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Supercuspidal representations are usually infinite-dimensional, so the size of such a representation cannot be measured by its dimension; the formal degree is a better alternative. Hiraga, Ichino, and Ikeda conjectured a formula for the formal degree of a supercuspidal in terms of its L-parameter only. Our first main result is to compute the formal degrees of the supercuspidal representations constructed by Yu. Our second result, using the first, is to verify that Kaletha's regular supercuspidal L-packets satisfy the conjecture. [ABSTRACT FROM AUTHOR]

This article, published in the Journal of Mathematical Sciences, discusses the concept of dimension polynomials and their applications in inversive difference fields. It introduces various definitions and notations related to dimension polynomials and their properties. The text also discusses the reduction of inversive difference polynomials and the concept of E-reduction. It provides definitions and explanations of terms such as leaders, coleaders, effective orders, and rank. The text concludes with remarks and examples illustrating the concepts discussed. [Extracted from the article]

The asymptotic dimension is an invariant of metric spaces introduced by Gromov in the context of geometric group theory. In this paper, we study the asymptotic dimension of metric spaces generated by graphs and their shortest path metric and show their applications to some continuous spaces. The asymptotic dimension of such graph metrics can be seen as a large scale generalisation of weak diameter network decomposition which has been extensively studied in computer science. We prove that every proper minor-closed family of graphs has asymptotic dimension at most 2, which gives optimal answers to a question of Fujiwara and Papasoglu and (in a strong form) to a problem raised by Ostrovskii and Rosenthal on minor excluded groups. For some special minor-closed families, such as the class of graphs embeddable in a surface of bounded Euler genus, we prove a stronger result and apply this to show that complete Riemannian surfaces have Assouad-Nagata dimension at most 2. Furthermore, our techniques allow us to determine the asymptotic dimension of graphs of bounded layered treewidth and graphs with any fixed growth rate, which are graph classes that are defined by purely combinatorial notions and properly contain graph classes with some natural topological and geometric flavours. [ABSTRACT FROM AUTHOR]

Operations in the theory of graphs has a substantial inuence in the analytical and factual dimensions of the domain. In the realm of chemical graph theory, topological descriptor serves as a comprehensive graph invariant linked with a specific molecular structure. The study on the Sombor index is initiated recently by Ivan Gutman. The triangle parallel graph comprises of the edges of subdivision graph along with the edges of the original graph. In this paper, we make use of combinatorial inequalities related with the vertices, edges and the neighborhood concepts as well as the other topological descriptors in the computations for the determination of bounds of Sombor index for certain corona products involving the triangle parallel graph. [ABSTRACT FROM AUTHOR]

Given a finite group \mathrm {G}, the faithful dimension of \mathrm {G} over \mathbb {C}, denoted by m_\mathrm {faithful}(\mathrm {G}), is the smallest integer n such that \mathrm {G} can be embedded in \mathrm {GL}_n(\mathbb {C}). Continuing the work initiated by Bardestani et al. [Compos. Math. 155 (2019), pp. 1618–1654], we address the problem of determining the faithful dimension of a finite p-group of the form \mathscr {G}_R≔\exp (\mathfrak {g}_R) associated to \mathfrak {g}_R≔\mathfrak {g}\otimes _\mathbb {Z}R in the Lazard correspondence, where \mathfrak {g} is a nilpotent \mathbb {Z}-Lie algebra and R ranges over finite truncated valuation rings. Our first main result is that if R is a finite field with p^f elements and p is sufficiently large, then m_\mathrm {faithful}(\mathscr {G}_R)=fg(p^f) where g(T) belongs to a finite list of polynomials g_1,\ldots,g_k, with non-negative integer coefficients. The latter list of polynomials is uniquely determined by the Lie algebra \mathfrak {g}. Furthermore, for each 1\le i\leq k the set of pairs (p,f) for which g=g_i is a finite union of Cartesian products \mathscr P\times \mathscr F, where \mathscr P is a Frobenius set of prime numbers and \mathscr F is a subset of \mathbb N that belongs to the Boolean algebra generated by arithmetic progressions. Previously, existence of such a polynomial-type formula for m_\mathrm {faithful}(\mathscr {G}_R) was only established under the assumption that either f=1 or p is fixed. Next we formulate a conjectural polynomiality property for the value of m_\mathrm {faithful}(\mathscr {G}_R) in the more general setting where R is a finite truncated valuation ring, and prove special cases of this conjecture. In particular, we show that for a vast class of Lie algebras \mathfrak {g} that are defined by partial orders, m_\mathrm {faithful}(\mathscr {G}_R) is given by a single polynomial-type formula. Finally, we compute m_\mathrm {faithful}(\mathscr {G}_R) precisely in the case where \mathfrak {g} is the free metabelian nilpotent Lie algebra of class c on n generators and R is a finite truncated valuation ring. [ABSTRACT FROM AUTHOR]

