materials

Abstract 2D materials possess a range of unique and exclusive properties due to their ultrathin feature, leading their forefront role in several research areas, including electronics, photonics, catalysis and renewable energy. To ensure a wider application for high‐quality 2D materials, there is a global pursuit to find new “industrial scale” methodologies for the facile fabrication of advanced 2D materials. Blowing method is a general and scalable strategy for synthesizing ultrathin materials with layered or nonlayered structures, which opens up a new avenue for economic and massive preparation of good‐quality nonlayered 2D nanosheets. This minireview summarizes the specific steps and principles of blowing method, focuses on the recent progress in preparing different categories of 2D materials, and further proposes an outlook for future opportunities in this growing field