Water removal from porous media by gas injection: experiments and simulation

The flow of a saturated gas through a porous medium, partially occupied by a liquid phase, causes evaporation due to gas expansion. This process, referred to as flow-through drying, is important in a wide variety of natural and industrial applications, such as natural gas production, convective drying of paper, catalysts, fuel cells and membranes. X-ray imaging experiments were performed to study the flow-through drying of water-saturated porous media during gas injection. The results show that the liquid saturation profile and the rate of drying are dependent on the viscous pressure drop, the state of saturation of the gas and the capillary characteristics of the porous medium. During the injection of a completely saturated gas, drying occurs only due to gas expansion. Capillary-driven flow from regions of high saturation to regions of low saturation lead to more uniform saturation profiles. During the injection of a dry gas, a drying front develops at the inlet and propagates through the porous medium. The experimental results are compared with numerical results from a continuum model. A good agreement is found for the case of sandstone. The comparison is less satisfactory for the experiments with limestone.     

Partitioning a Graph into Highly Connected Subgraphs

Given , a k‐proper partition of a graph G is a partition of such that each part P of induces a k‐connected subgraph of G. We prove that if G is a graph of order n such that , then G has a 2‐proper partition with at most parts. The bounds on the number of parts and the minimum degree are both best possible. We then prove that if G is a graph of order n with minimum degree where , then G has a k‐proper partition into at most parts. This improves a result of Ferrara et al. ( Discrete Math 313 (2013), 760–764), and both the degree condition and the number of parts is best possible up to the constant c.     

Secondary Metabolism Rearrangements in Linum usitatissimum L. after Biostimulation of Roots with COS Oligosaccharides from Fungal Cell Wall

In vitro culture of flax (Linum usitatissimum L.) was exposed to chitosan oligosaccharides (COS) in order to investigate the effects on the growth and secondary metabolites content in roots and shoots. COS are fragments of chitosan released from the fungal cell wall during plant–pathogen interactions. They can be perceived by the plant as pathogen-associated signals, mediating local and systemic innate immune responses. In the present study, we report a novel COS oligosaccharide fraction with a degree of polymerization (DP) range of 2–10, which was produced from fungal chitosan by a thermal degradation method and purified by an alcohol-precipitation process. COS was dissolved in hydroponic medium at two different concentrations (250 and 500 mg/L) and applied to the roots of growing flax seedlings. Our observations indicated that the growth of roots and shoots decreased markedly in COS-treated flax seedlings compared to the control. In addition, the results of a metabolomics analysis showed that COS treatment induced the accumulation of (neo)lignans locally at roots, flavones luteolin C-glycosides, and chlorogenic acid in systemic responses in the shoots of flax seedlings. These phenolic compounds have been previously reported to exhibit a strong antioxidant and antimicrobial activities. COS oligosaccharides, under the conditions applied in this study (high dose treatment with a much longer exposure time), can be used to indirectly trigger metabolic response modifications in planta, especially secondary metabolism, because during fungal pathogen attack, COS oligosaccharides are among the signals exchanged between the pathogen and host plant.     

Chemometrically Assisted Optimization of Pregabalin Fluorescent Derivatization Reaction with a Novel Xanthone Analogue and Validation of the Method for the Determination of Pregabalin in Bulk via a Plate Reader

Quantitation of chromophore-free analytes is always a challenge. To this purpose, derivatization of the analyte constitutes a common strategy, leading to a product with a strong signal. In the current study, a novel xanthone analogue was utilized for the first time for the derivatization of pregabalin, a model analyte with a primary amine moiety that lacks a chromophore. The fact that only the xanthene-based derivative, formed after the derivatization reaction fluoresces, enables avoiding its chromatographic separation from the reagent and thus reducing the analysis time of a series of samples in 1–2 min via a plate reader. The reaction conditions were optimized via a central composite design (CCD), with fluorescence signal as the measure of the yield. The following factors that affect the derivatization reaction were chosen: (a) temperature, (b) reaction time, and (c) triethylamine solution volume used to drive the reaction to completion. After the identification of the optimal conditions, the method was validated according to ICH guidelines, using a fluorescence plate reader for signal measurement (λ_ex = 540, λ_em = 615 nm). Finally, the newly developed high-throughput method was applied to the determination of drug content in pregabalin bulk.     

Minimax design of two-state k-out-of-n systems

The optimal size of k is specified for two-state k-out-of-n systems that may be functioning or fail in either state. It is assumed that the steady-state, success and failure probabilities are not known exactly. The problem is reduced to finding the saddle-point solution to a minimax optimization problem. An example shows that the minimax design is robust with regard to uncertainty.     

A 3-D finite-volume method for the Navier-Stokes equations with adaptive hybrid grids

This paper describes the development and application of a numerical scheme for the three-dimensional Navier-Stokes equations of viscous flow using hybrid (prismatic/tetrahedral) grids. Employment of prisms is a relatively new approach towards complex geometry high Reynolds number viscous flow computations. The body surface is covered with triangles, which provides geometric flexibility, while the structure of the mesh in the direction normal to the surface provides better resolution of the viscous stresses. The irregular areas between different prismatic layers covering the surfaces of the domain are filled with tetrahedral elements. Their triangular faces match the corresponding triangular faces of the prisms. A dual adaptation scheme is developed which employs both directional and isotropic local refinement/coarsening of the prisms and tetrahedra. The structure of the prisms is preserved by avoiding interfaces with mid-edge nodes.

Spatial discretization consists of a finite-volume, node-based scheme that is of the central-differencing type. The solution is marched in time using a Taylor series expansion following the Lax-Wendroff approach. The scheme employs a dual cells arrangement for evaluation of the viscous terms, which has the property of suppressing odd-even modes in the solution. A storage-efficient data structure is employed, which utilizes the structure of the prismatic grid in one of the directions.     

Variance and clustering

A measure of dissimilarity of real observations is introduced that is used to identify clusters and is based on ``gaps', and also on averages of selected subgroups of the observations. This measure is surprisingly associated with the sample variance in a way that leads to a new identity and interpretation of the notion of variance.

     

On integral representations of linear forms

Starting from a given *-algebra, we consider integral representations of positive linear forms on the hermitian spectrum of the algebra, providing necessary and sufficient conditions theorem. This specializes to previous results of R. S. Bucy—G. Maltese and G. Maltese for Banach *-algebras, and M. Fragoulopoulou for Imc *-algebras.