This work focuses on studying the adiabatic-connection in density functional theory in two dimensions. It employs a recently developed accurate form of wavefunction for two-electron systems. The explicit semianalytic form of the wavefunction makes it possible to calculate ground state wavefunctions, energies, densities, and the resulting properties for the scaled Coulomb interaction between the electrons at fixed density accurately. The results so obtained for the correlation energies are then used as the reference values for studying the performance of two-dimensional correlation energy functionals. [ABSTRACT FROM AUTHOR]

In this paper, we first study fs-modules, i.e., modules with finitely many small submodules. We show that every fs-module with finite hollow dimension is Noetherian. Also, we prove that an R-module M with finite Goldie dimension, is an fs-module if and only ifM = M1...M2, where M1 is semisimple and M2 is an fs-module with Soc(M2)M << M. Then, we investigate multiplication fs-modules over commutative rings and we prove that the lattices of R-submodules of M and S-submodules of M are coincide, where S = EndR(M). Consequently, MR and SM have the same Krull (Noetherian, Goldie and hollow) dimension. Further, we prove that for any self-generator multiplication module M, the fs-module as a right R-module and as a left S-module are equivalent. [ABSTRACT FROM AUTHOR]

Let R be an associative ring and let n be a non-negative integer. In this paper, we consider n-super finitely presented, Gorenstein n-weak injective and Gorenstein n-weak flat modules under change of rings. For an excellent extension S ≥ R, we show that the Gorenstein n-super finitely presented dimensions (resp., weak Gorenstein n-super finitely presented dimensions) of rings R and S coincide. [ABSTRACT FROM AUTHOR]

The classification and the geometry of corank one map germs from (C², 0) → (C³, 0) have been studied by Mond [1, 2]. In this paper we characterize the classification of map germs of corank at most 1, in terms of certain invariants. Moreover, by using this characterization, we develop an algorithm to compute the type of map germs with out computing the normal form. Also, we give its implementation in the computer algebra system SINGULAR [15]. [ABSTRACT FROM AUTHOR]

Given an integral p-adic variety, we observe that if the integral Hodge-de Rham spectral sequence behaves nicely, then the special fiber knows the Hodge numbers of the generic fiber. Applying recent advancements of integral p-adic Hodge theory, we show that such a nice behavior is guaranteed if the p-adic variety can be lifted to an analogue of second Witt vectors and satisfies some bound on dimension and ramification index. This is a (ramified) mixed characteristic analogue of results due to Deligne-Illusie, Fontaine-Messing, and Kato. Lastly, we discuss an example illustrating the necessity of the aforementioned lifting condition, which is of independent interest. [ABSTRACT FROM AUTHOR]

‎The golden ratio ϕ=1+5√2=1/61803398874... is the root of the polynomial x²−x−1=0‎, ‎and is the one of the important numbers in mathematics‎. ‎The golden ratio is also used in many fields of science‎. ‎The golden ratio appears in some patterns in nature‎, ‎including the spiral arrangement of leaves and other plant parts‎. ‎In this paper‎, ‎we present a sequence of golden numbers {ϕn}n and study their properties‎. [ABSTRACT FROM AUTHOR]

The aim of this work is to define a Sheffer stroke BM-algebra and to study some of its features. It is indicated that the axioms of a Sheffer stroke BM-algebra are independent. The relationship between a Sheffer stroke BMalgebra and a BM-algebra is stated. By presenting fundamental notions about Sheffer stroke B-algebras, it is proved that every Sheffer stroke BM-algebra is a Sheffer stroke B-algebra. After determining 0-commutative Sheffer stroke B-algebra, a Sheffer stroke Coxeter algebra and an associative Sheffer stroke BM-algebra, the relationships between this algebraic structures are shown. [ABSTRACT FROM AUTHOR]

I give a simple construction of certain Coulomb branches C3,4(G;E) of gauge theory in 3 and 4 dimensions defined by Nakajima et al. for a compact Lie group G and a polarisable quaternionic representation E. The manifolds C(G;0) are abelian group schemes (over the bases of regular adjoint Gc-orbits, respectively conjugacy classes), and C(G;E) is glued together from two copies of C(G;0) shifted by a rational Lagrangian section εV, the Euler class of the index bundle of a polarisation V of E. Extending the interpretation of C3(G;0) as "classifying space" for topological 2D gauge theories, I characterise functions on C3(G;E) as operators on the equivariant quantum cohomologies of M×V, for all compact symplectic G-manifolds M. The non-commutative version has an analogous description in terms of the Γ-function of V, appearing to play the role of Fourier transformed J-function of the gauged linear Sigma-model V/G. [ABSTRACT FROM AUTHOR]

