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The natural filtrations of infinite-dimensional Lie superalgebras of O -type over a field of positive characteristic are proved to be invariant under automorphisms by studying ad-nilpotent elements. We observe that two Lie superalgebras of O -type are isomorphic if and only if the integers in the definition of these Lie superalgebras are intrinsic. Thereby, all the Lie superalgebras of O -type are classified in the sense of isomorphism. [ABSTRACT FROM AUTHOR]

Let R be a ring with identity. The unit (respectively, unitary Cayley) graph of R is a simple graph G(R) (respectively, Γ(R)) with vertex set R, where two distinct vertices x and y are adjacent if and only if x + y (respectively, x − y) is a unit of R. In this paper, we explore when G(R) and Γ(R) are isomorphic for a finite ring R. Among other results, we prove that G(R) is isomorphic to Γ(R) for a finite ring R if and only if char(R/J(R))=2 or R/J(R)≅ℤ2 × S, where J(R) is the Jacobson radical of R and S is a finite ring. [ABSTRACT FROM AUTHOR]

The equivalence of the Haar system in a rearrangement invariant space on and a sequence of pairwise disjoint functions in some Lorentz space is known to imply that up to the equivalence of norms. We show that the same holds for the class of uniform disjointly homogeneous rearrangement invariant spaces and obtain a few consequences for the properties of isomorphic embeddings of such spaces. In particular, the space with is the only uniform -disjointly homogeneous rearrangement invariant space on with nontrivial Boyd indices which has two rearrangement invariant representations on the half-axis . [ABSTRACT FROM AUTHOR]

In this paper, I present the step from isomorphism to isodynamism in Gilbert Simondon's philosophy. For this, I first explain the isomorphism argument and some of its implications and critiques. Then, I discuss some elements of Simondon's individuation theory regarding being and becoming. Lastly, I analyze this change from isomorphism to isodynamism and I offer examples of some possible derivations of isodynamism. Basically, this process involves a change in perspective, from structural similarity to operational analogy--for example, between different levels of being (physicochemical, biological and psychosocial). [ABSTRACT FROM AUTHOR]

AbstractWith the Poincaré group R3, 1⋊O(3,1) as the model of departure, we focus, for n=p+q, p+q≥4 , on the affine indefinite orthogonal group Rp,q⋊SO(p,q) . Denote by hp, q the Lie algebra of the affine indefinite orthogonal group. We compute the Leibniz cohomology of hp, q with adjoint coefficients, written HL*(hp, q;hp, q) . We calculate several indefinite orthogonal invariants, and hp, q -invariants. [ABSTRACT FROM AUTHOR]

Clay minerals represent a class of hydrated phyllosilicates making up the fine-grained portions of rocks, sediments, and soils. Due to the advantages of abundant reserves, low prices, and wide applications, the development and utilization of clay minerals have received increasing attention in recent years. Isomorphic replacement is a common phenomenon in clay minerals, which is one of the main causes of changes in mineral chemical composition and physical and chemical properties. This article briefly describes the crystal structure of several clay minerals such as montmorillonite, vermiculite, palygorskite, kaolinite, and halloysite. It summarized the research status of the effect of isomorphic replacement on their structure and application performance. The research results can provide theoretical basis for the structural research and efficient resource utilization of clay minerals. [ABSTRACT FROM AUTHOR]

New data on the crystal structure and isomorphism of extra-framework components in the cancrinite-group mineral tounkite have been obtained using chemical and single-crystal X-ray diffraction data, as well as infrared, Raman, ESR, UV–Vis–near-IR absorption and photoluminescence spectroscopy methods. The crystal structure of tounkite is based on the aluminosilicate framework formed by the САСАСВСВСАСВ stacking sequence with ordered Si and Al atoms The framework hosts Losod and liottite cages as well as columns of cancrinite cages. It is shown that tounkite is characterized by wide variations of the chemical composition. Its simplified crystal–chemical formula is (Na+3.89–5.18K+0.15–1.64Ca2+2.30–2.58(Al6Si6O24)(SO42−,S52−,S4) 2−x (Cl−, HS−)1+y·nH2O (x, y, n < 1). The S2⦁− and S3⦁− radical anions may occur in some tounkite samples in minor amounts. These crystal–chemical features indicate that tounkite crystallizes under highly reducing conditions. All studied tounkite samples were polysynthetic twins. A large 10-layed cage formed at the border between twin components, connected by a rotation of 180° around the [001] axis, which may host the large S52− anion. [ABSTRACT FROM AUTHOR]

This paper is devoted to the research of the isomorphic multidimensional cyclic structure and multidimensional phase structure of the cyclic random process (CRP) and to its formation method, which enables a rigorous formalization of intuitive ideas concerning cyclic stochastic motion. The fundamental properties of the cyclic random process and analytical dependencies between the multidimensional cyclic structure, multidimensional phase structure and rhythm structure of the CRP have been established. This work shows that the CRP is able to take into account the cyclicity of multidimensional distribution functions of cyclic signals as well as the variability in the rhythm of the investigated signals. A subclass of the CRP is the periodic random process, which allows for the use of classical processing methods of cyclic signals with a regular rhythm. Based on a series of experiments, significant advantages of the CRP as a mathematical model of electrocardiographic signals (ECG) compared to the periodic random process are shown. [ABSTRACT FROM AUTHOR]

