Some Properties of Lattice Ordered Rings

Mathematical Notes -     

Estimation of the Sorption Activity of Silver Nanoparticles on Biodegradable Fibers of Natural and Artificial Origin

Russian Physics Journal - The specific features of the sorption activity of silver nanoparticles (AgNPs) on biodegradable polymers of natural (collagen) and artificial (polyamide 6.6) origin have...     

Formal proofs of operator identities by a single formal computation

A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be modelled by noncommutative polynomials and such a formal computation proves that the polynomial corresponding to the new identity lies in the ideal generated by the polynomials corresponding to the known identities. In order to prove an operator identity, however, just proving membership of the polynomial in the ideal is not enough, since the ring of noncommutative polynomials ignores domains and codomains. We show that it suffices to additionally verify compatibility of this polynomial and of the generators of the ideal with the labelled quiver that encodes which polynomials can be realized as linear operators. Then, for every consistent representation of such a quiver in a linear category, there exists a computation in the category that proves the corresponding instance of the identity. Moreover, by assigning the same label to several edges of the quiver, the algebraic framework developed allows to model different versions of an operator by the same indeterminate in the noncommutative polynomials.     

Small-Angle Neutron Scattering at the Pulsed Reactor IBR-2: Current Status and Prospects

Crystallography Reports - Neutron diffraction studies on the small-angle neutron spectrometer YuMO (Joint Institute for Nuclear Research, Dubna), based on the IBR-2 pulsed reactor, have been...     

Mesomorphism of Dichotomous Compounds; X-Ray Diffraction Analysis of 4-Chlorophenyl Hexadecyl Ether

Crystallography Reports - The crystal and molecular structures of Cl–C6H4–O–C16H33 (I) have been studied, and its differential scanning calorimetry (DSC) study is performed....     

Multi-analyte HPLC–DAD Method for Concurrent Analysis of Six Antimicrobials and Three Proton Pump Inhibitors Frequently used in Management of Helicobacter pylori Infection: Application to Simulated Intestinal Fluid Samples

Chromatographia - The present work deals with the optimization, validation and application of a versatile HPLC–DAD method for concurrent estimation of nine antimicrobials and proton pump...     

Persistent Monitoring by Multiple Unmanned Aerial Vehicles Using Bernstein Polynomials

Journal of Optimization Theory and Applications - A framework for monitoring a target modeled as Dubins car using multiple UAVs is proposed. The UAVs are subject to minimum and maximum speed,...     

Role of Conformational Changes of Hexameric Bacterial Uridine Phosphorylases in Substrate Binding

Crystallography Reports - Crystals of mutants of uridine phosphorylase from Shewanella oneidensis MR-1 at the active-site threonine residue were obtained, and the three-dimensional structures of...     

Neutron Scattering Techniques and Complementary Methods for Structural and Functional Studies of Biological Macromolecules and Large Macromolecular Complexes

Crystallography Reports - The review describes the application of small-angle scattering (SAS) of neutrons and complementary methods to study the structures of biomacromolecules. Here we cover SAS...