This article deals with the evolution operator of evolution algebras. We give a theorem that allows to characterize these algebras when this operator is a homomorphism of algebras of rank n−2 and this result in turn allows us to extend the classification of this type of algebras, given in a previous result by ourselves in 2021, up to the case of dimension 4. For this purpose, we analyze and make use of an algorithm for the degenerate case. A computational study of the procedure is also made. [ABSTRACT FROM AUTHOR]

The problem of computing periodic solutions can be expressed as a boundary value problem and solved numerically via piecewise collocation. Here, we extend to renewal equations the corresponding method for retarded functional differential equations in (K. Engelborghs et al., SIAM J Sci Comput., 22 (2001), pp. 1593–1609). The theoretical proof of the convergence of the method has been recently provided in (A. Andò and D. Breda, SIAM J Numer Anal., 58 (2020), pp. 3010–3039) for retarded functional differential equations and in (A. Andò and D. Breda, submitted in 2021) for renewal equations and consists in both cases in applying the abstract framework in (S. Maset, Numer Math., 133 (2016), pp. 525–555) to a reformulation of the boundary value problem featuring an infinite‐dimensional boundary condition. We show that, in the renewal case, the proof can also be carried out and even simplified when considering the standard formulation, defined by boundary conditions of finite dimension. [ABSTRACT FROM AUTHOR]

Let n ≥ 2 and d 1 , ... , d n ≥ 2 be integers, and F be a field. A vector u ∈ F d 1 ⊗ ⋯ ⊗ F d n is called a product vector if u = u [ 1 ] ⊗ ⋯ ⊗ u [ n ] for some u [ 1 ] ∈ F d 1 , ... , u [ n ] ∈ F d n . A basis composed of product vectors is called a product basis. In this paper, we show that the maximum dimension of subspaces of F d 1 ⊗ ⋯ ⊗ F d n with no product basis is equal to d 1 d 2 ⋯ d n − 2 if either (i) n = 2 or (ii) n ≥ 3 and # F > max ⁡ { d i : i ≠ n 1 , n 2 } for some n 1 and n 2. When F = C , this result is related to the maximum number of simultaneously distinguishable states in general probabilistic theories (GPTs). [ABSTRACT FROM AUTHOR]

Fix an abelian variety A0 and a non-isotrivial abelian scheme over a smooth irreducible curve, both defined over the algebraic numbers. Consider the union of all images of translates of a fixed finite-rank subgroup of A0, also defined over the algebraic numbers, by abelian subvarieties of A0 of codimension at least k under all isogenies between A0 and some fiber of the abelian scheme. We characterize the curves inside the abelian scheme which are defined over the algebraic numbers, dominate the base curve and potentially intersect this set in infinitely many points. Our proof follows the Pila-Zannier strategy. [ABSTRACT FROM AUTHOR]

We construct infinitely many new 1-parameter families of simply connected complete non-compact G2-manifolds with controlled geometry at infinity. The generic member of each family has so-called asymptotically locally conical (ALC) geometry. However, the nature of the asymptotic geometry changes at two special parameter values: at one special value we obtain a unique member of each family with asymptotically conical (AC) geometry; on approach to the other special parameter value the family of metrics collapses to an AC Calabi-Yau 3-fold. Our infinitely many new diffeomorphism types of AC G2-manifolds are particularly noteworthy: previously the three examples constructed by Bryant and Salamon in 1989 furnished the only known simply connected AC G2-manifolds. We also construct a closely related conically singular G2-holonomy space: away from a single isolated conical singularity, where the geometry becomes asymptotic to the G2-cone over the standard nearly Kähler structure on the product of a pair of 3-spheres, the metric is smooth and it has ALC geometry at infinity. We argue that this conically singular ALC G2-space is the natural G2 analogue of the Taub-NUT metric in 4-dimensional hyperKähler geometry and that our new AC G2-metrics are all analogues of the Eguchi-Hanson metric, the simplest ALE hyperKähler manifold. Like the Taub-NUT and Eguchi-Hanson metrics, all our examples are cohomogeneity one, i.e. they admit an isometric Lie group action whose generic orbit has codimension one. [ABSTRACT FROM AUTHOR]

In this article we investigate the relations between the Gorenstein projective dimensions of Λ -modules and their socles for n -minimal Auslander–Gorenstein algebras Λ. First we give a description of projective-injective Λ -modules in terms of their socles. Then we prove that a Λ -module N has Gorenstein projective dimension at most n if and only if its socle has Gorenstein projective dimension at most n if and only if N is cogenerated by a projective Λ -module. Furthermore, we show that n -minimal Auslander–Gorenstein algebras can be characterised by the relations between the Gorenstein projective dimensions of modules and their socles. [ABSTRACT FROM AUTHOR]