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]

We prove a strengthened version of Shavrukov's result on the non-isomorphism of diagonalizable algebras of two $\Sigma _1$ -sound theories, based on the improvements previously found by Adamsson. We then obtain several corollaries to the strengthened result by applying it to various pairs of theories and obtain new non-isomorphism examples. In particular, we show that there are no surjective homomorphisms from the algebra $(\mathfrak {L}_T, \Box _T\Box _T)$ onto the algebra $(\mathfrak {L}_T, \Box _T)$. The case of bimodal diagonalizable algebras is also considered. We give several examples of pairs of theories with isomorphic diagonalizable algebras but non-isomorphic bimodal diagonalizable algebras. [ABSTRACT FROM AUTHOR]

Complex neutrosophic graphs are created by combining complex neutrosophic sets with graph theory ideas. This provides a flexible framework for tackling complex problem-solving circumstances. Various processes, such as union, join, and composition, are thoroughly investigated to improve the administration of complicated neutrosophic graphs. This research also looks into the area of complicated neutrosophic graph homeomorphisms, investigating the transformations and mappings that occur inside these structures. This investigation advances our knowledge of the intrinsic features and linkages found in complicated neutrosophic graphs. Finally, our methodology's practical usefulness is demonstrated by its use in the design of hospital infrastructure. We illustrate the effectiveness of complicated neutrosophic graphs in addressing difficult design concerns and optimizing infrastructure solutions for practical deployment in this real-world scenario. [ABSTRACT FROM AUTHOR]

Despite various definitions of Smart Cities (SCs), it is challenging to characterize what “the best” Smart City would be. This is demonstrated by various frameworks of indicators and rankings, which present different cities as the smartest. This article aims to contribute to the understanding of concepts of SCs, focusing on 21 indicator frameworks, which were studied through text analysis and text mining techniques. The indicator frameworks were researched as units of analysis through an inductive interpretive approach. Frameworks of different regions (Europe, Asia, North and Latin America) were analyzed, and their results indicate that these frameworks are not immune to contextual factors affecting cities. They present categories and indicators that are, on the one hand, very similar, indicating an isomorphic trend, and, on the other, very different from each other due to the contextual influence of the environment and the stakeholders involved. The unprecedented contribution of this article is to show, using statistical analysis, that naming “the” SC would be an ineffectual task. [ABSTRACT FROM AUTHOR]

Isomorphism and homomorphism are fundamental topics in abstract algebra, but how mathematicians characterise the utility of these concepts remains understudied. Based on interviews with nine research-active mathematicians, we confirmed use of previously noted conceptual metaphors and noted new metaphors and metaphor clusters. We expand on prior work by highlighting five thematic contrasts between metaphors for these concepts: context dependent sameness, classification of objects versus computing maps, indistinguishable versus distinct objects, structure-preservation versus structure loss, and information gain versus structure loss. Implications include the centrality of sameness to thinking about isomorphism and homomorphism but the need for care in how that sameness is framed; the value of being able to attend to the object and map; the importance of being able to determine which structures are preserved and which are lost in context; and the existence of a conceptual purpose for homomorphism as a tool for changing perspectives. [ABSTRACT FROM AUTHOR]

In the spirit of some earlier studies of the authors, we discuss the alienation problem for ∨-additive and multiplicative mappings. This study enables us to answer two questions that were left open in [B. Al Subaiei and N. Jarboui, On the monoid of unital endomorphisms of a Boolean ring, Axioms 10(4) (2021) 305]. [ABSTRACT FROM AUTHOR]

Civilian-led, non-police crisis response services – which attend mental health crises that previously had received uniformed police response in many jurisdictions – have multiplied substantially alongside widespread calls for ‘de-tasking’ of police. Yet, these services inevitably engage in forms of ‘policing’ in both practical and sociological terms, if we understand policing to involve reducing harms and maintaining order under the shadow of police (state coercive) power. Seeing the rapid expansion of these services as the birth of a new organisational field, following organisational and institutional theories, this paper delineates possible futures of these services as they coalesce into increasingly isomorphic forms. The paper then considers the potential bases of legitimacy, organisational ethos and accountability that will develop around these services, and sets out challenges that the organisational field will face if it is to avoid becoming an extension of ‘the police’. [ABSTRACT FROM AUTHOR]

Motivated by the thesis work of Burkett, we here deduce some equivalent conditions for a supercharacter analog of nilpotent groups, S-nilpotent groups. Using isomorphism of supercharacters of groups, we also attempt to relate S-nilpotent groups and S-normal subgroups. Communicated by Mandi Schaeffer Fry [ABSTRACT FROM AUTHOR]

In the 21st century, three international military organizations with standing headquarters in the Global South have emerged in the field of military operations. These are the Southern Cross Peace Force in Latin America, the Africa Standby Force, integrating five subregional African forces, and the Peninsula Shield Force in the command structures of the Gulf Cooperation Council countries. This article examines interorganizational differences and similarities in these three important cases, aiming to provide a deeper understanding of their organizational forms within the global diffusion phenomenon of multinational military cooperation. The article uses a novel comparative framework that bridges a gap in systematic studies of multinational military organizations. It aims to provide a gateway for theoretical growth now and for future studies, in the Global South and elsewhere. [ABSTRACT FROM AUTHOR]

