There is a high mortality and long hospitalization period for severe cases with 2019 novel coronavirus disease (COVID-19) pneumonia. Therefore, it makes sense to search for a potential biomarker that could rapidly and effectively identify severe cases early. Clinical samples from 28 cases of COVID-19 (8 severe cases, 20 mild cases) in Zunyi District from January 29, 2020 to February 21, 2020 were collected and otherwise statistically analysed for biochemical markers. Serum urea, creatinine (CREA) and cystatin C (CysC) concentrations in severe COVID-19 patients were significantly higher than those in mild COVID-19 patients (P<0.001), and there were also significant differences in serum direct bilirubin (DBIL), cholinesterase (CHE) and lactate dehydrogenase (LDH) concentrations between severe and mild COVID-19 patients (P<0.05). Serum urea, CREA, CysC, DBIL, CHE and LDH could be used to distinguish severe COVID-19 cases from mild COVID-19 cases. In particular, serum biomarkers, including urea, CREA, CysC, which reflect glomerular filtration function, may have some significance as potential indicators for the early diagnosis of severe COVID-19 and to distinguish it from mild COVID-19. Glomerular filtration function injury in severe COVID-19 patients should also be considered by clinicians.

This paper deals with the asymptotic stability of theoretical solutions and numerical methods for systems of neutral differential equations x' = Ax'(t -r) + Bx(t) + Cx(t -~-), where A, B, and C are constant complex N x N matrices, and r > 0. A necessary and sufficient condition such that the differential equations are asymptotically stable is derived. We also focus on the numerical stability properties of adaptations of one-parameter methods. Further, we investigate carefully the characterization of the stability region.

In this paper, we study minimizers of the Hartree-type energy functional Ea(u)≔∫RN∇u(x)2+V(x)u(x)2dx−ap∫RNIα∗u(x)pu(x)pdx,a≥0 under the mass constraint ∫RNu2dx=1, where p=N+α+2N with α ∈ (0, N) for N ≥ 2 is the mass critical exponent. Here Iα denotes the Riesz potential and the trapping potential 0≤V(x)∈Lloc∞(RN) satisfies limx→∞V(x)=∞. We prove that minimizers exist if and only if a satisfies a&lt;a∗=Q22(p−1), where Q is a positive radially symmetric ground state of −Δu+u=(Iα∗up)up−2u in ℝN. The uniqueness of positive minimizers holds if a &gt; 0 is small enough. The blow-up behavior of positive minimizers as a↗a∗ is also derived under some general potentials. Especially, we prove that minimizers must blow up at the central point of the biggest inscribed sphere of the set Ω ≔ {x ∈ ℝN, V(x) = 0} if Ω&gt;0.

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