Igusa and Todorov introduced the φ function which generalizes the notion of projective dimension. We study the behavior of the φ function for cyclic Nakayama algebras of infinite global dimension. We prove that the supremum of values of φ is always an even number. In particular, we show that the φ -dimension is 2 if and only if the algebra satisfies certain symmetry conditions. Also, we give a sharp upper bound for φ -dimension in terms of the number of monomial relations which describes the algebra. [ABSTRACT FROM AUTHOR]

In this paper, we present a dual version of T. Brzeziński's results about Rota–Baxter systems which appeared in [Rota–Baxter systems, dendriform algebras and covariant bialgebras, J. Algebra460 (2016) 1–25]. Then as a generalization to bialgebras, we introduce the notion of Rota–Baxter bisystem and construct various examples of Rota–Baxter bialgebras and bisystems in dimensions 2, 3 and 4. On the other hand, we introduce a new type of bialgebras (named mixed bialgebras) which consist of an associative algebra and a coassociative coalgebra satisfying the compatible condition determined by two coderivations. We investigate coquasitriangular mixed bialgebras and the particular case of coquasitriangular infinitesimal bialgebras, where we give the double construction. Also, we show in some cases that Rota–Baxter cosystems can be obtained from a coquasitriangular mixed bialgebras. [ABSTRACT FROM AUTHOR]

In the last years, the sequence of codimensions of PI-algebras has been studied by several authors and the classification of unitary algebras, up to equivalence, with at most cubic codimension growth was given by Giambruno, La Mattina and Petrogradsky in 2007. In this paper, we establish a new approach by studying the possibilities of specific proper codimensions of a unitary algebra with growth n 4 in order to present a complete list of varieties generated by unitary algebras with polynomial growth n 4 . Also, we classify, up to PI-equivalence, the unitary algebras with growth n 5 whose leading coefficient of the polynomial describing the codimension sequence achieves the largest and the smallest possible value. [ABSTRACT FROM AUTHOR]

The notion of the Schur multiplier of a Lie algebra L was introduced by Batten in 1996. Recently, the first author introduced the concept of the c- nilpotent multiplier of a pair of Lie algebras and gave some exact sequences for the c-nilpotent multiplier of a pair of Lie algebras. The purpose of this paper is to derive some inequalities for dimension of the c-nilpotent multiplier of a pair of Lie algebras. [ABSTRACT FROM AUTHOR]

We study the construction of mutually unbiased bases such that all the bases are unextendible maximally entangled ones. By using some results from the theory of finite fields, we construct mutually unbiased unextendible maximally entangled bases in some bipartite systems of higher dimension: C 4 ⊗ C 5 , C 6 ⊗ C 7 , C 10 ⊗ C 11 and C 12 ⊗ C 13 , which extend the known result of C 2 ⊗ C 3 . We also generalize these results to more bipartie systems of specific dimension. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the linear dynamical system f : ℤ p t 2 → ℤ p t 2 , where ℤ p t is the ring of integers modulo p t (p is a prime). In order to facilitate the visualization of this system, we associate a graph Γ (A) on it, whose nodes are the points of ℤ p t 2 , and for which there is an arrow from α to β , when α A = β for a fixed 2 × 2 matrix A. In this paper, the in-degree of each node in Γ (A) is obtained, and a complete description of Γ (A) is given, when A is an idempotent matrix, or a nilpotent matrix, or a diagonal matrix. The results in this paper generalize Elspas' [1959] and Toledo's [2005]. [ABSTRACT FROM AUTHOR]

Purpose: Despite its envisaged benefits, integrated reporting (IR) has yet to achieve its "breakthrough", especially among small- and medium-sized enterprises (SMEs). This study aims to discern SME leaders' attitudes toward IR, and thereby to reveal managerial perceptions of both the potential benefits and the challenges that actually prevent them from embarking on IR. Design/methodology/approach: This explorative study is grounded on semi-structured interviews with 16 managers of large German SMEs, which yet do not apply IR but are potential candidates to implement it in the future. The engagement with non-preparers is expected to paint a more representative picture of actual reasons for IR (dis-)engagement compared to prior studies that address the few firms that have adopted IR and overcome its challenges. Applying Brown and Fraser's (2006) conceptual landscape, results are presented analogous to a business case-, stakeholder accountability- and critical theory dimension. Findings: Contrary to prior studies, which identified stakeholder accountability endeavors as kindling SME managers' interest in voluntary reporting initiatives, managers regard IR primarily as a business case, serving to achieve legitimacy, improve corporate image, reach out to professional investors and assist in employee recruitment. However, they refrained from actually adopting the novel reporting medium, which suggests that decision-makers might not believe the business case to be as unproblematic as claimed by the proponents of IR. This was traced back to three major impediments that currently inhibit SMEs from reporting in an integrated way, namely, a perceived lack of interest by the relevant publics, infeasibility of the IR concept to meet user needs and preparation costs. These drawbacks resemble those of earlier voluntary reporting experiments, calling into question the "revolutionary" character of IR. The study critically concludes that the future development of IR depends on addressing these barriers. Originality/value: To the best of the author's knowledge, this is the first explorative study to deliberately engage with IR non-preparers to draw conclusions on impediments to IR. The identification of relevant incentives and disincentives for IR among SME managers at first hand not only adds to the small extant IR research body and provides valuable insights for research, practice and standard setting but also contributes to the contemporary debate about dominant legitimacy-based explanations in the broader domain of social and environmental accounting and reporting. [ABSTRACT FROM AUTHOR]