Institutional theory has generated considerable insight into fundamental issues within sport. This study seeks to advance Washington and Patterson's review by providing an empirical review of institutional theory in sport. We follow Arksey and O'Malley's scoping review protocol to identify 188 sport-related institutional studies between 1979 and 2019. Our review provides evidence regarding the state of institutional scholarship within sport via an analysis of authorship, year, journal, methodology, method, study population, and use of institutional constructs (legitimacy, isomorphism, change, logics, fields, and work). Rather than a hostile takeover or a joint venture proposed in Washington and Patterson's review, the relationship between fields is more aptly described as a diffusion of ideas. By developing an empirical review of institutional studies in sport, we hope to expedite the diffusion of ideas between the two fields and work toward realizing the collective benefits any future joint venture may bring. [ABSTRACT FROM AUTHOR]

Globalisation, changes in technology and transportation, and isomorphic trends in the sector emphasise the need to identify the diversity of higher education institutions. As a response, classification mechanisms emerged in higher education in recent decades. While many studies on classification focus on the types and methodology, the examination of the utility of classifications is limited. Thus, this paper examines the perspectives of 14 people in critical positions on the Carnegie Basic Classification of Higher Education and is triangulated by institutional documents. The results revealed some important implications for policymakers and researchers. While the Carnegie Basic Classification seems to remain one of the significant sources in higher education, the availability of big data, along with varying new methodologies, began to threaten the usability of the classification system. Moreover, contrary to the role assigned to it earlier, Carnegie Basic Classification seems to contribute more to homogeneity in the system. [ABSTRACT FROM AUTHOR]

Bipolar objects are widespread in nature, and their two attributes describe the opposition and unity of the things. Motivated by characterizing fuzzy topological structures by means of fuzzy graphs, we propose a bipolar fuzzy topological graph to measure the features of bipolar fuzzy systems. The topological characteristics in bipolar neutrosophic and bipolar interval-valued fuzzy settings are discussed as well. Several instances are manifested to clarify new definitions and conclusions. Furthermore, the properties of edge calculating and graph isomorphic are determined. [ABSTRACT FROM AUTHOR]

Spurrite from Negra Mine, Queretaro, Mexico is characterized by a complex chemical composition. Its empirical formula derived based on electron microprobe, wet chemical analyses and gas chromatography of annealing products is H0.18Ca5.01Na0.05[(SiO4)1.91(SO4)0.08)][(CO3)0.71(BO3)0.28]O11. The mineral was studied by single-crystal X-ray diffraction (SCXRD) as well as infrared (IR), Raman and nuclear magnetic resonance (NMR) spectroscopy. According to spectroscopic data, boron has three-fold coordination and sulfur occurs in the mineral in the sulfate form. A significant portion of carbonate groups is substituted by BO33– anions. Charge compensation is achieved due to the substitution of a part of SiO44– anions by SO42– groups, as well as to the admixture of sodium. SCXRD shows that sodium occurs in its own site with a low occupancy. The studied sample is isotypic with the synthetic NaCa5(SiO4)2(BO3) compound. The IR spectrum shows possible partial protonation of the SiO4 tetrahedra whereas bands of H2O molecules and isolated OH– anions are not observed. Thermal behavior of B,S,Na-bearing spurrite from Negra Mine has been studied using powder high-temperature X-ray diffraction (HTXRD) together with boron poor and S-free spurrite from Fuka Area (Japan). The studied samples are stable up to ~ 1200 °C and ~ 1100 °C, respectively, whereas synthetic B,S-free spurrite decomposes at about 900 °C. The thermal expansion is significantly anisotropic and is observed mainly in the direction perpendicular to the ac plane which is coplanar with the layers of calcium polyhedra and anionic pseudo-layers formed by (C,B)O3 triangles and (Si,S)O4 tetrahedra. Isomorphism and a similarity of the thermal, baric and compositional (C-B substitution) deformations of spurrite-like structures are discussed. [ABSTRACT FROM AUTHOR]

An original CSIKE post-quantum cryptography algorithm is proposed as a modification of the CSIDH algorithm but with one public key instead of two. The conditions for its implementation on two classes of non-cyclic Edwards curves are substantiated. The properties of quadratic and twisted supersingular Edwards curves that form pairs of quadratic twist of order p + 1 ≡ 0 mod 8 over a prime field Fp are considered. A modification of the CSIDH algorithm and the CSIKE algorithm are presented, which are generated on the isogenies of these curves instead of the traditional arithmetic of curves in the Montgomery form. For isogenies of degrees 3, 5, and 7, the parameters of isogenic chains of non-cyclic supersingular Edwards curves are calculated and tabulated for p = 839. The implementation of the key encapsulation scheme with its encryption by Alice with Bob's public key is considered. A new randomized CSIKE algorithm with random equiprobable selection of the curve from two classes at each step of the isogeny chain is proposed. The probability of a successful side-channel attack in a randomized algorithm is estimated. It is proposed to abandon the calculation of the isogenic function ϕ(R) of a random point R, which significantly speeds up the algorithm. [ABSTRACT FROM AUTHOR]

In this work, we present a generalized isomorphism between field of symbolic nplithogenic set and R n+1, use it to study the most general form of symbolic plithogenic random variables and study its probabilistic properties including expectation, variance and moments generating function. We also use this isomorphism to study symbolic n-plithogenic probability density function and present many theorems related to it. As an application to this new theory, we study exponential distribution in its symbolic n-plithogenic form and derive its properties, like expected value and variance. Many examples were presented and solved successfully. This paper closes the grand gap in-plithogenic probability theory and paves the way to study many related theories like stochastic modeling and its applications. [ABSTRACT FROM AUTHOR]

