Discrete matrix Riccati equations with superposition formulas

An ordinary differential equation is said to have a superposition formula if its general solution can be expressed as a function of a finite number of particular solution. Nonlinear ODE's with superposition formulas include matrix Riccati equations. Here we shall describe discretizations of Riccati equations that preserve the superposition formulas. The approach is general enough to include q-derivatives and standard discrete derivatives.     

Synthesis of allylic alcohols via isoprene-, myrcene-, ocimene-, and piperylene-magnesium complexes

Use of Rieke's active magnesium permits to achieve two-step conversion of the title dienes into respective allylic alcohols $\text{1}$–$\text{11}$.     

Structural analysis of colloidal MnO x composites

We report on the detailed structure of MnO _x nanoparticles (MnO _x NP) which are either stabilized by cationic spherical polyelectrolyte brushes or by star-shaped cationic polyelectrolyte chains. In both cases, the polycation is composed of 2-(trimethylammonium)ethyl methacrylate chloride (TMAEMC). The analysis by transmission electron microscopy (TEM), cryogenic transmission electron microscopy (cryoTEM), and powder X-ray diffraction leads to the conclusion that the MnO _x nanoparticles in aqueous dispersed state are composed of only a few or even single lamellae of c-disordered potassium birnessite (birnessite). Using star-shaped pTMAEMC homopolymer for the synthesis of composite particles, we obtain MnO _x NP with an average diameter of about 5 nm. MnO _x NP immobilized on cationic spherical polyelectrolyte brush have a length of about 20 nm and a width of 1.6 nm. Comparison of the extended X-ray absorption fine structure (EXAFS) spectra of the MnO _x composites with reference spectra leads to the conclusion that all materials include c-disordered birnessite-type nanoparticles. A comparison of the energy shift of the Mn K-edge absorption peak of the X-ray absorption near-edge structure spectra of different manganese oxide reference materials with the different MnO _x NP revealed an average oxidation state of about 3.5–3.7 for synthesized compounds. No distinct structural difference is found when comparing the dried samples to samples dispersed in water. A comparison of the EXAFS data of the birnessite nanoparticles with the crystal structure of macroscopic systems showed a compression along the c direction accompanied by a slight elongation within the ab plane of the layered material.     

Design and synthesis of europium luminescent bio-probes featuring sulfobetaine moieties

Herein we report the straightforward preparation of chromophore-functionalized TACN ligand via Cu-free cross-coupling reactions using a common halogenated platform. This versatile methodology allows the preparation of original macrocyclic ligand featuring both optimized antenna for the sensitization of europium luminescence and sulfobetaine zwitterionic groups to ensure water solubility of the complex. In addition preliminary two-photon excited microscopy imaging experiments of fixed cells reveal that sulfobetaine groups are able to limit undesirable non specific interactions with biological surrounding.     

Functional Information: Towards Synthesis of Biosemiotics and Cybernetics

Biosemiotics and cybernetics are closely related, yet they are separated by the boundary between life and non-life: biosemiotics is focused on living organisms, whereas cybernetics is applied mostly to non-living artificial devices. However, both classes of systems are agents that perform functions necessary for reaching their goals. I propose to shift the focus of biosemiotics from living organisms to agents in general, which all belong to a pragmasphere or functional universe. Agents should be considered in the context of their hierarchy and origin because their semiosis can be inherited or induced by higher-level agents. To preserve and disseminate their functions, agents use functional information - a set of signs that encode and control their functions. It includes stable memory signs, transient messengers, and natural signs. The origin and evolution of functional information is discussed in terms of transitions between vegetative, animal, and social levels of semiosis, defined by Kull. Vegetative semiosis differs substantially from higher levels of semiosis, because signs are recognized and interpreted via direct code-based matching and are not associated with ideal representations of objects. Thus, I consider a separate classification of signs at the vegetative level that includes proto-icons, proto-indexes, and proto-symbols. Animal and social semiosis are based on classification, and modeling of objects, which represent the knowledge of agents about their body (Innenwelt) and environment (Umwelt).     

Self-interaction in the Bopp–Podolsky electrodynamics: Can the observable mass of a charged particle depend on its acceleration?

In this paper we obtain the expression for the self-force in the model with the Lagrangian containing additional terms, quadratic in Maxwell tensor derivatives (so-called Bopp–Podolsky electrodynamics). Features of this force are analyzed for various limiting cases. When a charged particle moves along straight line with a uniform acceleration, an explicit formula is found. In the framework of the considered model, an observable renormalized particle mass is shown to depend on its acceleration. This dependence allows, in principle, to extract experimentally a value of the particle bare mass.