Lp-regularity theory for semilinear stochastic partial differential equations with multiplicative white noise

We establish the $L_p$-regularity theory for a semilinear stochastic partial differential equation with multiplicative white noise: du = (a^{ij}u_{x^ix^j} + b^{i}u_{x^i} + cu + \bar b^{i}|u|^\lambda u_{x^i})dt + \sigma^k(u)dw_t^k,\quad (t,x)\in(0,\infty)\times\bR^d; \quad u(0,\cdot) = u_0, where $\lambda>0$, the set $\{ w_t^k,k=1,2,\dots \}$ is a set of one-dimensional independent Wiener processes, and the function $u_0 = u_0(\omega,x)$ is a nonnegative random initial data. The coefficients $a^{ij},b^i,c$ depend on $(\omega,t,x)$, and $\bar b^i$ depends on $(\omega,t,x^1,\dots,x^{i-1},x^{i+1},\dots,x^d)$. The coefficients $a^{ij},b^i,c,\bar{b}^i$ are uniformly bounded and twice continuous differentiable. The leading coefficient $a$ satisfies ellipticity condition. Depending on the diffusion coefficient $\sigma^k(u)$, we consider two different cases; (i) $\lambda\in(0,\infty)$ and $\sigma^k(u)$ has Lipschitz continuity and linear growth in $u$, (ii) $\lambda,\lambda_0\in(0,1/d)$ and $\sigma^k(u) = \mu^k |u|^{1+\lambda_0}$ ($\sigma^k(u)$ is super-linear). Each case has different regularity results. For example, in the case of $(i)$, for $\varepsilon>0$ u \in C^{1/2 - \varepsilon,1 - \varepsilon}_{t,x}([0,T]\times\bR^d)\quad \forall T<\infty, almost surely. On the other hand, in the case of $(ii)$, if $\lambda,\lambda_0\in(0,1/d)$, for $\varepsilon>0$ u \in C^{\frac{1-(\lambda d) \vee (\lambda_0 d)}{2} - \varepsilon,1-(\lambda d) \vee (\lambda_0 d) - \varepsilon}_{t,x}([0,T]\times\bR^d)\quad \forall T<\infty almost surely. It should be noted that $\lambda$ can be any positive number and the solution regularity is independent of nonlinear terms in case $(i)$. In case $(ii)$, however, $\lambda,\lambda_0$ should satisfy $\lambda,\lambda_0\in(0,1/d)$ and the regularities of the solution are affected by $\lambda,\lambda_0$ and $d$.Comment: 28 page

A regularity theory for stochastic generalized Burgers' equation driven by a multiplicative space-time white noise

We introduce the uniqueness, existence, $L_p$-regularity, and maximal H\"older regularity of the solution to semilinear stochastic partial differential equation driven by a multiplicative space-time white noise: $$u_t = au_{xx} + bu_{x} + cu + \bar b|u|^\lambda u_{x} + \sigma(u)\dot W,\quad (t,x)\in(0,\infty)\times\mathbb{R}; \quad u(0,\cdot) = u_0,$$ where $\lambda > 0$. The function $\sigma(u)$ is either bounded Lipschitz or super-linear in $u$. The noise $\dot W$ is a space-time white noise. The coefficients $a,b,c$ depend on $(\omega,t,x)$, and $\bar b$ depends on $(\omega,t)$. The coefficients $a,b,c,\bar{b}$ are uniformly bounded, and $a$ satisfies ellipticity condition. The random initial data $u_0 = u_0(\omega,x)$ is nonnegative. We have the maximal H\"older regularity by employing the H\"older embedding theorem. For example, if $\lambda \in(0,1]$ and $\sigma(u)$ has Lipschitz continuity, linear growth, and boundedness in $u$, for $T<\infty$ and $\varepsilon>0$, $$u \in C^{1/4 - \varepsilon,1/2 - \varepsilon}_{t,x}([0,T]\times\mathbb{R})\quad(a.s.).$$ On the other hand, if $\lambda\in(0,1)$ and $\sigma(u) = |u|^{1+\lambda_0}$ with $\lambda_0\in[0,1/2)$, for $T0$, $$u \in C^{\frac{1/2-(\lambda -1/2) \vee \lambda_0}{2} - \varepsilon,1/2-(\lambda -1/2) \vee \lambda_0 - \varepsilon}_{t,x}([0,T]\times\mathbb{R})\quad (a.s.).$$ It should be noted that if $\sigma(u)$ is bounded Lipschitz in $u$, the H\"older regularity of the solution is independent of $\lambda$. However, if $\sigma(u)$ is super-linear in $u$, the H\"older regularities of the solution are affected by nonlinearities, $\lambda$ and $\lambda_0.$Comment: 33 pages. arXiv admin note: text overlap with arXiv:2111.0330