This study examines the accessory wodginite and the discovery of titanium-bearing wodginite and Fe and Ti-bearing wodginite in lithium-fluorine granites from the Abu Dabbab and Nuweibi massifs in Eastern Egypt. The wodginite group's mineral association includes tantalum-bearing cassiterite and tin-bearing tantalum–niobate minerals: tantalite-(Mn), columbite-(Mn), and microlite. Three forms of wodginite crystallization were identified: (1) rims around columbite-(Mn) and tantalite-(Mn) varying from 1.5 to 21.9 μm in thickness, (2) micro-inclusions in cassiterite ranging from 5.4 to 27.0 μm in size, and (3) autonomous crystals measuring 3–124 μm in length. Wodginite in the Nuweibi massif is mainly found in porphyritic granite of late-stage porphyry intrusion. It has a similar composition to the worldwide wodginite of rare-metal granites, but exhibits a lower content of TiO2 (average 0.54%) and is a mineral indicator of rich tantalum ore deposits. In contrast, wodginite in the Abu Dabbab massif is replaced by titanium-bearing wodginite (Ti/(Sn + BTa + Ti + Fe3+) = 0.23) and is associated with Fe and Ti-bearing wodginite. Wodginite and Ti-bearing wodginite are maximally enriched in manganese (Mn/(Mn + Fe2+ +Ca) = 0.95), expressed in all intrusive phases of the massif, and are mineral indicators of tantalum-bearing granites with associated cassiterite-quartz mineralization. [ABSTRACT FROM AUTHOR]

Cavicchioli, O'Brien, and Spaggiari studied the number of isomorphism classes of irreducible groups of Fibonacci type as a function σ (n) of the number of generators n. In the case n = p l , where p is prime and l ≥ 1 , n ≠ 2 , 4 , they conjectured a function C (p l) , that is polynomial in p , for the value of σ (p l). We prove that C (p l) is an upper bound for σ (p l). We introduce a function τ (n) for the number of abelianised groups and conjecture a function D (p l) , that is polynomial in p , for the value of τ (p l) , when p l ≠ 2 , 4 , 5 , 7 , 8 , 13 , 23. We prove that D (p l) is an upper bound for τ (p l). We pose three questions that ask if particular pairs of groups with common abelianisations are non-isomorphic. We prove that if τ (p l) = D (p l) and each of these questions has a positive answer then σ (p l) = C (p l). [ABSTRACT FROM AUTHOR]

A Hom-group is the non-associative generalization of a group whose associativity and unitality are twisted by a compatible bijective map. In this paper, we give some new examples of Hom-groups, and show the first, second and third isomorphism theorems of Hom-groups. We also introduce the notion of Hom-group action, and as an application, we prove the first Sylow theorem for Hom-groups along the line of group actions. [ABSTRACT FROM AUTHOR]

In [V. I. Arnold, Simple singularities of curves, Proc. Steklov Inst. Math. 226(3) (1999) 20–28, Sec. 5, p. 32], Arnold writes: ‘Classification of singularities of curves can be interpreted in dual terms as a description of “co-artin” subalgebras of finite co-dimension in the algebra of formal series in a single variable (up to isomorphism of the algebra of formal series)’. In the paper, such a description is obtained but up to isomorphism of algebraic curves (i.e. this description is finer).Let K be an algebraically closed field of arbitrary characteristic. The aim of the paper is to give a classification (up to isomorphism) of the set of subalgebras 풜 of the polynomial algebra K[x] that contains the ideal xmK[x] for some m ≥ 1. It is proven that the set 풜 =∐m,Γ풜(m, Γ) is a disjoint union of affine algebraic varieties (where Γ∐ {0,m,m + 1,…} is the semigroup of the singularity and m − 1 is the Frobenius number). It is proven that each set 풜(m, Γ) is an affine algebraic variety and explicit generators and defining relations are given for the algebra of regular functions on 풜(m, Γ). An isomorphism criterion is given for the algebras in 풜. For each algebra A ∈풜(m, Γ), explicit sets of generators and defining relations are given and the automorphism group AutK(A) is explicitly described. The automorphism group of the algebra A is finite if and only if the algebra A is not isomorphic to a monomial algebra, and in this case |AutK(A)| < dim K(A/픠A) where 픠A is the conductor of A. The set of orders of the automorphism groups of the algebras in 풜(m, Γ) is explicitly described. [ABSTRACT FROM AUTHOR]

Throughout history, Anatolia has played a decisive role in the development of shopping culture. Different civilizations built special areas for shopping activities and left a rich shopping culture to the next ruler of Anatolia. In the first 100 years of the Republic of Turkey, the heritage continued with different elements, but the shopping centers, whose first representative was opened in 1988, became widespread in a short time and became the leading element of Anatolian shopping culture. In this study, it is aimed to examine the reasons behind the leading positions of shopping centers and based on secondary data, evaluations regarding isomorphism concept are completed. In this context, it is determined that shopping centers maintain their legitimacy and develop isomorphic features by combining the characteristics of successful historical representatives of Anatolian shopping culture and globally accepted standards. In addition, it is deduced that shopping centers with Glocal features would adapt more easily to new demands and would be the future leader of Anatolian shopping culture. [ABSTRACT FROM AUTHOR]

