New Investigations of the Crystal Structure of Lead Germanate Pb5Ge3O11

Crystallography Reports - Perfect stoichiometric Pb5Ge3O11 single crystals have been synthesized by the flux method. Their cationic and anionic stoichiometry is confirmed by chemical analysis. The...     

Fractional order models for the homogenization and wave propagation analysis in periodic elastic beams

Meccanica - The advancement of manufacturing techniques has led to a rapid increase in the design and fabrication of periodic and architectured materials for a variety of dynamics and wave...     

On the Homogenization of an Optimal Control Problem in a Domain Perforated by Holes of Critical Size and Arbitrary Shape

Doklady Mathematics - The paper studies the asymptotic behavior of the optimal control for the Poisson type boundary value problem in a domain perforated by holes of an arbitrary shape with...     

OntoMathPRO: An Ontology of Mathematical Knowledge

Doklady Mathematics - The article describes OntoMathPRO, the first Linked Open Data ontology of professional mathematical knowledge. The ontology is designed to represent mathematical concepts. The...     

The design of TOPK inhibitors using structure-based pharmacophore modeling and molecular docking based on an MD-refined homology model

Molecular Diversity - The TOPK enzyme (also known as PBK) is a serine-threonine protein kinase that is rarely detected in normal tissues yet is found to be overexpressed and activated in a variety...     

Characterizations of modalities and lex modalities

A reflective subuniverse in homotopy type theory is an internal version of the notion of a localization in topology or in the theory of ∞-categories. Working in homotopy type theory, we give new characterizations of the following conditions on a reflective subuniverse L: (1) the associated subuniverse $L^{\prime }$ of L-separated types is a modality; (2) L is a modality; (3) L is a lex modality; and (4) L is a cotopological modality. In each case, we give several necessary and sufficient conditions. Our characterizations involve various families of maps associated to L, such as the L-étale maps, the L-equivalences, the L-local maps, the L-connected maps, the unit maps ${\eta }_X$, and their left and/or right orthogonal complements. More generally, our main theorem gives an overview of how all of these classes related to each other. We also give examples that show that all of the inclusions we describe between these classes of maps can be strict.