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The most general description of quantum evolution up to a time τ is a completely positive tracing preserving map known as a dynamical map Λ ̂ (τ). Here, we consider Λ ̂ (τ) arising from suddenly coupling a system to one or more thermal baths with a strength that is neither weak nor strong. Given no clear separation of characteristic system/bath time scales, Λ ̂ (τ) is generically expected to be non-Markovian; however, we do assume the ensuing dynamics has a unique steady state, implying the baths possess a finite memory time τm. By combining several techniques within a tensor network framework, we directly and accurately extract Λ ̂ (τ) for a small number of interacting fermionic modes coupled to infinite non-interacting Fermi baths. First, we use an orthogonal polynomial mapping and thermofield doubling to arrive at a purified chain representation of the baths whose length directly equates to a time over which the dynamics of the infinite baths is faithfully captured. Second, we employ the Choi–Jamiolkowski isomorphism so that Λ ̂ (τ) can be fully reconstructed from a single pure state calculation of the unitary dynamics of the system, bath and their replica auxiliary modes up to time τ. From Λ ̂ (τ) , we also compute the time local propagator L ̂ (τ). By examining the convergence with τ of the instantaneous fixed points of these objects, we establish their respective memory times τ m Λ and τ m L . Beyond these times, the propagator L ̂ (τ) and dynamical map Λ ̂ (τ) accurately describe all the subsequent long-time relaxation dynamics up to stationarity. These timescales form a hierarchy τ m L ≤ τ m Λ ≤ τ re , where τre is a characteristic relaxation time of the dynamics. Our numerical examples of interacting spinless Fermi chains and the single impurity Anderson model demonstrate regimes where τre ≫ τm, where our approach can offer a significant speedup in determining the stationary state compared to directly simulating the long-time limit. Our results also show that having access to Λ ̂ (τ) affords a number of insightful analyses of the open system thus far not commonly exploited. [ABSTRACT FROM AUTHOR]

Prior research shows that using mimetic isomorphism to select price/quality product strategies results in superior performance in the United States, the European Union, and Japan for both developed economy and emerging market manufacturers. However, do these results generalize in the case of emerging market service providers? Due to the nature of services, customers cannot gauge service quality prior to consumption, and they must rely on other cues; commonly, consumers rely on the brand name as a proxy. We theorize that for emerging market service providers, choosing a strategy of "distinctiveness" (pursuing a nondominant price/quality strategy) offers a way to differentiate their offering from the mimetic choice, resulting in superior performance. Implications for theory and practice are discussed. [ABSTRACT FROM AUTHOR]

The Adaptive Solvent-Scaling (AdSoS) scheme [J. Chem. Phys. 155 (2021) 094107] is an adaptive-resolution approach for performing simulations of a solute embedded in a fine-grained (FG) solvent region surrounded by a coarse-grained (CG) solvent region, with a continuous FG ↔ CG switching of the solvent resolution across a buffer layer. Instead of relying on a distinct CG solvent model, AdSoS is based on CG models defined by a dimensional scaling of the FG solvent by a factor s, accompanied by the s-dependent modulation of its mass and interaction parameters. The latter changes are designed to achieve an isomorphism between the dynamics of the FG and CG models, and to preserve the dispersive and dielectric solvation properties of the solvent with respect to a solute at FG resolution. As a result, the AdSoS scheme minimizes the thermodynamic mismatch between different regions of the adaptive-resolution system. The present article generalizes the scheme initially introduced for a pure atomic liquid in slab geometry to more practically relevant situations involving (i) a molecular dipolar solvent (e.g., water); (ii) a radial geometry (i.e., spherical rather than planar layers); and (iii) the inclusion of a solute (e.g., water molecule, dipeptide, ion, or ion pair). [ABSTRACT FROM AUTHOR]

If Γ is a subalgebra of A , then an A -module is called a Harish-Chandra module if it is the direct sum of its generalized weight spaces with respect to Γ. Drozd, Futorny, and Ovsienko [4] defined a generalization of a central subalgebra called a Harish-Chandra subalgebra and showed that when Γ is a Harish-Chandra subalgebra of A the structure of Harish-Chandra A -modules can be described using information about the relationship between A and the cofinite maximal ideals of Γ. We extend the results of [4] by dropping the assumption that Γ is quasicommutative. We facilitate this by introducing an equivalence relation ∼ on the set cfs (Γ) of cofinite maximal ideals of Γ. We define Harish-Chandra block modules with respect to ∼ to be A -modules that are the direct sum of so called block spaces corresponding to the equivalence classes cfs (Γ) / ∼. If Γ is a Harish-Chandra block subalgebra of A with respect to ∼, then the structure of Harish-Chandra block modules can be described based on the relationship between A and cfs (Γ) / ∼. In particular, we give a decomposition of the category of Harish-Chandra block modules and the collection of isomorphism classes of irreducible Harish-Chandra block modules. Furthermore, we define a category A on cfs (Γ) / ∼ , and show the category of profinite A -modules is equivalent to the category of Harish-Chandra block modules. Taking Γ to be noetherian and quasicommutative, and ∼ to be the equality relation, we recover (in fact, a slight refinement of) results from [4]. Lastly, we provide a sufficient condition for when there are a finite number of isomorphism classes of simple Harish-Chandra block modules with a given support. [ABSTRACT FROM AUTHOR]