In this work, a crystal chemical analysis of the known experimentally deciphered crystal structures of tetrahedrite group minerals was carried out in order to reveal the relationships between the occupancies of anion crystallographic sites in the structures, their effective sizes and unit cell parameters. To achieve this aim, we analyzed the effective sizes of the 24g and 2a anion sites in 68 deciphered crystal structures of tetrahedrite group minerals according to the published data. The analysis was carried out using the TOPOSPro software package by partitioning the space into Voronoi–Dirichlet polyhedra (VDP). It has been shown theoretically for the first time that the content of a large sulfur ion and its deficiency affect the unit cell parameter. A linear correlation between the VDP volume of the anionic site of S2– (24g) and the unit cell parameter in minerals of the tetrahedrite group was established, which shows that the anionic substructure dictates the structural motif in this class of compounds. It was found that the change in the VDP volumes of sulfur anions is associated with different occupancies of anionic sites. It is found that the formula (unit cell) of the compound contains fewer than 13 sulfur ions in almost all deciphered crystal structures of tetrahedrite group minerals. It was concluded that the calculated VDP volume of the 24g anionic position less than 22 Å3 indicates a significant deficit in the anionic substructure. It was shown that, using information about the VDP volumes of all anionic and cationic sites in the structure, it is possible to predict the unit cell parameters of minerals of the tetrahedrite group with an accuracy of 0.01 Å. [ABSTRACT FROM AUTHOR]

This paper investigates the tensor product of a finite dimensional nilpotent evolution algebra. Some properties that translate from tensor products to factors and vice versa have been investigated, including the index of nilpotency and annihilator. The index of nilpotency of the tensor product of two nilpotent evolution algebras with different indexes of nilpotency is determined. Moreover, we investigate the tensorially decomposable of the 4-dimensional nilpotent evolution algebra. In addition, the decomposable nilpotent evolution algebra with the maximal index of nilpotency has been carried out. [ABSTRACT FROM AUTHOR]

It is of much interest to study the heavy hydrocarbon impact on the phase behavior of hydrocarbons. Using a method of the precision adiabatic calorimetry the phase equilibria in quaternary mixtures of methane, propane, octane, and nonane have been studied. The phase diagrams for investigated mixtures have been plotted based on the experimental data. The phase transitions were localized by the finite discontinuities in temperature derivatives of the thermodynamic potentials. The heat capacity, internal energy, pressure, and temperature derivative of pressure at constant volume were measured in the range 170–320 K, up to 40 MPa. Quaternary mixtures as quasi-binary mixtures are presented. The first quasi-component of the quasi-binary mixture is the binary mixture with the constant methane/propane ratio. The second quasi-component of the quasi-binary mixture is the binary mixture of octane and nonane. Investigated hydrocarbon system is the combination of the simple hydrocarbon mixtures for the low concentration of octane and nonane. In the earlier papers we presented the simple hydrocarbon mixtures for the low concentration of octane, nonane, and decane, and quaternary mixtures of methane, propane, octane, and decane for the low concentration of octane and decane, which are the combination of the simple hydrocarbon mixtures for the low concentration of octane and decane. Our investigations show that quaternary hydrocarbon mixture for the low concentration of octane and nonane as well as the simple hydrocarbon mixtures for the low concentration of octane, nonane, and decane split into three phases, the macrophase composed of methane, propane, octane, and nonane, and two microphases formed by octane and nonane. In this system octane and nonane dissolved in the macrophase partly. Besides, the heavy components provoke a split of the liquid part of the quaternary mixture into two liquid phases. [ABSTRACT FROM AUTHOR]

In a TAR (token addition/removal) reconfiguration graph, each vertex is a set of vertices, with an edge between two vertices if one can be obtained from the other by adding or removing one element. This paper considers the X-TAR graph of a base graph G where the vertices of the X-TAR graph of G are the X-sets of G, which are subsets of V(G) that satisfy certain conditions. Dominating sets, power dominating sets, zero forcing sets, and positive semidefinite zero forcing sets are all examples of X-sets. For graphs G and G ′ with no isolated vertices, it is shown that G and G ′ have isomorphic X-TAR graphs if and only if there is a relabeling of the vertices of G ′ such that G and the relabeled G ′ have exactly the same X-sets. These results are applied to show certain zero forcing TAR graphs are unique up to isomorphism of the base graph. Furthermore, results related to the connectedness of the zero forcing TAR graph are presented. [ABSTRACT FROM AUTHOR]

Business Schools have positioned themselves as one of the central axes of specialized education in the world, and Latin America is no exception to this phenomenon. International accreditations are one of the main aspects of its positioning, which homogeneous guidelines can lead to imitation and nondifferentiation processes, without adopting adaptation strategies to the needs of its context. For this, the sustainable development goals (SDGs) are studied as a context, through a content analysis of 229 strategic elements from 60 business schools in Latin America, Europe, Asia, North America, the Middle East and Africa, and Oceania is analyzed to identify if Latin American schools differ or have isomorphic behavior compared to schools in other regions. Similarly, a comparison is established with the strategic response of companies to the SDGs, to identify if there is an aligned position of business schools against the actions taken by these. It was found that Latin American business schools have a similar behavior in terms of linking sustainable development goals in their strategy with schools in other areas of the world. Moreover, the strategic response of business schools to these needs is not articulated with the actions taken by companies in Latin American, so it is interpreted that there is a double disarticulation of business schools, opening a field to generate differentiation and positioning in the short and medium term. [ABSTRACT FROM AUTHOR]

