Recent advances and challenges in the recovery and purification of cellular exosomes

Exosomes are nanovesicles secreted by most cellular types that carry important biochemical compounds throughout the body with different purposes, playing a preponderant role in cellular communication. Because of their structure, physicochemical properties and stability, recent studies are focusing in their use as nanocarriers for different therapeutic compounds for the treatment of different diseases ranging from cancer to Parkinson's disease. However, current bioseparation protocols and methodologies are selected based on the final exosome application or intended use and present both advantages and disadvantages when compared among them. In this context, this review aims to present the most important technologies available for exosome isolation while discussing their advantages and disadvantages and the possibilities of being combined with other strategies. This is critical since the development of novel exosome‐based therapeutic strategies will be constrained to the effectiveness and yield of the selected downstream purification methodologies for which a thorough understanding of the available technological resources is needed.     

Super-biderivations of not-finitely graded Lie superalgebras related to generalized super-Virasoro algebras

We mainly study the super-biderivations of not-finitely graded Lie superalgebras related to generalized super-Virasoro algebras. In particular, we prove that all super-biderivations of not-finitely graded Lie superalgebras related to generalized super-Virasoro algebras are inner.     

Quantizer–dequantizer operators as a tool for formulating the quantization procedure

We consider the quantization procedure and investigate the application of the quantizer–dequantizer method and star-product technique to construct associative products and the associative algebras formed by the quantizer–dequantizer operators and their symbols. The corresponding Lie algebras are also constructed. We study the case where the quantizer–dequantizer operators form a self-dual system and show that the structure constants of the Lie algebras satisfy some identity, in addition to the Jacobi identity. Using tomographic quantizer–dequantizer operators and their symbols, we construct the continuous associative algebra and the corresponding Lie algebra.     

正规Bihom-Lie代数的上边缘算子刻画

考虑正规Bihom-Lie代数(L,[?,?]?,α,β)的平凡表示， 给出了平凡表示对应的上边缘算子d； 证明了该算子的相关性质； 得到: 正规Bihom-Lie 代数(L,[?,?]?,α,β)与∧L*上的算子d之间存在一一对应关系。     

Topology and measure in logics for region-based theories of space

Space, as we typically represent it in mathematics and physics, is composed of dimensionless, indivisible points. On an alternative, region-based approach to space, extended regions together with the relations of ‘parthood’ and ‘contact’ are taken as primitive; points are represented as mathematical abstractions from regions.Region-based theories of space have been traditionally modeled in regular closed (or regular open) algebras, in work that goes back to [5] and [21]. Recently, logics for region-based theories of space were developed in [3] and [19]. It was shown that these logics have both a nice topological and relational semantics, and that the minimal logic for contact algebras, ${\mathbb{L}}_{min}^{cont}$ (defined below), is complete for both.The present paper explores the question of completeness of ${\mathbb{L}}_{min}^{cont}$ and its extensions for individual topological spaces of interest: the real line, Cantor space, the rationals, and the infinite binary tree. A second aim is to study a different, algebraic model of logics for region-based theories of space, based on the Lebesgue measure algebra (or algebra of Borel subsets of the real line modulo sets of Lebesgue measure zero). As a model for point-free space, the algebra was first discussed in [2]. The main results of the paper are that ${\mathbb{L}}_{min}^{cont}$ is weakly complete for any zero-dimensional, dense-in-itself metric space (including, e.g., Cantor space and the rationals); the extension ${\mathbb{L}}_{min}^{cont}+(Con)$ is weakly complete for the real line and the Lebesgue measure contact algebra. We also prove that the logic ${\mathbb{L}}_{min}^{cont}+(Univ)$ is weakly complete for the infinite binary tree.     

Derived equivalences between triangular matrix algebras

In this paper, we study derived equivalences between triangular matrix algebras using certain classical recollements. We show that special properties of these recollements actually characterize triangular matrix algebras and describe methods to construct tilting modules and tilting complexes inducing derived equivalences between them.     

A note on Bridgeland Hall algebras

In this note, let 𝒜 be a finitary hereditary abelian category with enough projectives. By using the associativity formula of Hall algebras, we give a new proof of the main theorem in [17 Yanagida, S. (2016). A note on Bridgeland’s Hall algebra of two-periodic complexes. Math. Z. 282(3):973–991.[Crossref], [Web of Science ®] , [Google Scholar]], which states that the Bridgeland Hall algebra of 2-cyclic complexes of projective objects in 𝒜 is isomorphic to the Drinfeld double Hall algebra of 𝒜.