A non-Abelian analogue of Whitney’s 2-isomorphism theorem

We give a non-Abelian analogue of Whitney’s 2-isomorphism theorem for graphs. Whitney’s theorem states that the cycle space determines a graph up to 2-isomorphism. Instead of considering the cycle space of a graph which is an Abelian object, we consider a mildly non-Abelian object, the 2-truncation of the group algebra of the fundamental group of the graph considered as a subalgebra of the 2-truncation of the group algebra of the free group on the edges. The analogue of Whitney’s theorem is that this is a complete invariant of 2-edge connected graphs: let G, G′ be 2-edge connected finite graphs; if there is a bijective correspondence between the edges of G and G′ that induces equality on the 2-truncations of the group algebras of the fundamental groups, then G and G′ are isomorphic.     

Synthesis of Conjugated Optically Active Polymetallocenes

The development of methodology for synthesizing new materials in which metal atoms are linked by hydrocarbons whose electronic conjugation is unbroken is described. The fundamental idea is to twist the hydrocarbons into helices. By attaching bulky groups to their precursors, the helices can be made to twist mainly in one direction. The molecules synthesized are helicenes capped by five-membered rings to which metals are attached. If the size of the helix is chosen appropriately, a polymeric structure forms in which hydrocarbon rings and metal atoms alternate. An oligomer with Structure 22 is the first such material prepared. It and related structures might be precursors of molecular solenoids, examples of which are not yet known.     

An Improved Method for the Mono-Hydroxymethylation of Pyridines. A Modification of the Minisci Procedure

The reaction of N-methoxy-derivatives of pyridines in methanol with ammonium persulphate gives improved yields of mono-hydroxymethylated products. In contrast to the original Minisci procedure the reaction requires only catalytic amounts of ammonium persulphate. Evidence is presented which establishes that the reaction does not proceed via an intramolecular pathway.     

Arginine-hydrolyzing enzymes for electrochemical biosensors

Since l-Arginine (Arg) is a semi-essential amino acid for humans, its adequate amount must be consumed in the diet to prevent certain negative consequences related to insufficient synthesis of this amino acid under specific physiological conditions. Arg metabolism results in the production of a biochemically diverse range of such products as urea, some amino acids, creatine, polyamines, nitric oxide, etc. Arg, an important biomarker in clinical diagnostics, is also used for prevention/treatment of different diseases, including cancer and COVID-19. Furthermore, it serves as an indicator of food and beverages quality.A variety of optic and electrochemical methods for Arg determination have already been suggested. The biosensor systems based on the enzymes of Arg metabolism were shown to be the most promising tools for Arg assay. This review focuses on the peculiarities of electrochemical biosensors for Arg assay based on the use of Arg-degrading enzymes and on the analysis of their advantages as compared to other approaches.     

Analysis of conditions for determining the thermophysical characteristics of energetic materials by the laser pulse method

An analysis of conditions for determining the thermophysical characteristics of energetic materials by the laser pulse method is performed. Based on the results of numerical solution of the heat conduction problems for a sample of a material irradiated with a short heating laser pulse corresponding to actual experimental conditions, the time dependences on the sample surface temperature are determined. The heat pulse duration required to determine the thermophysical properties of materials and the ignition delay time are compared. It is shown that the determination of the thermophysical characteristics of a typical energetic material by the laser pulse method is possible at pulse durations of no longer than 0.24 s.     

1/f Flux noise in Josephson phase qubits

We present a new method to measure 1/f noise in Josephson quantum bits (qubits) that yields low-frequency spectra below 1 Hz. A comparison of the noise taken at positive and negative bias of a phase qubit shows the dominant noise source to be flux noise and not junction critical-current noise, with a magnitude similar to that measured previously in other systems. Theoretical calculations show that the level of flux noise is not compatible with the standard model of noise from two-level state defects in the surface oxides of the films.     

Simple but Precise Engineering of Functional Nanocapsules through Nanoprecipitation

A general, rapid, and undemanding method to generate at will functional oil‐filled nanocapsules through nanoprecipitation is reported. On the basis of polymer and hexadecane/water/acetone phase diagrams, the composition can be set so that polymer chains preferentially stick at the interface of the oil droplets to create nanocapsules. The nanocapsules can be decorated with biorelevant molecules (biotin, fluorescent tags, metal nanoparticles) within the shell and loaded with hydrophobic molecules in a simple one‐pot procedure.     

A Microelectronic Sensor Device Powered by a Small Implantable Biofuel Cell

Biocatalytic buckypaper electrodes modified with pyrroloquinoline quinone (PQQ)-dependent glucose dehydrogenase and bilirubin oxidase for glucose oxidation and oxygen reduction, respectively, were prepared for their use in a biofuel cell. A small (millimeter-scale; 2×3×2 mm³) enzyme-based biofuel cell was tested in a model glucose-containing aqueous solution, in human serum, and as an implanted device in a living gray garden slug (Deroceras reticulatum), producing electrical power in the range of 2–10 μW (depending on the glucose source). A microelectronic temperature-sensing device equipped with a rechargeable supercapacitor, internal data memory and wireless data downloading capability was specifically designed for activation by the biofuel cell. The power management circuit in the device allowed the optimized use of the power provided by the biofuel cell dependent on the sensor operation activity. The whole system (power-producing biofuel cell and power-consuming sensor) operated autonomously by extracting electrical energy from the available environmental source, as exemplified by extracting power from the glucose-containing hemolymph (blood substituting biofluid) in the slug to power the complete temperature sensor system and read out data wirelessly. Other sensor systems operating autonomously in remote locations based on the concept illustrated here are envisaged for monitoring different environmental conditions or can be specially designed for homeland security applications, particularly in detecting bioterrorism threats.