History-dependent subdifferential inclusions and hemivariational inequalities in contact mechanics

We consider a class of subdifferential inclusions involving a history-dependent term for which we provide an existence and uniqueness result. The proof is based on arguments on pseudomonotone operators and fixed point. Then we specialize this result in the study of a class of history-dependent hemivariational inequalities. Such kind of problems arises in a large number of mathematical models which describe quasistatic processes of contact between a deformable body and an obstacle, the so-called foundation. To provide an example we consider a viscoelastic problem in which the frictional contact is modeled with subdifferential boundary conditions. We prove that this problem leads to a history-dependent hemivariational inequality in which the unknown is the velocity field. Then we apply our abstract result in order to prove the unique weak solvability of the corresponding contact problem.     

Strong immersion is a well-quasi-ordering for semicomplete digraphs

We prove that the strong immersion order is a well-quasi-ordering on the class of semicomplete digraphs, thereby strengthening a result of Chudnovsky and Seymour (2011, J. Comb. Theory, Series B, 101, 47–53) that this holds for the class of tournaments.     

Differential Tests for Plurisubharmonic Functions and Koch Curves

Potential Analysis - We study minimum sets of singular plurisubharmonic functions and their relation to upper contact sets. In particular we develop an algorithm checking when a naturally...     

Geometric properties of F-normed Orlicz spaces

Aequationes mathematicae - The paper deals with F-normed functions and sequence spaces. First, some general results on such spaces are presented. But most of the results in this paper concern...     

Phase transformation in shape memory alloys: a numerical approach for thermomechanical modeling via peridynamics

Meccanica - The work is devoted to the numerical aspects of the modeling tool elaborated to simulate the phenomenon of solid phase transformation in shape memory alloys. Particularly, a nonlocal...     

Quasi-arithmetic-type invariant means on probability space

Aequationes mathematicae - For a family $$(\mathscr {A}_x)_{x \in (0,1)}$$ of integral quasi-arithmetic means satisfying certain measurability-type assumptions we search for an integral mean K such...     

A Rapid Gas-Chromatography/Mass-Spectrometry Technique for Determining Odour Activity Values of Volatile Compounds in Plant Proteins: Soy,and Allergen-Free Pea and Brown Rice Protein

Plant-based protein sources have a characteristic aroma that limits their usage in various meat-alternative formulations. Despite being the most popular plant-based protein, the allergenicity of soy protein severely restricts the potential adoption of soy protein as an animal substitute. Thereby, allergen-free plant-protein sources need to be characterized. Herein, we demonstrate a rapid solid-phase-microextraction gas-chromatography/mass-spectrometry (SPME-GC/MS) technique for comparing the volatile aroma profile concentration of two different allergen-free plant-protein sources (brown rice and pea) and comparing them with soy protein. The extraction procedure consisted of making a 1:7 w/v aqueous plant protein slurry, and then absorbing the volatile compounds on an SPME fibre under agitation for 10 min at 40 °C, which was subsequently injected onto a GC column coupled to an MS system. Observed volatile concentrations were used in conjunction with odour threshold values to generate a Total Volatile Aroma Score for each protein sample. A total of 76 volatile compounds were identified. Aldehydes and furans were determined to be the most dominant volatiles present in the plant proteins. Both brown rice protein and pea protein contained 64% aldehydes and 18% furans, with minor contents of alcohols, ketones and other compounds. On the other hand, soy protein consisted of fewer aldehydes (46%), but a more significant proportion of furans (42%). However, in terms of total concentration, brown rice protein contained the highest intensity and number of volatile compounds. Based on the calculated odour activity values of the detected compounds, our study concludes that pea proteins could be used as a suitable alternative to soy proteins in applications for allergen-free vegan protein products without interfering with the taste or flavour of the product.     

Promising Antimicrobial Properties of Bioactive Compounds from Different Honeybee Products

Bee products have been known for centuries for their versatile healing properties. In recent decades they have become the subject of documented scientific research. This review aims to present and compare the impact of bee products and their components as antimicrobial agents. Honey, propolis, royal jelly and bee venom are bee products that have antibacterial properties. Sensitivity of bacteria to these products varies considerably between products and varieties of the same product depending on their origin. According to the type of bee product, different degrees of activity were observed against Gram-positive and Gram-negative bacteria, yeasts, molds and dermatophytes, as well as biofilm-forming microorganisms. Pseudomonas aeruginosa turned out to be the most resistant to bee products. An analysis of average minimum inhibitory concentration values for bee products showed that bee venom has the strongest bacterial effectiveness, while royal jelly showed the weakest antibacterial activity. The most challenging problems associated with using bee products for medical purposes are dosage and safety. The complexity and variability in composition of these products raise the need for their standardization before safe and predictable clinical uses can be achieved.     

Self-organisation of di(perfluorohexyl)hexane in Langmuir and LB films

Symmetrical triblock semifluorinated n-alkane, di(perfluorohexyl)hexane of the formula F(CF₂)₆(CH₂)₆(CF₂)₆F (abbreviated F₆H₆F₆), has been synthesised and investigated at the air/water interface. Our results show for the first time that this unusual film-forming material, completely hydrophobic in nature and possessing no polar group, is capable of stable film formation at the free water surface. The surface pressure–area isotherm of the studied compound exhibited two regions: corresponding to monotonous pressure rise, followed by a pseudo-plateau region. Visualisation of film structure with Brewster angle microscope (BAM) proved the formation of domains within the pseudo-plateau region. A closer insight into the structure of these domains with atomic force microscope (AFM) proved their ordered, circular shape. The average area of F₆H₆F₆ domain was found to depend on surface pressure value, as it is 4.98 ± 1.75 μm² at π = 1.2 mN/m to 16.54 ± 0.31 μm² at π = 1.7 mN/m. Following performed quantum-chemical calculations, it can be concluded that the observed surface aggregates from F₆H₆F₆ are formed by linear conformers with shifted CF and CH parts. The calculated domain thickness is between 20 and 21 Å, which perfectly agrees with the experimental value estimated from AFM measurements (20.3 ± 1.4 Å).