Solution and asymptotic analysis of a boundary value problem in the spring–mass model of running

We consider the classic spring–mass model of running which is built upon an inverted elastic pendulum. In a natural way, there arises an interesting boundary value problem for the governing system of two nonlinear ordinary differential equations. It requires us to choose the stiffness to ascertain that after a complete step, the spring returns to its equilibrium position. Motivated by numerical calculations and real data, we conduct a rigorous asymptotic analysis in terms of the Poicaré–Lindstedt series. The perturbation expansion is furnished by an interplay of two time scales what has an significant impact on the order of convergence. Further, we use these asymptotic estimates to prove that there exists a unique solution to the aforementioned boundary value problem and provide an approximation to the sought stiffness. Our results rigorously explain several observations made by other researchers concerning the dependence of stiffness on the initial angle of the stride and its velocity. The theory is illustrated with a number of numerical calculations.

     

Highly Enantioselective,Organocatalytic, and Scalable Synthesis of a Rare cis,cis-Tricyclic Diterpenoid

A highly enantioselective, organocatalytic, and scalable synthesis of a very unusual cis-decalin-cis-hydrindane tricyclic diterpenoid system has been achieved. Despite the prevalent pharmacological space that the related trans,trans and trans,cis-systems occupy, there have been no reports of an asymmetric synthesis of the cis,cis systems in the literature until now. We demonstrate the flexibility of our approach not only through access to a diverse range of products, all of which are attained in exceptionally high selectivities, but also by showing their easy conversion to the corresponding trans,cis-system and other derivatives.     

Modification of Polylactide Nonwovens with Carbon Nanotubes and Ladder Poly(silsesquioxane)

Electrospun nonwovens of poly(L-lactide) (PLLA) modified with multiwall carbon nanotubes (MWCNT) and linear ladder-like poly(silsesquioxane) with methoxycarbonyl side groups (LPSQ-COOMe) were obtained. MWCNT and LPSQ-COOMe were added to the polymer solution before the electrospinning. In addition, nonwovens of PLLA grafted to modified MWCNT were electrospun. All modified nonwovens exhibited higher tensile strength than the neat PLA nonwoven. The addition of 10 wt.% of LPSQ-COOMe and 0.1 wt.% of MWCNT to PLLA increased the tensile strength of the nonwovens 2.4 times, improving also the elongation at the maximum stress.     

Hydrotalcite-derived Co-containing mixed metal oxide catalysts for methanol incineration

The Co–Mg–Al mixed metal oxides were prepared by calcination of co-precipitated hydrotalcite-like precursors at various temperatures (600–800 °C), characterised with respect to chemical (AAS) and phase (XRD) composition, textural parameters (BET), form and aggregation of cobalt species (UV–vis-DRS) and their redox properties (H₂-TPR, cyclic voltammetry). Moreover, the process of thermal decomposition of hydrotalcite-like materials to mixed metal oxide systems was studied by thermogravimetric method combined with the analysis of gaseous decomposition products by mass spectrometry. Calcined hydrotalcite-like materials were tested as catalysts for methanol incineration. Catalytic performance of the oxides depended on cobalt content, Mg/Al ratio and calcination temperature. The catalysts with lower cobalt content, higher Mg/Al ratio and calcined at lower temperatures (600 or 700 °C) were less effective in the process of methanol incineration. In a series of the studied catalysts, the best results, with respect to high catalytic activity and selectivity to CO₂, were obtained for the mixed oxide with Co:Mg:Al molar ratio of 10:57:33 calcined at 800 °C. High activity of this catalyst was likely connected with the presence of a Co–Mg–Al spinel-type phases, containing easy reducible Co³⁺ cations, formed during high-temperature treatment of the hydrotalcite-like precursor.     

Positive Effect of Cannabis sativa L. Herb Extracts on Skin Cells and Assessment of Cannabinoid-Based Hydrogels Properties

The skin is an organ that is constantly exposed to many external factors that can affect its structure and function. Due to the presence of different cannabinoid receptors on many types of skin cells, cannabinoids can interact directly with them. Therefore, as part of this work, the impact of two types of Cannabis sativa L. herb extracts on keratinocytes and fibroblasts was assessed. The content of biologically active compounds such as phenols, flavonoids, chlorophylls and cannabinoids was evaluated. The antioxidant capacity of prepared extracts using the DPPH radical, H₂DCFDA probe and measurement of superoxide dismutase activity was also assessed. The cytotoxicity of hemp extracts was determined using the Alamar Blue, Neutral Red and LDH assays. The ability of the extracts to inhibit the activity of matrix metalloproteinases, collagenase and elastase, was assessed. Preparations of model hydrogels were also prepared and their effect on transepidermal water loss and skin hydration was measured. The obtained results indicate that hemp extracts can be a valuable source of biologically active substances that reduce oxidative stress, inhibit skin aging processes and positively affect the viability of skin cells. The analysis also showed that hydrogels based on cannabis extracts have a positive effect on skin hydration.     

Synthesis and Tuberculostatic Activity of 1,3-Thiazacycloalkyl[3,2-b]-1,2,4-triazoles

The 4-hydroxyalkyl-1,2,4-triazole-3-thiones cyclization allowed us to work out the effective method of 1,3-thiazacycloalkyl[3,2-b]-1,2,4-triazoles synthesis. Some of the compounds that were obtained were tested for their tuberculostatic activity.     

A concise synthesis of tetrahydroisoquinoline-1-carboxylic acids using a Petasis reaction and Pomeranz–Fritsch–Bobbitt cyclization sequence

A sequence of two reactions: the Petasis reaction, in which an aminoacetaldehyde acetal was used as the amine component, followed by Pomeranz–Fritsch–Bobbitt cyclization, has been shown to be a convenient and simple method for the synthesis of tetrahydroisoquinoline-1-carboxylic acids. Using this method several acids have been prepared in good to excellent yields and characterized as hydrochloride salts.     

Thermal transformation of polyacrylonitrile deposited on SBA-15 type silica

Thermogravimetry, diffuse reflectance infrared Fourier transform spectroscopy, and X-ray photoelectron spectroscopy (XPS) were used for the studying of thermally induced structural changes of polyacrylonitrile (PAN) deposited on the surface of SBA-15 type mesoporous silica. Polymer was introduced onto the support by the precipitation polymerization of acrylonitrile in aqueous suspension of SBA-15. Low temperature transformation (to 723?K) of the deposited PAN was analyzed. It was found that at about 523?K, exothermic cyclization of polymer chains to the so-called ladder form of PAN occurred. However, the total cyclization of PAN required higher carbonization temperatures, at which gradual dehydrogenation followed by graphitization was initiated. XPS revealed that the cyclic form of PAN and a relatively large amount of carbonyl species, formed during the carbonization of the PAN/SBA-15 composite at 623?K, were responsible for the high sorption capacity in the methyl?Cethyl ketone (MEK) vapor elimination. The efficiency in the MEK adsorption was also influenced by the content of PAN-derived carbon deposited on the SBA-15 surface.