The following article is an inquiry into the aesthetic valences of the concept of pattern as informed by the contrasting frameworks of Gestalt psychology and information theory. On the trail of its object, it evokes the historical context of the Post-War American aesthetic theory and technological culture and enters into a critical dialogue with texts by its main interlocutors Rudolf Arnheim and György Kepes. The article demonstrates that both theorists grapple with the challenges issued by advances in computation and the epistemological implications of visions of data processing (even machine learning research) ascendant in their time. The discussion has a philosophical orientation in paying particular attention to matters of abstraction underlying patterns, the temporality of pattern formation, and the dimension of subjectivity; it highlights the fundamental oppositions between discrete and holistic coding, as well as quality and quantity. Finally, in its departure from Kepes’s intervention in the relationship between science and art, the article situates the question of pattern in the context of the history of science, putting it in contact with influential treatments of objectivity in the discourse of Lorraine Daston and Peter Galison, but more critically, in the work of Donna Haraway. [ABSTRACT FROM AUTHOR]

The prevailing approaches to modeling interactive uncertainty with epistemic models in economics are state‐based and type‐based. We explicitly formulate two general procedures that transform state models into type models and vice versa. Both transformation procedures preserve the belief hierarchies as well as the common prior assumption. By means of counterexamples it is shown that our procedures are not inverse to each other. However, if attention is restricted to maximally reduced epistemic models, then isomorphisms can be constructed and an inverse relationship emerges. [ABSTRACT FROM AUTHOR]

For scientific optimization in developing multiple-airport systems of the route network layout, in Beijing-Tianjin-Hebei, Yangtze River Delta, Greater Bay Area, Chengdu-Chongqing Economic Zone the China' s four major airport group as the research object, based on complex network analysis method to build the multiple-airport systems of airline passenger transport network model, to measure the basic features of the airline network structure, centrality and isomorphism among the members of the four major multiple airport systems. The results show that the airline networks of the four multiple-airport systems all have the characteristics of small world network and scale-free. The network has a high degree of centralization, with a close centralized trend, uneven distribution of airline between airports, great differences in accessibility, and prominent control role of hub airports. The degree of airline homogeneity among the members of the Yangtze River Delta multiple-airport systems is significantly higher than the other three multiple-airport systems. [ABSTRACT FROM AUTHOR]

There are six different classes of endomorphisms for a graph. The sets of these endomorphisms always form a chain under the inclusion of sets. In order to study these different endomorphisms more systematically, Böttcher and Knauer proposed the concept of the endomorphism type of a graph in 1992. In this paper, we explore the six different classes of endomorphisms of graph P (3 m + 1 , 3) . In particular, the endomorphism type of P (3 m + 1 , 3) is given. [ABSTRACT FROM AUTHOR]

Crystal-chemical features of a sulfide-bearing variety of the cancrinite-group mineral balliranoite from the Tuluyskoe lapis lazuli deposit, Baikal Lake area, Siberia, Russia, have been investigated using a multimethodic approach based on infrared (IR), Raman, and electron spin resonance (ESR), as well as ultraviolet, visible and near infrared (UV–Vis–near IR) absorption spectroscopy methods, luminescence spectroscopy, electron microprobe analysis, selective sorption of CO2 and H2O from annealing products, and single-crystal X-ray structure analysis. Holotype balliranoite and its sulfate analogue, davyne, were studied for comparison. The crystal-chemical formula of the studied sample from Tultuyskoe is Na5.4K0.1Ca2.4(Si6Al6O24)Cl2[(CO3)0.7(SO4)0.18S*0.95Cl0.1(H2O)0.16], where the content of the wide zeolite channel is given in square brackets; S* is total sulfide sulfur occurring as disordered S2●−, cis- and trans-S4, S52−, minor S3●−, and HS− groups. The presence of S52− and HS− groups, the absence of CO2 molecules, and the association with pyrrhotite and Fe-free pargasite indicate that the studied sample crystallized under highly reducing, low-temperature conditions, unlike holotype balliranoite whose formation was related to the Somma-Vesuvius volcanic complex, Italy. Irradiation of balliranoite from Tultuyskoe with X-rays results in the transformations of polysulfide groups other than S3●− into S3●− in accordance with the scheme: S52− → S2●− + S3●−; 3S2●− → 2S3●− + e−; S4 + S2●− + e− → 2S3●−; S4 + S2●− + e− → 2S3●−; S4 + S52− + e− → 3S3●− (e− = electron). [ABSTRACT FROM AUTHOR]

Despite growing attention to electoral brands, political scientists have largely remained "color blind," neglecting parties' chromatic choices. Moreover, scholars dedicated limited attention to how party organizations converge on the use of similar structures and communication strategies, thereby engaging in a process of institutional isomorphism. We seek to simultaneously fill both gaps by examining the logos of more than 300 parties in 35 democracies during the latest political elections. Our findings show that a strong relationship exists between ideology and the use of certain color hues: left-wing party logos mainly display hues at the red end of the color spectrum, while blue hues prevail among right-wing parties. Likeminded parties' chromatic isomorphism, however, is moderated by country and party-specific factors. Notably, the correlation between color hue and ideology is stronger in Western Europe and among older parties. [ABSTRACT FROM AUTHOR]