In this paper, we construct a new class of simple smooth modules over the affine algebra A 1 (1). Specifically, we present a family of sl (2) ˆ -modules W φ for functions φ which are not Whittaker functions, and provide a simplicity criterion as well as an isomorphism theorem for such modules. For each simple sl (2) ˆ -module W φ , a class of simple sl (2) ˜ -module W φ , γ is also constructed for any constant γ. The sl (2) ˆ -modules W φ are weight modules, while the sl (2) ˜ -modules W φ , γ are not. [ABSTRACT FROM AUTHOR]

Quillen's Resolution Theorem in algebraic K -theory provides a powerful computational tool for calculating K -groups of exact categories. At the level of K 0 , this result goes back to Grothendieck. In this article, we first establish an extriangulated version of Grothendieck's Resolution Theorem. Second, we use this Extriangulated Resolution Theorem to gain new insight into the index theory of triangulated categories. Indeed, we propose an index with respect to an extension-closed subcategory N of a triangulated category C and we prove an additivity formula with error term. Our index recovers the index with respect to a contravariantly finite, rigid subcategory X defined by Jørgensen and the second author, as well as an isomorphism between K 0 sp (X) and the Grothendieck group of a relative extriangulated structure C R X on C when X is n -cluster tilting. In addition, we generalize and enhance some results of Fedele. Our perspective allows us to remove certain restrictions and simplify some arguments. Third, as another application of our Extriangulated Resolution Theorem, we show that if X is n -cluster tilting in an abelian category, then the index introduced by Reid gives an isomorphism K 0 (C R X) ≅ K 0 sp (X). [ABSTRACT FROM AUTHOR]

In this paper we study the (Cohen-Macaulay) type of orders over Dedekind domains in étale algebras. We provide a bound for the type, and give formulas to compute it. We relate the type of the overorders of a given order to the size of minimal generating sets of its fractional ideals, generalizing known results for Gorenstein and Bass orders. Finally, we give a classification of the ideal classes with multiplicator ring of type 2, with applications to the computations of the conjugacy classes of integral matrices and the isomorphism classes of abelian varieties over finite fields. [ABSTRACT FROM AUTHOR]

We describe a procedure for the generation of functional digraphs up to isomorphism; these are digraphs with uniform outdegree 1, also called mapping patterns, finite endofunctions, or finite discrete-time dynamical systems. This procedure is based on a reverse search algorithm for the generation of connected functional digraphs, which is then applied as a subroutine for the generation of arbitrary ones. Both algorithms output solutions with O (n 2) delay and require linear space with respect to the number n of vertices. [ABSTRACT FROM AUTHOR]

Aspect-based sentiment analysis (ABSA) aims to predict sentiment orientations towards textual aspects by extracting insights from user comments. While pretrained large language models (LLMs) demonstrate proficiency in sentiment analysis, incorporating syntactic and semantic features into ABSA remains a challenge. Additionally, employing LLMs for sentiment analysis often requires significant computational resources, rendering them impractical for use by individuals or small-scale entities. To address this, we propose the semiotic signal integration network (SSIN), which effectively combines syntactic and semantic features. The core syncretic information network leverages isomorphism and syntax to enhance knowledge acquisition. The semantically guided syntactic attention module further enables integrated semiotic representations via sophisticated attention mechanisms. Experiments on the publicly available SemEval dataset show that SSIN performs better than existing state-of-the-art ABSA baselines and LLMs such as Llama and Alpaca with high accuracy and macro-F1 scores. Moreover, our model demonstrates exceptional interpretability and the ability to discern both positive and negative sentiments, which is vitally important for real-world applications such as social media monitoring, health care, and customer service. Code is available at https://github.com/AmbitYuki/SSIN. [ABSTRACT FROM AUTHOR]

The Dutch othering discourse represents Moroccans as the most problematized group in society. Their designation as such entails being homogeneously perceived as the backward others whose culture is incompatible with the mainstream. In this rhetoric, men are represented as being oppressive patriarchs and women as passive victims who need to be rescued. This article examines alternative representations of Moroccan-Dutch people in Daria Bukvic's (2021) Meskina and the undeniable heterogeneity of their experiences and subjectivities. The film provides progressive portrayals of Moroccan-Dutch women as independent individuals with agency and full control over themselves, their choices, bodies, decisions, and men as supportive and open minded. It foregrounds their heterogeneity and agency through a focus on their negotiations and constructions of their subjectivities to answer back the essentializing Dutch discourse which constructs their otherness on the premise of being isomorphic. The analysis confirms that the film functions as a counter narrative to the established othering rhetoric in the Netherlands through problematizing the conventional attributes and traits associated with Moroccan-Dutch subjects and simultaneously deconstructing their alleged isomorphism. [ABSTRACT FROM AUTHOR]

