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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]

Staic defined symmetric cohomology of groups and studied that the secondary symmetric cohomology group is corresponding to group extensions and the injectivity of the canonical map from symmetric cohomology to classical cohomology. In this paper, we define symmetric cohomology and symmetric Hochschild cohomology for cocommutative Hopf algebras. The first one is a generalization of symmetric cohomology of groups. We give an isomorphism between symmetric cohomology and symmetric Hochschild cohomology, which is a symmetric version of the classical result about cohomology of groups by Eilenberg and MacLane and cohomology of Hopf algebras by Ginzburg and Kumar. Moreover, to consider the condition that symmetric cohomology coincides with classical cohomology, we investigate the projectivity of a resolution which gives symmetric cohomology. [ABSTRACT FROM AUTHOR]

Let p be a prime number and k = F ¯ p , the algebraic closure of the finite field F p of p elements. Let G be a connected reductive group defined over F p and B be a Borel subgroup of G (not necessarily defined over F p ). Let k H be the group algebra of a group H over k . We show that for each (one-dimensional) character θ of B (not necessarily rational), there is a unique (up to isomorphism) irreducible k G -module L (θ) containing θ as a k B -submodule, and moreover, L (θ) is isomorphic to a parabolic induction from a finite-dimensional irreducible k L -module for some Levi subgroup L of G . Thus, we have classified and constructed all (abstract) irreducible k G -modules with B -stable line (i.e. an one-dimensional k B -submodule). As a byproduct, we give a new proof of a result of Borel and Tits on the classification of finite-dimensional irreducible k G -modules. [ABSTRACT FROM AUTHOR]

We prove that the Drinfeld center Z (C) of a pivotal finite tensor category C comes with the structure of a ribbon Grothendieck–Verdier category in the sense of Boyarchenko–Drinfeld. Phrased operadically, this makes Z (C) into a cyclic algebra over the framed E 2 -operad. The underlying object of the dualizing object is the distinguished invertible object of C appearing in the well-known Radford isomorphism of Etingof–Nikshych–Ostrik. Up to equivalence, this is the unique ribbon Grothendieck–Verdier structure on Z (C) extending the canonical balanced braided structure that Z (C) already comes equipped with. The duality functor of this ribbon Grothendieck–Verdier structure coincides with the rigid duality if and only if C is spherical in the sense of Douglas–Schommer-Pries–Snyder. The main topological consequence of our algebraic result is that Z (C) gives rise to an ansular functor, in fact even a modular functor regardless of whether C is spherical or not. In order to prove the aforementioned uniqueness statement for the ribbon Grothendieck–Verdier structure, we derive a seven-term exact sequence characterizing the space of ribbon Grothendieck–Verdier structures on a balanced braided category. This sequence features the Picard group of the balanced version of the Müger center of the balanced braided category. [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]

The infrastructure to support human societies' safety, health, and utility supply can not be negotiated, and to have basic reliability in monitoring tasks, plural or dual surveillance, rooted in biologic senses, is needed. To fit the contemporary wireless communication, MIMO (multi-in multi-out) being incorporated with suggested network prototypes, aimed especially on the naturally bipartite Honeycomb Tori (HT) for cellular communications, to prevent information loss, interference, unexpected changes caused by such as clogged water. The mutually independent Hamiltonian Path (MIHP) property can be used for parallel processing and supporting cipher coding to offer efficiency, integrity, and privacy. Isomorphism between Honeycomb Tori and Generalized Honeycomb Tori (GHT) is utilized; mathematical HT(m) m ≥ 2 can be presented as GHT (m, 6m, 3m). Setting rational configurations, incremental scalability qualifying, it is proved that GHT (m, n, n/2) "even m, n ≥ 12" and "odd m > 1, n ≥ 10," which naturally include full Honeycomb Tori, can have a property dual MIHP. [ABSTRACT FROM AUTHOR]

Consider a large labeled graph (network), denoted the target. Subgraph matching is the problem of finding all instances of a small subgraph, denoted the query, in the target graph. Unlike the majority of existing methods that are restricted to graphs with labels solely on vertices, our proposed approach, named can effectively handle graphs with labels on both vertices and edges. ntroduces an efficient new vertex/edge domain data structure filtering procedure to speed up subgraph queries. The procedure, called path-based reduction, filters initial domains by scanning them for paths up to a specified length that appear in the query graph. Additionally, ncorporates existing techniques like variable ordering and parent selection, as well as adapting the core search process, to take advantage of the information within edge domains. Experiments in real scenarios such as protein–protein interaction graphs, co-authorship networks, and email networks, show that s faster than state-of-the-art systems varying the number of distinct vertex labels over the whole target graph and query sizes. [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]

