Linear stability analysis of the natural convection in inclined rotating parallel plates

The linear stability analysis of the natural convection in a rectangular tilted infinite cavity filled with a Boussinesq fluid subject to Coriolis force is presented. The bottom and top surfaces have fixed temperatures. Both unstable and stable thermal conditions are studied (heated from below and heated from above respectively). The rotation axis passes through the center and it is orthogonal to the hot and cold surfaces. The stability equations were solved using the Tau–Chebyshev spectral method. The critical Rayleigh number and critical wave number were obtained for several rotation rates and different orientation of convective oblique rolls in a range of inclination of the cavity from 0 to 120 degrees. The stability analysis show that rotation rate affects the basic velocity profile, onset of convection, wave number and critical orientation of convective rolls.     

Asymptotic conditional distribution of exceedance counts: fragility index with different margins

We consider a random vector X, whose components are neither necessarily independent nor identically distributed. The fragility index (FI), if it exists, is defined as the limit of the expected number of exceedances among the components of X above a high threshold, given that there is at least one exceedance. It measures the asymptotic stability of the system of components. The system is called stable if the FI is one and fragile otherwise. In this paper, we show that the asymptotic conditional distribution of exceedance counts exists, if the copula of X is in the domain of attraction of a multivariate extreme value distribution, and if the marginal distribution functions satisfy an appropriate tail condition. This enables the computation of the FI corresponding to X and of the extended FI as well as of the asymptotic distribution of the exceedance cluster length also in that case, where the components of X are not identically distributed.     

Synthesis,Characterization, and Optimization Studies of Starch/Chicken Gelatin Composites for Food-Packaging Applications

The indiscriminate use of plastic in food packaging contributes significantly to environmental pollution, promoting the search for more eco-friendly alternatives for the food industry. This work studied five formulations (T1–T5) of biodegradable cassava starch/gelatin films. The results showed the presence of the starch/gelatin functional groups by FT-IR spectroscopy. Differential scanning calorimetry (DSC) showed a thermal reinforcement after increasing the amount of gelatin in the formulations, which increased the crystallization temperature (Tc) from 190 °C for the starch-only film (T1) to 206 °C for the film with 50/50 starch/gelatin (T3). It also exhibited a homogeneous surface morphology, as evidenced by scanning electron microscopy (SEM). However, an excess of gelatin showed low compatibility with starch in the 25/75 starch/gelatin film (T4), evidenced by the low Tc definition and very rough and fractured surface morphology. Increasing gelatin ratio also significantly increased the strain (from 2.9 ± 0.5% for T1 to 285.1 ± 10.0% for T5) while decreasing the tensile strength (from 14.6 ± 0.5 MPa for T1 to 1.5 ± 0.3 MPa for T5). Water vapor permeability (WVP) increased, and water solubility (WS) also decreased with gelatin mass rising in the composites. On the other hand, opacity did not vary significantly due to the films’ cassava starch and gelatin ratio. Finally, optimizing the mechanical and water barrier properties resulted in a mass ratio of 53/47 cassava starch/gelatin as the most appropriate for their application in food packaging, indicating their usefulness in the food-packaging industry.     

Stability of Gorenstein categories

We show that an iteration of the procedure used to define theGorenstein projective modules over a commutative ring R yieldsexactly the Gorenstein projective modules. Specifically, givenan exact sequence of Gorenstein projective R-modules

such that the complexes Hom_R(G, H) and Hom_R(H,G) are exact for each Gorenstein projective R-module H, themodule Coker() is Gorensteinprojective. The proof of this result hinges upon our analysisof Gorenstein subcategories of abelian categories.     

Developing CRISPR/Cas9-Mediated Fluorescent Reporter Human Pluripotent Stem-Cell Lines for High-Content Screening

Application of the CRISPR/Cas9 system to knock in fluorescent proteins to endogenous genes of interest in human pluripotent stem cells (hPSCs) has the potential to facilitate hPSC-based disease modeling, drug screening, and optimization of transplantation therapy. To evaluate the capability of fluorescent reporter hPSC lines for high-content screening approaches, we targeted EGFP to the endogenous OCT4 locus. Resulting hPSC–OCT4–EGFP lines generated expressed EGFP coincident with pluripotency markers and could be adapted to multi-well formats for high-content screening (HCS) campaigns. However, after long-term culture, hPSCs transiently lost their EGFP expression. Alternatively, through EGFP knock-in to the AAVS1 locus, we established a stable and consistent EGFP-expressing hPSC–AAVS1–EGFP line that maintained EGFP expression during in vitro hematopoietic and neural differentiation. Thus, hPSC–AAVS1–EGFP-derived sensory neurons could be adapted to a high-content screening platform that can be applied to high-throughput small-molecule screening and drug discovery campaigns. Our observations are consistent with recent findings indicating that high-frequency on-target complexities appear following CRISPR/Cas9 genome editing at the OCT4 locus. In contrast, we demonstrate that the AAVS1 locus is a safe genomic location in hPSCs with high gene expression that does not impact hPSC quality and differentiation. Our findings suggest that the CRISPR/Cas9-integrated AAVS1 system should be applied for generating stable reporter hPSC lines for long-term HCS approaches, and they underscore the importance of careful evaluation and selection of the applied reporter cell lines for HCS purposes.     