Purpose: The paper aims to present a conceptual framework that helps in incorporating sustainability into software projects, highlights the importance of project sustainability and provides an extensive review of recent relevant contributions across various fields. Design/methodology/approach: The authors carried out a systematic bibliographic search on relevant published materials to analyse links between the two disciplines (sustainability and software projects). Furthermore, content analysis was applied to the final selected publications to identify and classify relevant triple bottom line (TBL) aspects to develop the framework. Findings: The inclusion of TBL-related aspects is the most efficient and effective method used to incorporate sustainability into projects. Most of the relevant contributions in the software literature have focussed on either project product or project process or on one or two dimensions of sustainability rather than the three dimensions of the TBL theory. This study contributes by proposing a conceptual framework that encompasses TBL-related aspects for incorporating sustainability into processes and products of software projects. Research limitations/implications: Validating the proposed framework empirically could be an interesting research issue. In addition, future works may focus on different types of industries, such as information systems, telecommunications and service sectors, which have seldom been studied in the literature. Practical implications: Software companies – or other relevant organisations – may use the proposed framework as a measurement tool to evaluate the environmental and social impacts of their current products and project management practices. Consequently, these organisations may pay more attention to incorporating sustainability into their project management practices. Originality/value: The proposed framework may contribute towards a more sustainable orientation by providing a unique combination of TBL-related aspects that gives academics and practitioners a better understanding of how software projects can be managed sustainably. [ABSTRACT FROM AUTHOR]

We propose to describe the gauge sector of an asymptotically safe field theory in d = 4 − 𝜖 dimensions as a scalar theory on fixed AdS in (d + 1) -dimensions using the holographic dictionary. [ABSTRACT FROM AUTHOR]

Under some dimension restrictions, we prove that totally umbilical hypersurfaces of Spin c manifolds carrying a parallel, real or imaginary Killing spinor are of constant mean curvature. This extends to the Spin c case the result of Kowalski stating that, every totally umbilical hypersurface of an Einstein manifold of dimension greater or equal to 3 is of constant mean curvature. As an application, we prove that there are no extrinsic hypersheres in complete Riemannian Spin manifolds of non-constant sectional curvature carrying a parallel, Killing or imaginary Killing spinor. [ABSTRACT FROM AUTHOR]

We investigate the question which communication tasks can be accomplished within a given operational theory. The concrete task is to find out which communication matrices have a prepare-and-measure implementation with multiple states and a single measurement from a given theory, without using shared randomness. To set a general framework for this question we develop the ultraweak matrix majorization in the set of communication matrices. This preorder gives us means to determine when one communication task is more difficult than another. Furthermore, we introduce several monotones which can be used to compare and characterize the communication matrices. We observe that not only do the monotones allow us to compare communication matrices, but also their maximal values in a given theory are seen to relate to some physical properties of the theory. The maximal values can then be thought as 'dimensions', allowing us to compare different theories to each other. We analyse the introduced monotones one by one and demonstrate how the set of implementable communication matrices is different in several theories with the focus being mainly on the difference between classical and quantum theories of a given dimension. [ABSTRACT FROM AUTHOR]

It has been conjectured that all graded Artinian Gorenstein algebras of codimension three have the weak Lefschetz property over a field of characteristic zero. In this paper, we study the weak Lefschetz property of associated graded algebras A of the Apéry set of M -pure symmetric numerical semigroups generated by four natural numbers. In 2010, Bryant proved that these algebras are graded Artinian Gorenstein algebras of codimension three. In a recent article, Guerrieri showed that if A is not a complete intersection, then A is of form A = R / I with R = K [ x , y , z ] and I = (x a , y b − x b − γ z γ , z c , x a − b + γ y b − β , y b − β z c − γ) , where 1 ≤ β ≤ b − 1 , max ⁡ { 1 , b − a + 1 } ≤ γ ≤ min ⁡ { b − 1 , c − 1 } and a ≥ c ≥ 2. We prove that A has the weak Lefschetz property in the following cases: • max ⁡ { 1 , b − a + c − 1 } ≤ β ≤ b − 1 and γ ≥ ⌊ β − a + b + c − 2 2 ⌋ ; • a ≤ 2 b − c and | a − b | + c − 1 ≤ β ≤ b − 1 ; • one of a , b , c is at most five. [ABSTRACT FROM AUTHOR]