This work focuses on the synthesis of non-redundant planar kinematic chains applied to parallel manipulators, where the mobility of the kinematic chains is constrained by the planar workspace, allowing for kinematic chains with up to three degrees-of-freedom. The synthesis process consists of two stages. First, a graph generator enumerates non-isomorphic biconnected graphs representing planar kinematic chains with up to three degrees-of-freedom and seven loops. Subsequently, graphs associated to chains with rigid subchains are removed using a degeneracy identification method based on matroid theory. Concise results are presented for chains with up to five loops. For chains with six and seven loops, results are categorized based on link partitions for a direct comparison with previous results. These findings align with prior research, with minor variations in the reported chain numbers. These variations can be attributed to several factors, including graph generation, isomorphism testing, fractionation, and subchain identification. These factors are comprehensively discussed and examined. [ABSTRACT FROM AUTHOR]

Similar to other countries, Australian firms are increasingly using corporate foundations (CFs) to manage their philanthropic giving. While research has explored the global expansion of CFs, there has been limited understanding on why they are established. This study involving 16 Australian CF managers used qualitative thematic analysis to identify the following four motivational factors that most influence organizational establishment of CFs: 1) centralizing corporate giving; 2) stakeholder influences; 3) financial advantages of foundation structure; and 4) strategic benefits to the establishing firm. The results suggest most Australian firms establish CFs to undertake strategic philanthropy, assisting those in need while capitalizing on the legitimizing social benefits. Many also use it to market activities to their staff, thereby enhancing internal engagement and retention. Yet despite such positive benefits, there is rarely a reduction in principal-agency costs when using a structured CF controlled by corporate executives rather than ad-hoc corporate giving. Furthermore, the decision to establish a CF is often based on normative isomorphism (copying competitors). Additionally, no CFs were established for direct taxation benefits, rather most were focused on the tax benefits associated with employee giving and donations from the general public. The uniqueness of these results, compared with other research, suggests there could be differing motivations to establish CFs based on the organization and the environment of the country where it is located. [ABSTRACT FROM AUTHOR]

We describe all possible coactions of finite groups (equivalently, all group gradings) on two-dimensional Artin-Schelter regular algebras. We give necessary and sufficient conditions for the associated Auslander map to be an isomorphism, and determine precisely when the invariant ring for the coaction is Artin-Schelter regular. The proofs of our results are combinatorial and exploit the structure of the McKay quiver associated to the coaction. [ABSTRACT FROM AUTHOR]

In this paper we study the set of MV-algebras with given prime spectrum and we introduce the class of spectral MV-algebras. An MV-algebra is spectral if it is generated by the union of all its prime ideals (or proper ideals, or principal ideals, or maximal ideals). Among spectral MV-algebras, special attention is devoted to bipartite MV-algebras. An MV-algebra is bipartite if it admits an homomorphism onto the MV-algebra of two elements. We prove that both bipartite MV-algebras and spectral MV-algebras can be finitely axiomatized in first order logic. We also prove that there is only, up to isomorphism, a set of MV-algebras with given prime spectrum. A further part of the paper is devoted to some relations between bipartite MV-algebras and their states. Recall that a state on an MV-algebra is a generalization of a probability measure on a Boolean algebra. Particular states are the states with Bayes' property. We show that an MV-algebra admits a state with the Bayes' property if and only if it is bipartite. [ABSTRACT FROM AUTHOR]

Let H k r denote an r -uniform hypergraph with k edges and r + 1 vertices, where k ≤ r + 1 (it is easy to see that such a hypergraph is unique up to isomorphism). The known general bounds on its Turán density are π (H k r) ≤ k − 2 r for all k ≥ 3 , and π (H 3 r) ≥ 2 1 − r for k = 3. We prove that π (H k r) ≥ (C k − o (1)) r − (1 + 1 k − 2) as r → ∞. In the case k = 3 , we prove π (H 3 r) ≥ (1.7215 − o (1)) r − 2 as r → ∞ , and π (H 3 r) ≥ r − 2 for all r. [ABSTRACT FROM AUTHOR]

Reference placement is promising to handle the increasing complexity in printed circuit board (PCB) designs, which aims to find the isomorphism of the placed template in component combination to reuse the placement. In this paper, we convert the netlist information into a graph and then model the reference placement as a subgraph matching problem. Since the state-of-the-art subgraph matching methods usually recursively search the solutions and suffer from high time and memory consumption in large-scale designs, we develop a novel subgraph matching algorithm D2BS with diversity tolerance and improved backtracking to guarantee matching quality and efficiency. The D2BS algorithm is founded on a data structure called the candidate space (CS) structure. We build and filter the candidate set for each query node according to our designed features to construct the CS structure. During the CS optimization process, a graph diversity tolerance strategy is adopted to achieve efficient inexact matching. Then, hierarchical matching is developed to search the template embeddings in the CS structure guided by branch backtracking and matched-node snatching strategies. Based on the industrial PCB designs, experimental results show that D2BS outperforms the state-of-the-art subgraph matching method in matching accuracy and running time. [ABSTRACT FROM AUTHOR]