The recent results of the accurate calorimetric measurements of phase equilibria in ternary mixtures of methane, propane, and nonane have been presented. The heat capacity, internal energy, pressure, and temperature derivative of pressure at constant volume were measured in the range 160–340 K, up to 30 MPa. The phase transitions were localized by the finite discontinuities in temperature derivatives of the thermodynamic potentials. The phase diagrams for ternary mixtures of methane, propane, and nonane have been plotted based on the experimental data. These data are supplemented with the earlier measurements of two ternary hydrocarbon systems for the low concentration of octane and decane. Our investigations show that hydrocarbon mixture for the low concentration of nonane as well as the hydrocarbon mixtures for the low concentration of octane and decane split into two phases, the nonane-lean macrophase and the microphase formed by nonane. Besides, nonane provokes a split of the liquid part of a ternary mixture into two liquid phases, the nonane-rich phase and the nonane-lean phase. [ABSTRACT FROM AUTHOR]

This article examines the practices that maintain the gender asymmetry in transnational migratory religious organisations, as exemplified by the Polish organisations of the Roman Catholic Church (so-called Polish Catholic Missions). Based on interviews with women and men involved in these structures as well as on our observations during fieldwork, we reconstruct the gendered division of work in such organisations, with a special focus on differentiation within the area of religious functions. Drawing on integrative theories of gender (especially of Raewyn Connell) and on the new institutionalist understanding of organisations, we investigate how and why these transnational religious bodies resist the normative pressures regarding gender equality stemming from the egalitarian contexts in which they function (England, Belgium, and Sweden). [ABSTRACT FROM AUTHOR]

Through guidelines, terms of service and algorithmic curation, digital platforms such as YouTube encourage creators to produce content that fits with the commercial goals of the platform. Scholars have argued that this pressure to conform might lead to uniformity, or isomorphism, in the ways organizations manage their presence on platforms. This article contributes to the debate on isomorphism by taking a bottom-up approach and ask to which extent creators on YouTube pursue similar, or different, strategies for uploading and monetizing content. Through quantitative and qualitative analyses of a sample of YouTube channels, we show how content creators adapt to, negotiate with, and defy institutional pressures. In the end, we find greater support for diversification, that is, polymorphism, than concentration in the ways organizations manage their presence on the platform. This has implications for how we understand platform power and integrate institutional theories in communication research. [ABSTRACT FROM AUTHOR]

We define a four-dimensional Lie algebra g in this paper and then prove that this Lie algebra is solvable but not nilpotent. Due to the fact that g is a Lie algebra, ∀ x , y ∈ g , [ x , y ] = − [ y , x ] , that is, the operation [ , ] has anti symmetry. Symmetry is a very important law, and antisymmetry is also a very important law. We studied the structure of Poisson algebras on g using the matrix method. We studied the necessary and sufficient conditions for the automorphism of this class of Lie algebras, and give the decomposition of its automorphism group by A u t (g) = G 3 G 1 G 2 G 3 G 4 G 7 G 8 G 5 , or A u t (g) = G 3 G 1 G 2 G 3 G 4 G 7 G 8 G 5 G 6 , or A u t (g) = G 3 G 1 G 2 G 3 G 4 G 7 G 8 G 5 G 3 , where G i is a commutative subgroup of A u t (g) . We give some subgroups of g's automorphism group and systematically studied the properties of these subgroups. [ABSTRACT FROM AUTHOR]

Rechargeable lithium–oxygen batteries (LOBs) are regarded as one of the most promising candidates for the next generation of energy storage devices. Nevertheless, the lack of understanding of the relationships between structure, property, and performance of catalysts limits the rational development of efficient cathode catalysts, and therefore, hinders the commercial application of LOBs. Herein, a d‐band center regulation strategy is proposed to construct an isomorphism composite of NiS2‐CoS2@nitrogen‐doped carbon (NiS2‐CoS2@NC) as an advanced cathode catalyst for boosting the electrocatalytic activities of LOBs. Density functional theory calculations reveal that the introduction of Ni atoms not only redistributes the internal charges on the isomorphism structure but also modulates the adsorption capacities of the intermediates by tuning the d‐band center, thus promoting oxygen reduction reaction/oxygen evolution reaction kinetics and reducing the reaction overpotentials. As expected, NiS2‐CoS2@NC catalyzed LOBs present superior electrochemical performance including large initial discharge/charge specific capacity of 14 551/13 563 mAh g−1, an ultralong cycle life over 490 cycles at a current density of 500 mA g−1, and excellent rate performance. The insight into the regulation of the adsorption capacity of the catalyst by tailoring its d‐band center facilitates the rational construction of efficient electrocatalysts for LOBs and other electrocatalytic systems. [ABSTRACT FROM AUTHOR]