This article examines the communication style used by officials in public media to announce the decisions taken and the necessary measures in relation to the restriction of the spread of Covid-19. Two case studies with Bulgaria and the United Kingdom will be observed illustrating two different kinds of rhetoric and outlining the cultural differences from the perspective of Hofstede's cultural dimension theory. In Bulgaria, the announcements used in public speaking to the people about the pandemic measures were focused on provoking an emotional response from the negative spectrum such as instigating fear and panic. In the UK, the Government's statements were appealing to the positives of compassion, national pride, and constructive action with everyone's involvement. [ABSTRACT FROM AUTHOR]

In the increasingly competitive hotel environment, decision-makers must consider the risks and benefits of remaining independent or affiliating with a brand or consortium. This research sought to understand the level of importance associated with a set of motivating factors considered by Portuguese four- and five-hoteliers as it relates to remaining independent or affiliating. The study results suggest that independent hoteliers rank control over decision making and shorter decision making as most important in remaining independent, and increased sales and more aggressive marketing as most important in the decision to affiliate. Affiliated hoteliers rank shorter decision making and absence of fees as most important in remaining independent, and increased sales, brand value, and more aggressive marketing as most important in the decision to affiliate. Interestingly, independence and freedom were considered less important in the decision to remain independent, by all respondents. We apply Hofstede's cultural dimensions theory to explain some of the key findings. [ABSTRACT FROM AUTHOR]

A system of linear constraints can be unsatisfiable and yet admit a solution in the form of quantum observables whose correlated outcomes satisfy the constraints. Recently, it has been claimed that such a satisfiability gap can be demonstrated using tensor products of generalized Pauli observables in odd dimensions. We provide an explicit proof that no quantum-classical satisfiability gap in any linear constraint system can be achieved using these observables. We prove a few other results for linear constraint systems modulo d > 2. We show that a characterization of the existence of quantum solutions when d is prime, due to Cleve et al, holds with a small modification for arbitrary d. We identify a key property of some linear constraint systems, called phase-commutation, and give a no-go theorem for the existence of quantum solutions to constraint systems for odd d whenever phase-commutation is present. As a consequence, all natural generalizations of the Peres–Mermin magic square and pentagram to odd prime d do not exhibit a satisfiability gap. [ABSTRACT FROM AUTHOR]

We consider the pure electric type power-law Lagrangian in nonlinear electrodynamics theory of dimensions n + 1. Conformally flat form of Bertotti–Robinson type spacetimes are obtained in all these dimensions with the specific power , which naturally excludes n = 4. This particular dimension is considered separately which is not of power-law form. [ABSTRACT FROM AUTHOR]

We describe the resurgence properties of some partition functions corresponding to field theories in dimension 0. We show that these functions satisfy linear differential equations with polynomial coefficients and then use elementary stability results for holonomic functions to prove resurgence properties, enhancing the previously known results on growth estimates for the formal series involved, which had been obtained through a delicate combinatorics. [ABSTRACT FROM AUTHOR]

In Enochs' relative homological dimension theory occur the (co)resolvent and (co)proper dimensions, which are defined by proper and coproper resolutions constructed by precovers and preenvelopes, respectively. Recently, some authors have been interested in relative homological dimensions defined by just exact sequences. In this paper, we contribute to the investigation of these relative homological dimensions. First we study the relation between these two kinds of relative homological dimensions and establish some transfer results under adjoint pairs. Then relative global dimensions are studied, which lead to nice characterizations of some properties of particular cases of self-orthogonal subcategories. At the end of this paper, relative derived functors are studied and generalizations of some known results of balance for relative homology are established. [ABSTRACT FROM AUTHOR]

This study was carried out on Sille agglomerate which is a typical volcanic welded bimrock. Two precious historical monuments, Koimesis Tes Panagias Church and Sekili hill settlement carved in Sille agglomerate, have maintained their stability without any support for centuries although suffering from weathering and various stability problems. However, due to its heterogeneity and sampling difficulties, the overall strength of Sille agglomerate has not been investigated yet. This paper presents the relationships between fragmentation fractal dimension (DF), fractal dimension of rough block surfaces (DR), number of blocks (BN), and volumetric block proportion (VBP) and the overall uniaxial compressive strength (UCS) of the Sille agglomerate. By using these properties as inputs, three statistically significant empirical models were developed for estimating the UCS of the Sille agglomerate. The results revealed that the DF and DR may be good predictors to estimate the UCS of welded volcanic bimrocks, and defining the properties of blocks by means of fractal theory provides significant contribution to the estimation of the UCS. It is observed that the failure planes in the core samples predominantly pass through the boundaries between matrix and blocks, and such behavior may indicate that the weakest component of the Sille agglomerate is boundaries. Accordingly, the UCS decreases due to the high DR values which create more or further weakest zones in the bimrocks. Finally, it is concluded that the negative correlation between the UCS and the VBP was attributed to increase of the DR due to the increase of the VBP. [ABSTRACT FROM AUTHOR]