A subalgebra of the full matrix algebra M n (K) , K a field, satisfying the identity [ x 1 , y 1 ] [ x 2 , y 2 ] ⋯ [ x q , y q ] = 0 is called a D q subalgebra of M n (K). In the paper we deal with the structure, conjugation and isomorphism problems of maximal D q subalgebras of M n (K). We show that a maximal D q subalgebra A of M n (K) is conjugated with a block triangular subalgebra of M n (K) with maximal commutative diagonal blocks. By analysis of conjugations, the sizes of the obtained diagonal blocks are uniquely determined. It reduces the problem of conjugation of maximal D q subalgebras of M n (K) to the analogous problem in the class of commutative subalgebras of M n (K). Further examining conjugations, in case A is contained in the upper triangular matrix algebra U n (K) , we prove that A is already in a block triangular form. We consider the isomorphism problem in a certain class of maximal D q subalgebras of M n (K) which contain all D q subalgebras of M n (K) with maximum dimension. In case K is algebraically closed, we invoke Jacobson's characterization of maximal commutative subalgebras of M n (K) with maximum (K -)dimension to show that isomorphic subalgebras in this class are already conjugated. To illustrate it, we invoke results from [19] and find all isomorphism (equivalently conjugation) classes of D q subalgebras of M n (K) with maximum possible dimension, in case K is algebraically closed. [ABSTRACT FROM AUTHOR]

This paper studies groups and their coset monoids. The anti-abnormal subgroups of a group are firstly introduced and investigated. It is shown that a group is an N ˜ -group if and only if each subgroup of it is anti-abnormal. Also, it is proved that the coset semigroups of N ˜ -groups are exactly the E-reflexive inverse semigroups which are factorisable and the natural connection between their semilattice of idempotents and lattice of subgroups of their group of units is a dual isomorphism. Finally, some characterizations of the coset semigroups of S-groups (U-groups and residually central groups respectively) are given. This extends McAlister's result in 1980. [ABSTRACT FROM AUTHOR]

Most of the modern natural language processing (NLP) techniques are based on the vector space models of language, in which each word is represented by a vector in a high dimensional space. One of the earliest successes was demonstrated by the four-term analogical reasoning task: what is to C as B is to A? The trained word vectors form "parallelograms" representing the quadruple of words in analogy. This discovery in NLP offers us insight into our understanding of human semantic representation of words via analogical reasoning. Despite successful applications of the large-scale language models, it has not been fully understood why such parallelograms emerge by learning through natural language data. As the vector space model is not optimized to form parallelograms, the key structure related to geometric shapes of word vectors is expected to be in the data, rather than the models. In the present article, we test our hypothesis that such parallelogram arrangement of word vectors readily exists in the co-occurrence statistics of language. Our approach focuses more on the data itself, and it is different from the existing theoretical approach trying to find the mechanism of parallelogram formation in the algorithms and/or vector arithmetic operations on word vectors. First, our analysis suggested that analogical reasoning is possible by decomposition of the bigram co-occurrence matrix. Second, we demonstrated the formation of a parallelepiped, a more structured geometric object than a parallelogram, by creating a small artificial corpus and its word vectors. With these results, we propose a refined form of distributional hypothesis pointing out an isomorphism between a sort of symmetry or exchangeability and word co-occurrence statistics. [ABSTRACT FROM AUTHOR]

Let Σ = (G,σ) be a signed graph with a vertex set V (G). A set D ⊆ V (G) is said to be a double dominating set of Σ if it satisfies the following conditions: (i) |N[v] ∩ D|≥ 2 for each v ∈ V (G), and (ii) Σ[D,Dc] is balanced, where N[v] denotes the closed neighborhood of v and Σ[D,Dc] denotes the subgraph induced by the edges of Σ with one end vertex in D and the other end vertex in Dc. The minimum size among all the double dominating sets of Σ is the double domination number γ×2(Σ) of Σ. In this study, we investigated this parameter for signed complete graphs. We prove that, for n ≥ 5, if (Kn,σ) is a signed complete graph, then 2 ≤ γ×2(Kn,σ) ≤ n − 1 and these bounds are sharp. Moreover, for all signed complete graphs over Kn we determined their possible double domination numbers. Finally, we compute the double domination numbers of all signed complete graphs of orders up to six. [ABSTRACT FROM AUTHOR]

AbstractWe study the concept of extended derivations of algebras which expands diverse definitions of generalized derivations given in the literature. We concentrate on the family of the anti-commutative algebras and classify such spaces of derivations by considering a suitable notion of equivalence when we restrict attention to sucssh algebras. Afterwards, we investigate a link between the well-known (α,β,γ) -derivations and some new extended derivations obtained in our classification. Finally, we present applications of extended derivations to study degenerations of algebras. [ABSTRACT FROM AUTHOR]

We study the representation theory of a hybrid quantum group at root of unity \zeta introduced by Gaitsgory. After discussing some basic properties of its category \mathcal {O}, we study deformations of the category \mathcal {O}. For subgeneric deformations, we construct the endomorphism algebra of big projective object and compute it explicitly. Our main result is an algebra isomorphism between the center of deformed category \mathcal {O} and the equivariant cohomology of \zeta-fixed locus on the affine Grassmannian attached to the Langlands dual group. [ABSTRACT FROM AUTHOR]