This study investigates the evolution of evaluation approaches within the charitable sector, emphasising the proliferation of options throughout waves of evaluation diffusion. We draw on imprinting theory to describe the persistence of specific practices despite the emergence of alternatives. The research aims to examine the imprinted values and practices of earlier evaluation waves on the current practice of evaluation by documenting the current methodological practice in a large sample of evaluation reports. The study illuminates the enduring impact of theory-driven evaluation, introduced in the 1980s, on current practices. However, it also reveals how this approach has evolved over subsequent evaluation waves, acquiring divergent characteristics. This imprinting is not only due to effectiveness but also due to normative pressures, which prioritise conformity with norms over practical utility. The study highlights the potential consequences of this imprinting, including management-focused evaluations and mission drift. We conclude by offering practical options to address tensions within the field and call for further research to better understand the nuances of decision-making in evaluation approaches. [ABSTRACT FROM AUTHOR]

In artificial intelligence problems, connected with the study of complex structured objects which are described in the terms of properties of their elements and relationships between these elements, it is convenient to use predicate calculus formulas, more precisely elementary conjunctions of atomic predicate formulas. In such a case, the problem of extraction common properties of objects arises. The common properties of complex structured objects are set by formulas with variables as arguments, which, up to the names of the arguments, coincide with the subformulas of the objects under study, that is, are isomorphic to these subformulas. Previously, the authors developed algorithms for checking such formulas for isomorphism, as well as for extraction the maximal common subformula of two elementary conjunctions of predicate formulas with a single predicate symbol. Two algorithms, the first of which solves this problem for elementary conjunctions containing two predicate symbols, and the second for an arbitrary number of predicate symbols are proposed in this paper using the last-mentioned algorithm. Estimates of the computational complexity of the presented algorithms are proved. The algorithm is implemented in Python. [ABSTRACT FROM AUTHOR]

With the developments in technology, the phenomenon of digitalization, which is reflected in every segment of society, has also spread to organizations, which are a subsystem of society. With this change, organizations have tried to develop strategies that can adapt to change in order to take part in competition in the sector in which they operate. In this study, the digital services offered by banks to SMEs are analyzed from the perspective of institutional isomorphism. Banks are among the types of organizations where digitalization is most observed today. In this context, the digital services offered by banks for the digitalization of SMEs were investigated using content analysis method. The digital services offered by banks for SMEs were analyzed over a five-year period according to their annual and integrated reports. According to the results obtained from the analysis, isomorphism was found in the services offered by banks for the digitalization of SMEs. The isomorphism in these services is also reflected in the digital transformation practices offered to SMEs. In addition, as a result of the research findings, a general increase was observed in the digital services offered by banks to SMEs on a yearly basis. However, the increase in the services offered during the pandemic period attracted attention. [ABSTRACT FROM AUTHOR]

A vertex-degree-based topological index φ associates a real number to a graph G which is invariant under graph isomorphism. It is defined in terms of the degrees of the vertices of G and plays an important role in chemical graph theory, especially in QSPR/QSAR investigations. A subset of k edges in G with no common vertices is called a k-matching of G, and the number of such subsets is denoted by m G , k . Recently, this number was naturally extended to weighted graphs, where the weight function is induced by the topological index φ. This number was denoted by m k G , φ and called the k-matchings of G with respect to the topological index φ. It turns out that m 1 G , φ = φ G , and so for k ≥ 2 , the k-matching numbers m k G , φ can be viewed as kth order topological indices which involve both the topological index φ and the k-matching numbers. In this work, we solve the extremal value problem for the number of 2-matchings with respect to general sum-connectivity indices SC α , over the set T n of trees with n vertices, when α is a real number in the interval − 1 , 0. [ABSTRACT FROM AUTHOR]

This work introduces the notion of a hesitant bipolar-valued intuitionistic fuzzy graph (HBVIFG), which reflects four different characterizations: membership with positive/negative aspects and non-membership with positive/negative aspects, incorporating multi-dimensional alternatives in all of its information. HBVIFG generalizes both HBVFG and BVHFG due to its diversified nature in observing four perspectives along with multiple attributes in a piece of information. Numerous studies, examples, and graphical representations emphasize the concept's distinctiveness and importance. The following graph theory terms are defined: strong directed HBVIFG, full directed HBVIFG, directed spanning HBVIFSG, directed HBVIFSG, and partial directed hesitant bipolar-valued intuitionistic fuzzy subgraph (HBVIFSG). Examples of operations utilizing two HBVIFGs are Cartesian, direct, lexicographical, and strong products. A scenario is used to generate the mapping of relations, which includes homomorphism, isomorphism, weak isomorphism, and co-weak isomorphism. We describe a directed HBVIFG application that employs an algorithm to determine the most dominant person and self-persistent person in a social system and a comparative study is also provided. The proposed method provides a more detailed framework for assessing the most dominant and self-persistent individual in a social network across multi-level attributes along with positive and negative side membership and non-membership grades in each element of a network. [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]

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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]