Generation of Multiple Bioactive Macrolides by Hybrid Modular Polyketide Synthases in Streptomyces venezuelae

AbstractThe plasmid-based replacement of the multifunctional protein subunits of the pikromycin PKS in S. venezuelae by the corresponding subunits from heterologous modular PKSs resulted in recombinant strains that produce both 12- and 14-membered ring macrolactones with predicted structural alterations. In all cases, novel macrolactones were produced and further modified by the DesVII glycosyltransferase and PikC hydroxylase, leading to biologically active macrolide structures. These results demonstrate that hybrid PKSs in S. venezuelae can produce a multiplicity of new macrolactones that are modified further by the highly flexible DesVII glycosyltransferase and PikC hydroxylase tailoring enzymes. This work demonstrates the unique capacity of the S. venezuelae pikromycin pathway to expand the toolbox of combinatorial biosynthesis and to accelerate the creation of novel biologically active natural products

Dissociating stable nitrogen molecules under mild conditions by cyclic strain engineering

All quiet on the nitrogen front. The dissociation of stable diatomic nitrogen molecules (N-2) is one of the most challenging tasks in the scientific community and currently requires both high pressure and high temperature. Here, we demonstrate that N-2 can be dissociated under mild conditions by cyclic strain engineering. The method can be performed at a critical reaction pressure of less than 1 bar, and the temperature of the reaction container is only 40 degrees C. When graphite was used as a dissociated N* receptor, the normalized loading of N to C reached as high as 16.3 at/at %. Such efficient nitrogen dissociation is induced by the cyclic loading and unloading mechanical strain, which has the effect of altering the binding energy of N, facilitating adsorption in the strain-free stage and desorption in the compressive strain stage. Our finding may lead to opportunities for the direct synthesis of N-containing compounds from N-2

Postreperfusion Blood Pressure Variability After Endovascular Thrombectomy Affects Outcomes in Acute Ischemic Stroke Patients With Poor Collateral Circulation

Background and Purpose: We evaluated the effect of 24 h blood pressure variability (BPV) on clinical outcomes in acute ischemic stroke patients with successful recanalization after endovascular recanalization therapy (ERT).Methods: Patients with anterior circulation occlusion were evaluated if they underwent ERT based on multiphase computed tomography angiography and achieved successful recanalization (≥thrombolysis in cerebral ischemia 2b). Collateral degrees were dichotomized based on the pial arterial filling score, with a score of 0–3 defined as a poor collateral status. BPV parameters include mean, standard deviation, coefficient of variation, and variation independent of the mean (VIM) for systolic blood pressure (SBP), diastolic blood pressure (DBP), mean blood pressure, and pulse rate (PR). These parameters were measured for 24 h after ERT and were analyzed according to occlusion sites and stroke mechanisms. Associations of BPV parameters with clinical outcomes were investigated with stratification based on the baseline collateral status.Results: BPV was significantly different according to the occlusion sites and stroke mechanisms, and higher BPV was observed in patients with internal carotid artery occlusion or cardioembolic occlusion. After adjustment for confounders, most BPV parameters remained significant to predict functional outcomes at 3 months in patients with poor collateral circulation. However, no significant association was found between BPV parameters and clinical outcomes in patients with good collateral circulation.Conclusion: Postreperfusion BP management by decreasing BPV may have influence on improving clinical outcome in cases of poor collateral circulation among patients achieving successful recanalization after ERT

Fully integrated lab-on-a-disc for simultaneous analysis of biochemistry and immunoassay from whole blood

We report a fully integrated device that can perform both multiple biochemical analysis and sandwich type immunoassay simultaneously on a disc. The whole blood is applied directly to the disposable &quot;lab-on-a-disc&quot; containing different kinds of freeze-dried reagents for the blood chemistry analysis as well as reagents required for the immunoassay. The concentrations of different kinds of analytes are reported within 22 min by simply inserting a disc to a portable device. Using the innovative laser irradiated ferrowax microvalves together with the centrifugal microfluidics, the total process of plasma separation, metering, mixing, incubation, washing, and detection is fully automated. The analyzer is equipped with an optical detection module to measure absorbances at 10 different wavelengths to accommodate the various kinds of reaction protocols. Compared to the conventional blood analysis done in clinical laboratories, it is advantageous for point-of-care applications because it requires a smaller amount of blood (350 mu L vs. 3 mL), takes less time (22 min vs. several days), does not require specially trained operators or expensive instruments to run biochemical analysis and immunoassay separately.close554