This study proposes an agent-based model to theoretically investigate the effects of social culture on innovation diffusion. The model assumes that social culture (i.e., individualism, power distance, and uncertainty avoidance from Hofstede's cultural dimension theory) has a direct effect on the small-world network structure and individual characteristics. We further explore how the characteristics of innovation influence the diffusion process. We find that individualism has a positive effect on the diffusion speed in the early stage, whereas uncertainty avoidance and power distance have negative effects on innovation diffusion. The effect of uncertainty avoidance on the diffusion speed turns positive after the early stage of diffusion and the negative effect of power distance becomes positive in the late stage. We compare real-world diffusion data with the proposed agent-based model, finding some similarities in the diffusion patterns. The characteristics of innovation affect innovation diffusion when the uncertainty avoidance is high. However, when both uncertainty avoidance and individualism are low, the effect of the characteristics of an innovation on diffusion is restricted. [ABSTRACT FROM AUTHOR]

Motivated by various applications and examples, the standard notion of potential for dynamical systems has been generalized to almost additive and asymptotically additive potential sequences, and the corresponding thermodynamic formalism, dimension theory and large deviations theory have been extensively studied in the recent years. In this paper, we show that every such potential sequence is actually equivalent to a standard (additive) potential in the sense that there exists a continuous potential with the same topological pressure, equilibrium states, variational principle, weak Gibbs measures, level sets (and irregular set) for the Lyapunov exponent and large deviations properties. In this sense, our result shows that almost and asymptotically additive potential sequences do not extend the scope of the theory compared to standard potentials, and that many results in the literature about such sequences can be recovered as immediate consequences of their counterpart in the additive case. A corollary of our main result is that all quasi-Bernoulli measures are weak Gibbs. [ABSTRACT FROM AUTHOR]

A large class of supersymmetric quantum field theories, including all theories with N = 2 supersymmetry in three dimensions and theories with N = 2 supersymmetry in four dimensions, possess topological–holomorphic sectors. We formulate Poisson vertex algebras in such topological–holomorphic sectors and discuss some examples. For a four-dimensional N = 2 superconformal field theory, the associated Poisson vertex algebra is the classical limit of a vertex algebra generated by a subset of local operators of the theory. [ABSTRACT FROM AUTHOR]

This paper focus on the compact Ahlfors–David regular subsets of fractals. For this, we introduce the Ahlfors–David regular dimension and study its basic properties. Based on these properties and some known results in dimension theory of fractals, we compute Ahlfors–David Regular dimension for Moran sets and McMullen sets. [ABSTRACT FROM AUTHOR]

With the growing number of impact evaluations worldwide, the question of how to apply this evidence in policy making processes has arguably become the main challenge for evidence-based policy making. How can policy makers predict whether a policy will have the same impact in their context as it did elsewhere, and how should this influence the policy's design and implementation? This paper suggests that failures of external validity (both in transporting and scaling up policy) can be understood as arising from an interaction between a policy's theory of change and a dimension of the context in which it is being implemented. The paper surveys existing approaches to analyzing external validity, and suggests that there has been more focus on the generalizability of impact evaluation results than on the applicability of evidence to specific contexts. To help fill this gap, the study develops a method of "mechanism mapping" that maps a policy's theory of change against salient contextual assumptions to identify external validity problems and suggest appropriate policy adaptations. In deciding whether and how to adapt a policy, there is a fundamental informational trade-off between the strength of evidence on the policy from other contexts and the policy maker's information about the local context. [ABSTRACT FROM AUTHOR]

A novel reduction procedure for covariant classical field theories, reflecting the generalized symplectic reduction theory of Hamiltonian systems, is presented. The departure point of this reduction procedure consists in the choice of a submanifold of the manifold of solutions of the equations describing a field theory. Then, the covariance of the geometrical objects involved, will allow to define equations of motion on a reduced space. The computation of the canonical geometrical structure is performed neatly by using the geometrical framework provided by the multisymplectic description of covariant field theories. The procedure is illustrated by reducing the D'Alembert theory on a five-dimensional Minkowski space-time to a massive Klein–Gordon theory in four dimensions and, more interestingly, to the Schrödinger equation in 3 + 1 dimensions. [ABSTRACT FROM AUTHOR]