The Choi representation of completely positive trace preserving (CPTP) maps, i.e. quantum channels is often used in the context of quantum information and computation as it is easy to work with. It is a correspondence between CPTP maps and quantum states also termed as the Choi–Jamiołkowski isomorphism. It is especially useful if a parametrization of the set of CPTP maps is needed in order to consider a general map or optimize over the set of these. Here we provide a brief introduction to this topic, focusing on certain useful calculational techniques which are presented in full detail. [ABSTRACT FROM AUTHOR]

AbstractWe find an explicit form of the inverse isomorphism from Shapiro’s lemma in terms of inhomogeneous cocycles and apply it to construct special nonsplit coverings of groups with a unique conjugacy class of involutions. [ABSTRACT FROM AUTHOR]

This paper presents a formula for the a-number of certain maximal curves characterized by the equation yq+1 2 = xm + x over the finite field 픽q2. a-number serves as an invariant for the isomorphism class of the p-torsion group scheme. By utilizing the action of the Cartier operator on H0(풳, Ω1), we establish a closed formula for the a-number of 풳. [ABSTRACT FROM AUTHOR]

In this paper we introduce the galaxy of Coxeter groups (of finite rank) – an infinite dimensional, locally finite, ranked simplicial complex which captures isomorphisms between finite rank Coxeter systems. In doing so, we would like to suggest a new framework to study the isomorphism problem for Coxeter groups. We prove some structural results about this space, provide a full characterization in small ranks and propose many questions. In addition we survey known tools, results and conjectures. Along the way we show profinite rigidity of triangle Coxeter groups – a result which is possibly of independent interest. [ABSTRACT FROM AUTHOR]

Two subsets A, B of the plane are betweenness isomorphic if there is a bijection f : A → B such that, for every x, y, z ∈ A, the point f(z) lies on the line segment connecting f(x) and f(y) if and only if z lies on the line segment connecting x and y. In general, it is quite difficult to tell whether two given subsets of the plane are betweenness isomorphic. We concentrate on the case when each of the sets A, B is of the form C ∪ D where C is a circle and D is a finite set. We fully characterize the betweenness isomorphism classes in the family of all circles with three collinear points inside. In particular, we show that there are only countably many isomorphism classes, for which we provide an algebraic description. [ABSTRACT FROM AUTHOR]

In this study, we introduce the Sheffer stroke L-algebra and prove some fundamental theorems, propositions and lemmas of Sheffer Stroke L-algebras. The notions of filter and ultrafilter for Sheffer stroke L-algebra are studied. We give subalgebra and normal subset definitions of a Sheffer stroke L-algebras. Moreover, a homomorphism between Sheffer stroke L-algebras is introduced and isomorphism theorems are presented. Finally, we give three new algorithms for Sheffer stroke L-algebras. Thus, it is contributed to researchers on different application areas by presenting an algorithmic approach on this subject, for the first time in the literature. [ABSTRACT FROM AUTHOR]

Suppose R is a local ring with invariants p , n , r , m , k and m r = 4 , that is R of order p 4. Then, R = R 0 + u R 0 + v R 0 + w R 0 has maximal ideal J = u R 0 + v R 0 + w R 0 of order p (m − 1) r and a residue field F of order p r , where R 0 = G R (p n , r) is the coefficient subring of R. In this article, the goal is to improve the understanding of linear codes over small-order non-chain rings. In particular, we produce the MacWilliams formulas and generator matrices for linear codes of length N over R. In order to accomplish that, we first list all such rings up to isomorphism for different values of p , n , r , m , k. Furthermore, we fully describe the lattice of ideals in R and their orders. Next, for linear codes C over R, we compute the generator matrices and MacWilliams identities, as shown by numerical examples. Given that non-chain rings are not principal ideals rings, it is crucial to acknowledge the difficulties that arise while studying linear codes over them. [ABSTRACT FROM AUTHOR]

For a finite dimensional algebra |$A$|⁠ , the notion of |$g$| -fan |$\Sigma (A)$| is defined from two-term silting complexes of |$\textsf{K}^{\textrm{b}}(\textsf{proj} A)$| in the real Grothendieck group |$K_{0}(\textsf{proj} A)_{\mathbb{R}}$|⁠. In this paper, we discuss the theory of shards to |$\Sigma (A)$|⁠ , which was originally defined for a hyperplane arrangement. We establish a correspondence between the set of join-irreducible elements of torsion classes of |$\textsf{mod}A$| and the set of shards of |$\Sigma (A)$| for |$g$| -finite algebra |$A$|⁠. Moreover, we show that the semistable region of a brick of |$\textsf{mod}A$| is exactly given by a shard. We also give a poset isomorphism of shard intersections and wide subcategories of |$\textsf{mod}A$|⁠. [ABSTRACT FROM AUTHOR]

