The structure of the 3-separations of 3-connected matroids

Tutte defined a k-separation of a matroid M to be a partition (A,B) of the ground set of M such that |A|,|B|k and r(A)+r(B)−r(M)<k. If, for all m<n, the matroid M has no m-separations, then M is n-connected. Earlier, Whitney showed that (A,B) is a 1-separation of M if and only if A is a union of 2-connected components of M. When M is 2-connected, Cunningham and Edmonds gave a tree decomposition of M that displays all of its 2-separations. When M is 3-connected, this paper describes a tree decomposition of M that displays, up to a certain natural equivalence, all non-trivial 3-separations of M.     

Long-Term Impact of Wind Erosion on the Particle Size Distribution of Soils in the Eastern Part of the European Union

Wind erosion is the leading cause of soil degradation and air pollution in many regions of the world. As wind erosion is controlled by climatic factors, research on this phenomenon is urgently needed in soil and land management in order to better adapt to climate change. In this paper, the impact of wind erosion on the soil surface in relation to particle size distribution was investigated. Changes in percentage of sand, silt and clay fractions based on historical KPP data (1961–1970), LUCAS data base (2009), and field measurements (2016) were analysed in five cadastral areas impacted by wind erosion (Záhorie Lowlands, Slovakia). With the use of GIS tools, models of spatial distribution of sand, silt, clay and erodible fraction (EF) content were developed based on those measurements. Our findings proved that soil texture change driven by wind erosion could happen relatively quickly, and a significant proportion of soil fine particles may be carried away within a few years. The results indicate that the soil surface became much rougher over the period of more than 50 years, but also that the accumulation of fraction of the silt particles occurred in most of the areas affected by the erosive effect.     

Effort dynamics of a delay-induced prey–predator system with reserve

This paper describes a prey?Cpredator fishery system with prey dispersal in a two-patch environment, one of which is a free fishing zone and the other a protected zone. The proposed system reflects the dynamic interaction between the net economic revenue and the fishing effort used to harvest the population in presence of a suitable tax. Local as well as global stability of the system is analyzed. The optimal taxation policy is formulated and solved with the help of Pontryagin??s maximal principle. The objective of the paper is to achieve the sustainability of the fishery, keeping the ecological balance, and maximize the monetary social benefit. The dynamical behavior of the delay system is further analyzed through incorporating discrete type gestational delay of predators, and the existence of Hopf bifurcation phenomenon is checked at the interior equilibrium point. Moreover, we use normal form method and center manifold theorem to examine the nature of the Hopf bifurcation. Theoretical results are verified with the help of numerical examples and graphical illustrations.     

2‐(6‐Bromo­pyridin‐2‐yl)‐6‐methyl‐[1,3,6,2]­diox­aza­borocane,a new stable (pyridin‐2‐yl)­boronic acid derivative

The crystal structure of the first reported non‐substituted N‐methyl­diox­aza­borocane confirms that the presence of a methyl group attached to the N atom introduces an NB bond length that is longer than that in a simple diox­aza­borocane ring. The presence of more N atoms in the vicinity of the B atom in the title compound [systematic name: 6a‐(6‐bromo­pyridin‐2‐yl)‐3a‐methyl‐2,3,4,5‐tetra­hydro‐1,6‐dioxa‐3a‐aza‐6a‐borapentalene], C₁₀H₁₄BBrN₂O₂, does not modify significantly any structural parameter in the diox­aza­borocane ring. On the other hand, a small asymmetry appears in the bond angles of the pyridine C atom next to the B atom.     