We study the problem of embedding minimal dynamical systems into the shift action on the Hilbert cube [ 0 , 1 ] N Z . This problem is intimately related to the theory of mean dimension, which counts the average number of parameters for describing a dynamical system. Lindenstrauss proved that minimal systems of mean dimension less than cN for c = 1 / 36 can be embedded in [ 0 , 1 ] N Z , and asked what is the optimal value for c. We solve this problem by showing embedding is possible when c = 1 / 2 . The value c = 1 / 2 is optimal. The proof exhibits a new interaction between harmonic analysis and dynamical coding techniques. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to examine the effect of the emotional attachment strength of family members to their business on the quality of the voluntary disclosure of their key performance indicator (KPI). More specifically, the authors focused on the effect of two dimensions of the socio-emotional theory, i.e. "family influence and control" and "firm dynasty succession." Design/methodology/approach: The authors performed a content analysis of annual reports for a sample of 87 French families listed in CAC All-Tradable to calculate a disclosure quality index of KPI. The authors proxied the "family influence and control" by the proportion of family members appointed in the board. To identify the "firm dynasty succession" concern, the authors classified firms according to the generation they belonged to. The authors estimated a cross-sectional linear regression model to meet the research objective. Findings: This study confirms the role of the family affective attachment in decreasing the quality of KPI disclosure in such a way to preserve its socio-emotional wealth. The family firms' principals who desire to sustain their control on the firm, to perpetuate the business for future generations and to protect their emotional wealth tend to avoid the disclosure of credible and reliable KPI information. Practical implications: The findings have meaningful practical implications. First, they provide relevant insights into the regulatory bodies of the financial reporting regarding the increasing appeal for making KPI disclosure mandatory. Second, as the family businesses are the most widespread proprietorship in the French context, the effect of the family agenda on the quality of the KPI should be of interest to various policymakers and financial statements' users of such firms. Third, the results inform nonfamily shareholders regarding the importance of selecting representatives on the board that should share similar interest with regard to KPI disclosure. Social implications: From a societal perspective, this study is relevant in taking into account the critical role the family businesses have in the French economy. This study should help the minority shareholders to protect their interests and maximize their wealth within the family firm because it sheds light on the influence that family members have on hiding key information on the firm's real performance. Originality/value: To the best of the authors' knowledge, no prior study in the family firms literature has examined the quality of voluntary disclosure of KPI. Although most previous studies merely compared family and nonfamily firms in terms of voluntary disclosure, the authors acknowledge and address the heterogeneity between family firms. The authors contribute to the few prior empirical validations of SEW implication on voluntary disclosure decisions by testing the effect of an additional dimension, which is family dynasty. [ABSTRACT FROM AUTHOR]

In this article, I present and try to defend the vital force theory of the meaning of life with particular focus on the transcendentalist dimension of the theory, on which an immanentist interpretation ultimately depends. I argue that the appeal to God as the ultimate guarantor of meaning follows from the recognition of the pessimism and nihilism that a wholly naturalistic account of meaning engenders. Since the individual is not an absolute value and must ultimately surrender the life she so cherishes against the background of epistemic ignorance of the purpose of her existence, strong commitment to a naturalistic account of meaning must lead to the conclusion that human life is ultimately meaningless. Adopting an analytical and expository method, I explore ways that the vital force theory of meaning combats the idea that since the individual is the measure of meaningfulness and since she is not an absolute value, her life is ultimately meaningless, in the context of her location in a seemingly purposeless universe. I conclude that the pessimism that accompanies the naturalistic framework also compromises the transcendentalist framework of vitalism. [ABSTRACT FROM AUTHOR]

There exists an index theory to classify strictly local quantum cellular automata in one dimension (Fidkowski et al. in Interacting invariants for Floquet phases of fermions in two dimensions, 2017. arXiv:1703.07360; Gross et al. in Commun Math Phys 310(2):419–454, 2012; Po et al. in Phys Rev B 96: 245116, 2017). We consider two classification questions. First, we study to what extent this index theory can be applied in higher dimensions via dimensional reduction, finding a classification by the first homology group of the manifold modulo torsion. Second, in two dimensions, we show that an extension of this index theory (including torsion) fully classifies quantum cellular automata, at least in the absence of fermionic degrees of freedom. This complete classification in one and two dimensions by index theory is not expected to extend to higher dimensions due to recent evidence of a nontrivial automaton in three dimensions (Haah et al. in Nontrivial quantum cellular automata in higher dimensions, 2018. arXiv:1812.01625). Finally, we discuss some group theoretical aspects of the classification of quantum cellular automata and consider these automata on higher dimensional real projective spaces. [ABSTRACT FROM AUTHOR]

Sachdev-Ye-Kitaev (SYK) is a concrete solvable model with non-Fermi liquid behavior and maximal chaos. In this work, we study the entanglement Rényi entropy for the subsystems of the SYK model in the Kourkoulou-Maldacena states. We use the path-integral approach and take the saddle point approximation in the large-N limit. We find a first-order transition exist when tuning the subsystem size for the q = 4 case, while it is absent for the q = 2 case. We further study the entanglement dynamics for such states under the real-time evolution for noninteracting, weakly interacting and strongly interacting SYK(-like) models. [ABSTRACT FROM AUTHOR]