We classify twistings of Grothendieck's differential operators on a smooth variety |$X$| in prime characteristic |$p$|⁠. We prove that isomorphism classes of twistings are in bijection with |$H^{2}(X,\mathbb{Z}_{p}(1))$|⁠ , the degree 2, weight 1 syntomic cohomology of |$X$|⁠. We also discuss the relationship between twistings of crystalline and Grothendieck differential operators. Twistings in mixed characteristic are also analyzed. [ABSTRACT FROM AUTHOR]

For closed subgroups L and R of a compact Lie group G, a left L-space X, and an L-equivariant continuous map A : X → G/R, we introduce the twisted action of the equivariant cohomology H• R(pt, k) on the equivariant cohomology H• L(X, k). Considering this action as a right action, H• L(X, k) becomes a bimodule together with the canonical left action of H• L(pt, k). Using this bimodule structure, we prove an equivariant version of the Künneth isomorphism. We apply this result to the computation of the equivariant cohomologies of Bott–Samelson varieties and to a geometric construction of the bimodule morphisms between them. [ABSTRACT FROM AUTHOR]

Cobalt is a critical and strategic metal mainly found as associated element in several types of deposits, of which skarn‐type deposits are the major sources. Han‐Xing type skarn iron deposit, having high grade iron ore and associated cobalt, is a typical skarn‐type iron ore in China. But the complete recovery and exploitation of cobalt are restricted because of the lower grade of related cobalt and the dearth of prior research on its occurrence condition and enrichment mechanism. In this paper, pyrite from five typical ore deposits in the Han‐Xing area was studied by using electron probe microanalysis (EPMA) and laser‐ablation inductively‐coupled‐plasma mass‐spectrometry (LA–ICP–MS) techniques to decipher the occurrence state and enrichment mechanism of associated cobalt in skarn‐type iron deposits. The results show that Co2+ replaces Fe2+ in pyrite through isomorphism. The distribution of cobalt in pyrite from different deposits varies greatly, that is, in the Xishimen iron deposit, the cobalt content is comparatively enriched in the pyrite's core. In contrast, in other deposits, the cobalt content is concentrated in the pyrite's rims, where it can be up to 1000 times higher than in the core. The cobalt mineralization in Han‐Xing area can be divided into several stages. The sulphur element of sulphide is mainly derived from evaporite, while cobalt mineralization occurred in the early stage with pyrite formation or in the late stage by metasomatism/cementation of Co‐rich ore‐forming fluid. The magma assimilated with the Ordovician evaporite not only promoted iron mineralization, but also became the main controlling factor for cobalt enrichment. [ABSTRACT FROM AUTHOR]

It is well known that, up to isomorphism, there is a unique simple group of order 168. The projective special linear groups PSL(2, 7) and PSL(3, 2) are concrete examples of such groups, and are therefore isomorphic. This isomorphism is not obvious, but it has been clarified from several viewpoints. Here we use purely group-theoretic methods—the Sylow theorems, Poincaré's theorem, and the orbit-stabilizer theorem—to show that any simple group of order 168 has a natural action on the projective line over F 7 , so it is isomorphic to PSL(2, 7). We discuss an analogous action on the projective plane over F 2 described by Smith and Tabachnikova. Both geometries are constructed using conjugacy classes of maximal subgroups. This gives another proof of the uniqueness theorem and may dispel some of the air of mystery that often surrounds the isomorphism between PSL(2, 7) and PSL(3, 2). [ABSTRACT FROM AUTHOR]

In 1981, Gerhard Gierz and Jimmie Lawson gave a necessary condition for a complete lattice to be quasicontinuous using an equation. However, whether quasicontinuous lattices can be characterized by equations has remained unknown. In this paper, we give an equational characterization of quasicontinuous complete semilattices. Furthermore, we investigate congruences of quasicontinuous complete semilattices. We derive the first isomorphism theorem for quasicontinuous complete semilattices in the context of C-congruences. As a consequence, we show that the category of all continuous complete semilattices with maps preserving directed sups and nonempty infs is a reflective full subcategory of quasicontinuous complete semilattices. [ABSTRACT FROM AUTHOR]

We obtain partial affirmative answers to the question of whether the isomorphism of the unitary groups of two C*-algebras, either as topological groups or as discrete groups, implies the isomorphism of the C*-algebras as real C*-algebras. [ABSTRACT FROM AUTHOR]

Graph pattern matching is widely used in real-world applications, such as social network analysis. Since the traditional subgraph isomorphism is NP-complete and often too restrictive to catch sensible matches, relaxed graph pattern matching models are used. However, existing algorithms suffer from limited linear scalability and restricted degrees of parallelism. In this paper, we propose fast parallel algorithms, GPGS and GPDS, for graph simulation and dual simulation, respectively. They make most use of the GPU performance by adopting the edge-centric processing model. We perform parallel computations on the data graph edges to evaluate the matching constraints for each vertex allowing for fast and scalable algorithms. To the best of our knowledge, we present the first GPU-based algorithms for graph simulation and dual simulation. Extensive experiments on synthetic and real-world data graphs demonstrate that our algorithms significantly outperform existing methods, achieving up to 74.8 × acceleration for GPGS and up to 114.2 × acceleration for GPDS. [ABSTRACT FROM AUTHOR]

