in addition to exploring constructions and properties of limits and colimits in categories of topologicalalgebras, we study special subcategories of topological algebras and their properties. in particular, undercertain conditions, reflective subcategories when paired with topological structures give rise to reflectivesubcategories and epireflective subcategories give rise to epireflective subc...

these are notes from introductory survey lectures given at the institute for studies in theoretical physics and mathematics (ipm), teheran, in 2008 and 2010. we present the definition and the fundamental properties of fomin-zelevinsky’s cluster algebras. then, we introduce quiver representations and show how they can be used to construct cluster variables, which are the canonical generators of ...

‎in this paper first we define the morphism between geometric spaces in two different types‎. ‎we construct two categories of $uu$ and $l$ from geometric spaces then investigate some properties of the two categories‎, ‎for instance $uu$ is topological‎. ‎the relation between hypergroups and geometric spaces is studied‎. ‎by constructing the category $qh$ of $h_{v}$-groups we answer the question...

Erratum, 11 July 2022: This is an updated version of the original paper \cite{Moore1} in which notion reparametrization category was incorrectly axiomatized. Details on changes to are provided Appendix.A a small topologically enriched semimonoidal such that structure induces semigroup objects, all spaces maps contractible and each map can be decomposed (not necessarily unique way) as tensor pro...

We compared bark proteins from four contrasting (blister rust-resistant versus susceptible) half-sib seedling pairs of western white pine (Pinus monticola D. Don). Pooled proteins from resistant and susceptible groups (four trees per group) were separated by two-dimensional gel electrophoresis, silver stained, and analyzed with the aid of a laser scanner interfaced with a computerized gel docum...

The problem of defining Semi-Simplicial Types (SSTs) in Homotopy Type Theory (HoTT) has been recognized as important during the Year of Univalent Foundations at the Institute of Advanced Study [14]. According to the interpretation of HoTT in Quillen model categories [5], SSTs are type-theoretic versions of Reedy fibrant semi-simplicial objects in a model category and simplicial and semi-simplic...

Properties of categories enriched over the category metric spaces are investigated and applied to a study well-known constructions Banach spaces. We prove e.g. that weighted limits colimits exist in metric-enriched iff ordinary ε-(co)equalizers given by ε-(co)isometries for all ε. An object is called approximately injective w.r.t. morphism h:A→A′ morphisms from A into it arbitrarily close those...

We develop a theory of infinity properads enriched in general symmetric monoidal category. These are defined as presheaves, satisfying Segal condition and Rezk completeness condition, over certain categories graphs. In particular, we introduce new category level graphs which also allow us to give framework for algebras an properad. show that one can vary the without changing underlying theory. ...

Gram-positive bacteria are an important pathogenic factor for bacterial pneumonia. The aim of the present study was to identify the differentially expressed genes (DEGs) and to explore their associated pathways or expression patterns. Expression profiling of gene arrays from two independent datasets, GSE6269 and GSE35716, were downloaded from the Gene Expression Omnibus. The DEGs between periph...

The paradoxical response of Streptococcus sanguinis to drugs prescribed for dental and clinical practices has complicated treatment guidelines and raised the need for further investigation. We conducted a high throughput study on concomitant transcriptome and proteome dynamics in a time course to assess S. sanguinis behaviour under a sub-inhibitory concentration of ampicillin. Temporal changes ...