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The purpose of this note is to establish isomorphisms up to bounded torsion between relative$K_{0}$-groups and Chow groups with modulus as defined by Binda and Saito.

We construct isomorphism between super ℏ-Yangian \\(Y_ (sl(1,\\,1))\\) of special linear superalgebra \\(sl(1,\\,1)\\) and quantum loop superalgebra \\(U_ (Lsl(1,\\,1))\\).

We extend T. Y. Thomas’s approach to projective structures, over the complex analytic category, by involving the$\\unicode[STIX]{x1D70C}$-connections. This way, a better control of projective flatness is obtained and, consequently, we have, for example, the following application: if the twistor space of a quaternionic manifold$P$is endowed with a complex projective structure then$P$can be locally identified, through quaternionic diffeomorphisms, with the quaternionic projective space.

We produce an isomorphism$E_{\\infty }^{m,-m-1}\\cong \\text{Nrd}_{1}(A^{\\otimes m})$between terms of the$\\text{K}$-theory coniveau spectral sequence of a Severi–Brauer variety$X$associated with a central simple algebra$A$and a reduced norm group, assuming$A$has equal index and exponent over all finite extensions of its center and that$\\text{SK}_{1}(A^{\\otimes i})=1$for all$i>0$.

Let V be a compact and irreducible complex space of complex dimension v whose regular part is endowed with a complete Hermitian metric h. Let π:M→V be a resolution of V. Under suitable assumptions on h we prove that H2,∂¯v,q(reg(V),h)≅H∂¯v,q(M),q=0,…,v.Then we show that the previous isomorphism applies to the case of Saper-type Kähler metrics, as introduced by Grant Melles and Milman, and to the case of complete Kähler metrics with finite volume and pinched negative sectional curvatures.

We show that a complete bipartite graph Kpe,pf, where p is an odd prime, has an edge-transitive embedding in an orientable surface with all faces bounded by simple cycles if and only if e = f. There are exactly p2(e-1) such embeddings up to isomorphism. Among them, pe-1 are orientably regular, one of which is reflexible and pe-1-1 form chiral pairs. The remaining p2(e-1)-pe-1 embeddings are non-regular (not arc-transitive). All of these embeddings have genus12(pe-1)(pe-2).

Structural thinking, defined as the identification of relationships among the elements of a system and their use to understand its functioning, is relevant in both scientific modelling and Mathematics Education. Due to the lack of explicit models to describe this type of thinking, this study aims to characterize the structural thinking present in Galois' first memoir, “Memoir on the Conditions for the Solvability of Equations by Radicals”. This treatise is significant for introducing the mathematical notion of group and the study of algebraic structures. Based on documentary analysis, the treatise and its historical context were examined, leading to the identification of three key characteristics of structural thinking: the study of structure–behavior relationships, isomorphism as a modelling mechanism, and the development of a macrostructural view.

Integrates the concept of an m-semilattice with the theory of soft sets, and introduces definitions for soft m-semilattices, soft sub-m-semilattices, soft ideals, and ideal soft m-semilattices. Several algebraic properties of soft m-semilattice are proved, especially those after combining the concepts of intersection, union, and direct product of soft sets. After establishing the definition of soft m-semilattice homomorphism, the relationship between m-semilattice homomorphism, m-semilattice isomorphism, soft m-semilattice homomorphism and soft m-semilattice, soft sub m-semilattice, soft ideal, ideal soft m-semilattice is studied.

Starting with a Cuntz algebra O n constructed by n isometries, we discuss a C * -algebra consisting of elements of a fixed size k square matrix, where the entries of matrix are from the Cuntz algebra n . It is surprising to find that if k divides n , the resulting C * -algebra of matrix is isomorphic to the Cuntz algebra n . We extend this result to cases where k is larger than n , showing that the same conclusion holds provided that every prime factor of k divides n .

In this paper, on the one hand, we prove that for n≥2 any subbundle of T∗Tn with bounded fibers symplectically embeds into a trivial subbundle of T∗Tn where the fiber is an irrational cylinder. This not only resolves an open problem in Gong and Xue (Nonlinearity 33:6297–6348, 2020) (which was stated for the 4-dimension case, that is, n=2) and also generalizes to any higher-dimensional situation. The proof is based on some version of Dirichlet’s approximation theorem. On the other hand, we generalize a main result in Gong and Xue (Nonlinearity 33:6297–6348, 2020), showing that any π~1(M)-trivial Liouville diffeomorphism on T∗M (for instance, a diffeomorphism induced by an isometry on M) does not change the full marked length spectrum of a Finsler metric F on M, up to a lifting of the Finsler metric F to the unit codisk bundle DF∗M. The proof is based on persistence module theory.