Tetramethyl guanidine-assisted synthesis and thermal crosslinking of multifunctional benzoxazine monomers based on natural phloretic acid

An efficient strategy to synthesize novel biobased multifunctional benzoxazine compounds was developed using the 1,1,3,3-tetramethyl guanidine (TMG)-triggered esterification of natural phloretic acid with organic halides as a key synthetic step. First, phloretic acid was combined with either aniline or furfurylamine to prepare the corresponding carboxylic acid-functional monobenzoxazine monomer. Next, the use of TMG enabled an efficient esterification of these compounds with di-, tri-, and tetra-functional benzyl bromide compounds at room temperature to afford a series of new multi-benzoxazine monomers tethered to an aromatic core. The effect of the functionality of the monomers on the curing process was analyzed, indicating that the reactivity during the thermally induced ring-opening increases with the number of furan and oxazine rings in the monomers. The resulting thermosets revealed good correlation between the number of oxazine rings in the structure of the monomer and the properties of the crosslinked materials. Furfurylamine-based polybenzoxazines showed improved thermal behavior compared to the aniline-based systems, due to the role of furan rings. All materials showed high T_g, good thermal stability, and promising flame retardancy properties.     

Peptide modified mesoporous silica nanocontainers

Here we report a new peptide modified mesoporous silica nanocontainer (PMSN) as a novel controlled release system. The peptides are part of a stimuli responsive nanovalve and ensure an efficient cellular uptake.     

Variational Solution of Stochastic Schrödinger Equations With Power-Type Nonlinearity

We investigate a Schrödinger problem with multiplicative Gaussian noise term and power-type nonlinearity on a bounded one-dimensional domain. In order to prove the existence and uniqueness of the variational solution, a further process will be introduced which allows to transform the stochastic nonlinear Schrödinger problem into a pathwise one. Galerkin approximations and compact embedding results are used.     

Equilibrium Diffusion on the Cone of Discrete Radon Measures

Let \({\mathbb {K}(\mathbb {R}^{d})}\) denote the cone of discrete Radon measures on \(\mathbb {R}^{d}\). There is a natural differentiation on \(\mathbb {K}(\mathbb {R}^{d})\): for a differentiable function \(F:\mathbb {K}(\mathbb {R}^{d})\to \mathbb {R}\), one defines its gradient \(\nabla ^{\mathbb {K}}F\) as a vector field which assigns to each \(\eta \in \mathbb {K}(\mathbb {R}^{d})\) an element of a tangent space \(T_{\eta }(\mathbb {K}(\mathbb {R}^{d}))\) to \(\mathbb {K}(\mathbb {R}^{d})\) at point η. Let \(\phi :\mathbb {R}^{d}\times \mathbb {R}^{d}\to \mathbb {R}\) be a potential of pair interaction, and let μ be a corresponding Gibbs perturbation of (the distribution of) a completely random measure on \(\mathbb {R}^{d}\). In particular, μ is a probability measure on \(\mathbb {K}(\mathbb {R}^{d})\) such that the set of atoms of a discrete measure \(\eta \in \mathbb {K}(\mathbb {R}^{d})\) is μ-a.s. dense in \(\mathbb {R}^{d}\). We consider the corresponding Dirichlet form

$$\mathcal{E}^{\mathbb{K}}(F,G)={\int}_{\mathbb K(\mathbb{R}^{d})}\langle\nabla^{\mathbb{K}} F(\eta), \nabla^{\mathbb{K}} G(\eta)\rangle_{T_{\eta}(\mathbb{K})}\,d\mu(\eta). $$

Integrating by parts with respect to the measure μ, we explicitly find the generator of this Dirichlet form. By using the theory of Dirichlet forms, we prove the main result of the paper: If d ≥ 2, there exists a conservative diffusion process on \(\mathbb {K}(\mathbb {R}^{d})\) which is properly associated with the Dirichlet form \(\mathcal {E}^{\mathbb {K}}\).