High binding capacity surface grafted monolithic columns for cation exchange chromatography of proteins and peptides

Poly(glycidyl methacrylate-co-ethylene methacrylate) monoliths have been prepared in 100 μm i.d. capillaries and their epoxy groups hydrolyzed to obtain poly(2,3-dihydroxypropyl methacrylate-co-ethylene methacrylate) matrix. These polymers were then photografted in a single step with 2-acrylamido-2-methyl-1-propanesulfonic acid and acrylic acid to afford stationary phases for a strong and a weak cation exchange chromatography, respectively. Alternatively, poly(ethylene glycol) methacrylate was used for grafting in the first step in order to enhance hydrophilicity of the support followed by photografting with 2-acrylamido-2-methyl-1-propanesulfonic acid or acrylic acid in the second step. These new columns were used for the separation of proteins and peptides. A mixture of ovalbumin, α-chymotrypsinogen, cytochrome c, ribonuclease A and lysozyme was used to assess the chromatographic performance for large molecules while a cytochrome c digest served as a model mixture of peptides. All tested columns featured excellent mass transfer as demonstrated with very steep breakthrough curves. The highest binding capacities were found for columns prepared using the two step functionalization. Columns with sulfonic acid functionalities adsorbed up to 21.5 mg/mL lysozyme while the capacity of the weak cation exchange column functionalized with acrylic acid was 29.2 mg/mL.     

Synthesis, mechanism of formation, and molecular orbital calculations of arylamidoximes

Abstract  

A simple and easy synthesis of ten arylamidoximes from arylnitriles and hydroxylamine is described. The formation of the arylamides has been observed to a much lesser extent in the present work. A new mechanism for the formation of arylamidoximes, as well as arylamides, from arylnitriles and hydroxylamine is suggested. Quantum mechanical calculations have been carried out to support this mechanism. The enthalpy of formation in conjunction with atomic charges of the reactants and intermediates helped to understand more about the generation of the products.     

Copper-catalyzed addition of water affording highly substituted furan and unusual formation of naphthofuran ring from 3-(1-alkenyl)-2-alkene-1-al

We have developed a novel one-pot reaction to generate highly substituted furan through the addition of water followed by oxidation and unusual cyclization to naphthofuran ring under the same reaction condition.     

Oil in water emulsions stabilized by maillard conjugates of sodium caseinate-locust bean gum

Conjugates composed by sodium caseinate and locust bean gum (LBG) were produced through Maillard reaction in order to enhance their emulsifying properties. The reactions were performed (80?°C/76% relative humidity) at three protein/polysaccharide ratios (0.3, 0.6, 1.2), and the conjugates were added in emulsions at two pH values (3.5 and 7). The formation of protein-polysaccharide conjugates was confirmed by SDS-polyacrylamide gel electrophoresis and by FTIR spectra. At both pH values, the conjugates subjected to longer reaction times presented less emulsifying capability, probably due to insoluble compounds formation. Furthermore, the conjugates provided high stability in O/W emulsions at pH 7 due to the electrostatic repulsion of protein charged groups. However, even though the conjugates were not charged at pH 3.5, the stabilization process occurred at this condition probably due to the formation of a thicker interfacial layer, which provided an increase in steric repulsion between the droplets. Thus, the conjugates formed by sodium caseinate and locust bean gum can be characterized as a good emulsifying agent to be applied in different pH conditions.     

Comparison of Insulin Determination on NiNPs/chitosan‐ MWCNTs and NiONPs/chitosan‐MWCNTs Modified Pencil Graphite Electrode

The rising amount of patients suffering for diabetes mellitus increases the requirements for effective insulin sensors. Carbon materials are a suitable choice for the development of insulin sensors due to their electrochemical characteristics. Pencil graphite electrodes (PGE) represent the trade‐off between price and excellent conductive properties. The modification of PGE by NiO and Ni nanoparticles fixed by chitosan results in surface area enlargement and improved electrocatalytic properties. This paper is focused on the comparison of different properties of Ni and NiO nanoparticles and their effect on redox reaction mechanism of insulin and detection characteristics. The electrode modified by Ni nanoparticles displays linear range of 1 μM–5 μM (R² 0.80), limit of detection (LOD) of 4.34 μM and sensitivity of 0.12 μA/μM. On the other hand, the electrode modified by NiO nanoparticles displays enhanced electrochemical characteristics such as linear range of 0.05 μM–5 μM (R² 0.99), limit of detection of 260 nM and sensitivity of 0.64 μA/μM. These properties make the NiO nanoparticles modified PGE the appropriate candidate for insulin determination.