In this paper, we study the category of modules over the Smith algebra which are free of finite rank over the unital polynomial subalgebra generated by the Cartan element h and obtain families of such simple modules of arbitrary rank. In the case of rank one we obtain a full description of the isomorphism classes, a simplicity criterion, and an algorithm to produce all composition series. We show that all such modules have finite length and describe the composition factors and their multiplicity. [ABSTRACT FROM AUTHOR]

Social networks have become integral to daily life, allowing users to connect and share information. The efficient analysis of social networks benefits fields such as epidemiology, information dissemination, marketing, and sentiment analysis. However, the direct publishing of social networks is vulnerable to privacy attacks such as typical 1-neighborhood attacks. This attack can infer the sensitive information of private users using users' relationships and identities. To defend against these attacks, the k-anonymity scheme is a widely used method for protecting user privacy by ensuring that each user is indistinguishable from at least k − 1 other users. However, this approach requires extensive modifications that compromise the utility of the anonymized graph. In addition, it applies uniform privacy protection, ignoring users' different privacy preferences. To address the above challenges, this paper proposes an anonymity scheme called TC α -PIA (Tree Clustering and α -Partial Isomorphism Anonymization). Specifically, TC α -PIA first constructs a similarity tree to capture subgraph feature information at different levels using a novel clustering method. Then, it extracts the different privacy requirements of each user based on the node cluster. Using the privacy requirements, it employs an α -partial isomorphism-based graph structure anonymization method to achieve personalized privacy requirements for each user. Extensive experiments on four public datasets show that TC α -PIA outperforms other alternatives in balancing graph privacy and utility. [ABSTRACT FROM AUTHOR]

In previous works, we have proven that there are local tetrads in four-dimensional curved Lorentzian spacetimes that can be written in terms of two kinds of local structures, the skeletons and the gauge vectors. These tetrads diagonalize locally and covariantly the stress–energy tensors for systems of differential equations of the Einstein–Maxwell kind in the Abelian electromagnetic case, or of the Einstein–Maxwell–Yang-Mills kind when non-Abelian Yang–Mills fields are included, along with suitable Yang–Mills stress–energy tensors. Under local Lorentz transformations, these new tetrads conserve their skeleton-gauge vector structure. In this short paper, we will prove that given any general unit orthogonal tetrad in spacetime, we will be able to construct a new tetrad in the skeleton-gauge vector form. We will prove a theorem stating that the original orthonormal tetrad can be constructed or reexpressed with this same local tetrad skeleton-gauge vector structures. The theorems proved in this paper will enable the demonstration of new results in group isomorphism theorems in the future. [ABSTRACT FROM AUTHOR]

In this paper, we present an isomorphism that connects a code of length n over 픽qm to a code of length mn over 픽q. We define criteria for identifying linear complementary pair (LCP) and linear complementary dual (LCD) codes by utilizing this isomorphism. We also introduce the notion of ℓ-LCP of codes into the LCP framework and give a necessary and sufficient condition for their characterization. We also provide a necessary and sufficient condition for the existence of an maximum distance separable (MDS) ℓ-LCP of codes. These insights into the structural properties of codes offer promising avenues for their application in various fields, particularly in the realm of finite fields. [ABSTRACT FROM AUTHOR]

Sandpile groups are a subtle graph isomorphism invariant, in the form of a finite abelian group, whose cardinality is the number of spanning trees in the graph. We study their group structure for graphs obtained by attaching a cone vertex to a tree. For example, it is shown that the number of generators of the sandpile group is at most one less than the number of leaves in the tree. For trees on a fixed number of vertices, the paths and stars are shown to provide extreme behavior, not only for the number of generators, but also for the number of spanning trees, and for Tutte polynomial evaluations that count the recurrent sandpile configurations by their numbers of chips. [ABSTRACT FROM AUTHOR]

Let G be a semisimple complex algebraic group with a simple Lie algebra , and let ℳ G 0 denote the moduli stack of topologically trivial stable G -bundles on a smooth projective curve C. Fix a theta characteristic κ on C which is even in case dim is odd. We show that there is a nonempty Zariski open substack κ of ℳ G 0 such that H i (C , ad (E G) ⊗ κ) = 0 , i = 1 , 2 , for all E G ∈ κ . It is shown that any such E G has a canonical connection. It is also shown that the tangent bundle T U κ has a natural splitting, where U κ is the restriction of κ to the semi-stable locus. We also produce an isomorphism between two naturally occurring Ω M G r s 1 -torsors on the moduli space of regularly stable M G r s . [ABSTRACT FROM AUTHOR]

The article titled "Congruence-Simple Acts Over Completely Simple Semigroups" explores the characterization of simple and congruence-simple acts over a completely simple semigroup. The authors provide definitions and explanations of terms used in semigroup theory and act theory, and pay tribute to mathematician Aleksandr Vasilievich Mikhalev in the introduction. The text discusses congruences and associated subgroups, introducing lemmas and theorems to establish the relationship between congruences and subgroups. It also explores the properties of congruence-simple acts and provides a classification for different types of congruence-simple acts, with the goal of finding the maximal proper congruences of a given act. The authors declare no conflict of interest and acknowledge financial support for their research. [Extracted from the article]