Rechargeable lithium–oxygen batteries (LOBs) are regarded as one of the most promising candidates for the next generation of energy storage devices. Nevertheless, the lack of understanding of the relationships between structure, property, and performance of catalysts limits the rational development of efficient cathode catalysts, and therefore, hinders the commercial application of LOBs. Herein, a d‐band center regulation strategy is proposed to construct an isomorphism composite of NiS2‐CoS2@nitrogen‐doped carbon (NiS2‐CoS2@NC) as an advanced cathode catalyst for boosting the electrocatalytic activities of LOBs. Density functional theory calculations reveal that the introduction of Ni atoms not only redistributes the internal charges on the isomorphism structure but also modulates the adsorption capacities of the intermediates by tuning the d‐band center, thus promoting oxygen reduction reaction/oxygen evolution reaction kinetics and reducing the reaction overpotentials. As expected, NiS2‐CoS2@NC catalyzed LOBs present superior electrochemical performance including large initial discharge/charge specific capacity of 14 551/13 563 mAh g−1, an ultralong cycle life over 490 cycles at a current density of 500 mA g−1, and excellent rate performance. The insight into the regulation of the adsorption capacity of the catalyst by tailoring its d‐band center facilitates the rational construction of efficient electrocatalysts for LOBs and other electrocatalytic systems. [ABSTRACT FROM AUTHOR]

In this article, we apply a new class of fuzzy control functions to approximate a Cauchy additive mapping in fuzzy Banach space (FBS). Further, considering the unital FBS (UFBS), we will investigate the isomorphisms defined in this space. By introducing several specific functions and choosing the optimal control function from among these functions, we evaluate the Cauchy–Optimal stability (C–O-stability) for all defined mappings. [ABSTRACT FROM AUTHOR]

This article reviews the history of world university rankings and their large-scale impact. It then analyzes some of the criticism of the world ranking systems before exploring their impact in the context of Thai universities. The authors' assertions centre on the premise that much of the criticism of these ranking systems can be divided into three broad categories: criticism of their conceptualization and guiding ideology, criticism of the methodology that they employ, and criticism of their influence on universities and other stakeholders. These criticisms cut across national borders; however, some apply to a greater extent in certain contexts, for example in developing countries such as Thailand. The article then details how these ranking systems have shifted academic attention from teaching quality to research production through the creation of annual performance assessments which are heavily skewed towards research and the creation of lucrative research product rewards systems which can create an organisational hierarchy of faculty based solely on research output through academic positions and financial rewards. Although some may criticize the Asian universities' and faculty's, i.e., the 'players" responses to the academic rankings, these responses are predictable and rational adaptations to the 'game' that has been imposed on them. [ABSTRACT FROM AUTHOR]

Innovation is widely considered the lifeblood of organizational survival and growth. However, despite its importance, innovation diffusion does not take place spontaneously in organizations. In fact, diffusion of innovations (DoI) in project-based organizations (PBOs) is widely considered notoriously lukewarm. Nevertheless, it is inspiring to observe that project teams could suddenly change their lukewarm attitude in DoI when they receive pressure from the authority and industrial associations, or when they notice their peers starting to adopt an innovation. There seem to be some isomorphic pressures such as coercive, mimetic, and normative pressures that drive DoI. This research aims to identify the source factors of the isomorphic pressures that can be used to catalyze innovation diffusion with a focus on construction PBOs. It does so by conducting a 3-year in-depth case study in an international construction firm using a mixed-method approach including semiconstructed interviews and nonparticipatory observations. The research identified 12 specific source factors under the three categories of isomorphic pressure, i.e., coercive pressure, mimetic pressure, and normative pressure. Coercive pressure can arise from organizational policy, company culture, and influence from seniors; memetic pressure can stem from the influence of peer project teams as well as change agents such as innovation champions; and normative pressure derives from the sharing in regular events/meetings and related training. The practical contribution is that based on the source factors identified, top managers can tactically create such pressures to catalyze DoI meanwhile avoiding excessive pressures that might hinder DoI in their companies. Future studies are recommended to unravel the mechanism through which these source factors interact to take an effect, and based on that, devise the strategies that can harness the isomorphic pressures to boost DoI. [ABSTRACT FROM AUTHOR]

Two fractional factorial designs are called isomorphic if one can be obtained from the other by relabeling the factors, reordering the runs and switching the levels of factors. Given a set of all orthogonal designs (ODs) with n runs, q levels and s factors, it may have several non-isomorphic subclasses. Once a new OD with this design size is generated, it is interesting to know which subclass it belongs to. In this paper, we review several existing methods, which can classify newly generated ODs to the correct non-isomorphic subclass. We also propose two new non-isomorphic detection methods. They can be utilized for the design classification purpose and take some advantages over the existing methods in terms of computation efficiency and classification capability. [ABSTRACT FROM AUTHOR]

A self-complementary graph is a simple graph that is isomorphic to its complement. Thus, a graph G is selfcomplementary if there is an isomorphism from G to Gc. Due to the special structure of these graphs, they are rare in number compared to arbitrary simple graphs with the same number of vertices. The main goal of the paper is to identify self-complementary graphs through the definition and analysis of their basic properties, especially the existence of an isomorphism between two such graphs. However, the paper also contains results related to the construction of selfcomplementary graphs, and some of their more complex properties are listed. Furthermore, the emphasis in this paper is also the construction of some special classes of self-complementary graphs, especially those with 8 vertices, with the fact that the text is accompanied by figures in order to better observe of their properties. The last part of the paper contains a smaller number of assertions about the 3-cycles and paths in self-complementary graphs. [ABSTRACT FROM AUTHOR]