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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}_{\\hslash }({\\mathfrak{s}}{\\mathfrak{l}}(1,\\,1))\\) of special linear superalgebra \\({\\mathfrak{s}}{\\mathfrak{l}}(1,\\,1)\\) and quantum loop superalgebra \\({U}_{\\hslash }(L{\\mathfrak{s}}{\\mathfrak{l}}(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$i>0$.

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 [2], the first two authors generalized the concept of 𝑛-isoclinism to the class of all pairs of groups. In this paper, we extend that notion to 𝑣-isologism and study the details of this notion. In addition, it is shown that every pair of groups is 𝑣-isologic with a quotient irreducible pair of groups. Finally, as an application, we drive some inequalities for the Baer-invariant of a pair of groups.

We study extensions of the Election Isomorphism problem, focused on the existence of isomorphic subelections. Specifically, we propose the Subelection Isomorphism and the Maximum Common Subelection problems and study their computational complexity and approximability. Using our problems in experiments, we provide some insights into the nature of several statistical models of elections

In this paper we give a complete description of the Bieri–Neumann–Strebel–Renz invariants of the Lodha–Moore groups. The second author previously computed the first two invariants, and here we show that all the higher invariants coincide with the second one, which finishes the complete computation. As a consequence, we present a complete picture of the finiteness properties of normal subgroups of the first Lodha–Moore group. In particular, we show that every finitely presented normal subgroup of the group is of type $\\textrm{F}_\\infty$ , answering a question posed in Oberwolfach in 2018. The proof involves applying a variation of Bestvina–Brady discrete Morse theory to the so called cluster complex X introduced by the first author. As an application, we also demonstrate that a certain simple group S previously constructed by the first author is of type $\\textrm{F}_\\infty$ . This provides the first example of a type $\\textrm{F}_\\infty$ simple group that acts faithfully on the circle by homeomorphisms, but does not admit any nontrivial action by $C^1$ -diffeomorphisms, nor by piecewise linear homeomorphisms, on any 1-manifold.