The Kuratowski graphs K 3 , 3 and K 5 characterize planarity. Counting distinct 2-cell embeddings of these two graphs on orientable surfaces was previously done by Mull (1999) and Mull et al. (2008), using Burnside's Lemma and automorphism groups of K 3 , 3 and K 5 , without actually constructing the embeddings. We obtain all 2-cell embeddings of these graphs on the double torus, using a constructive approach. This shows that there is a unique non-orientable 2-cell embedding of K 3 , 3 , and 14 orientable and 17 non-orientable 2-cell embeddings of K 5 on the double torus, which are explicitly obtained using an algorithmic procedure of expanding from minors. Therefore we confirm the numbers of embeddings obtained by Mull (1999) and Mull et al. (2008). As a consequence, several new polygonal representations of the double torus are presented. Rotation systems for the one-face embeddings of K 5 on the triple torus are also found, using exhaustive search. [ABSTRACT FROM AUTHOR]

Walker's cancellation theorem for abelian groups tells us that if A$A$ is finitely generated and G$G$ and H$H$ are such that A⊕G≅A⊕H$A \oplus G \cong A \oplus H$, then G≅H$G \cong H$. Deveau showed that the theorem can be effectivized, but not uniformly. In this paper, we expand on Deveau's initial analysis to show that the complexity of uniformly outputting an index of an isomorphism between G$G$ and H$H$, given indices for A$A$, G$G$, H$H$, the isomorphism between A⊕G$A \oplus G$ and A⊕H$A \oplus H$, and the rank of A$A$, is 0′$\mathbf {0^{\prime }}$. Moreover, we find that the complexity remains 0′$\mathbf {0^{\prime }}$ even if the generators in the copies of A$A$ are specified. [ABSTRACT FROM AUTHOR]

Stanley asked whether a tree is determined up to isomorphism by its chromatic symmetric function. We approach Stanley's problem by studying the relationship between the chromatic symmetric function and other invariants. First, we prove Crew's conjecture that the chromatic symmetric function of a tree determines its generalized degree sequence, which enumerates vertex subsets by cardinality and the numbers of internal and external edges. Second, we prove that the restriction of the generalized degree sequence to subtrees contains exactly the same information as the subtree polynomial, which enumerates subtrees by cardinality and number of leaves. Third, we construct arbitrarily large families of trees sharing the same subtree polynomial, proving and generalizing a conjecture of Eisenstat and Gordon. [ABSTRACT FROM AUTHOR]

A module over a ring R is pure projective provided it is isomorphic to a direct summand of a direct sum of finitely presented modules. We develop tools for the classification of pure projective modules over commutative noetherian rings. In particular, for a fixed finitely presented module M, we consider Add ⁡ ( M ) {\operatorname{Add}(M)} , which consists of direct summands of direct sums of copies of M. We are primarily interested in the case where R is a one-dimensional, local domain, and in torsion-free (or Cohen–Macaulay) modules. We show that, even in this case, Add ⁡ ( M ) {\operatorname{Add}(M)} can have an abundance of modules that are not direct sums of finitely generated ones. Our work is based on the fact that such infinitely generated direct summands are all determined by finitely generated data. Namely, idempotent/trace ideals of the endomorphism ring of M and finitely generated projective modules modulo such idempotent ideals. This allows us to extend the classical theory developed to study the behaviour of direct sum decomposition of finitely generated modules comparing with their completion to the infinitely generated case. We study the structure of the monoid V * ⁢ ( M ) {V^{*}(M)} , of isomorphism classes of countably generated modules in Add ⁡ ( M ) {\operatorname{Add}(M)} with the addition induced by the direct sum. We show that V * ⁢ ( M ) {V^{*}(M)} is a submonoid of V * ⁢ ( M ⊗ R R ^ ) {V^{*}(M\otimes_{R}\widehat{R})} , this allows us to make computations with examples and to prove some realization results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate various elegant filters and congruences of the class of core regular double Stone algebras (briefly CRD-Stone algebras). We define and characterize the concepts of k-filters and principal k-filters of a core regular double Stone algebra with the core element k, as well as their algebraic structures. We also look at k- { ∗ } -congruences and principal k- { ∗ } -congruences of a CRD-Stone algebra L that are induced by k-filters and principal k-filters of L, respectively. We find an isomorphism between the lattice F k (L) of all k-filters of L (the lattice F k p (L) principal k-filters of L) and the lattice C o n k ∗ (L) of all k- { ∗ } -congruences on L (the lattice C o n k ∗ (L) of all principal k- { ∗ } -congruences) of a CRD-Stone algebra L. [ABSTRACT FROM AUTHOR]

In this paper, we establish the pathconnectedness of H-wavelet sets in a reducing subspace H of L²(R). [ABSTRACT FROM AUTHOR]