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The increasing attention to sustainability issues in finance has brought a proliferation of environmental, social, and governance (ESG) metrics and rating providers that results in divergences among the ESG ratings. Based on a sample of Italian listed firms, this paper investigates these divergences through a framework that decomposes ESG ratings into a value and a weight component at the pillar (i.e. E, S, and G) and category (i.e. sub-pillar) levels. We find that weights divergence and social and governance indicators are the main drivers of rating divergences. The research contributes to develop a new tool for analyzing ESG divergences and provides a number of recommendations for researchers and practitioners, stressing the need to understand what is really measured by the ESG rating agencies and the need for standardization and transparency of ESG measurement to favor a more homogeneous set of indicators.

This study has set to compare the usefulness of the regional integration efforts taken by two important economic blocs, SAARC and ASEAN, within the Asian continent to reduce the regional income inequality. Therefore, the existence of income convergence (or divergence) among the SAARC and ASEAN countries is the aim of this study. To investigate whether (or not) there exists income convergence across the SAARC and ASEAN blocs over the period of 1970-2017, $\beta$-convergence, σ-convergence and club convergence estimation methods have been applied. The results confirm the convergence of income across the ASEAN member countries, which is absent for the SAARC member countries at the intra-regional level. Although we considered all countries of the SAARC and ASEAN blocs together in the panel, an evidence of income convergence over the years has been found. The analysis supports the view of trade liberalization and recommends investing in the human capital to narrow down the regional disparity in future. To achieve a favorable impact of Asian rising growth, regional integration is important, for that a collective policy framework at the regional level is needed for both SAARC and ASEAN.

In this study, the critical load and natural vibration frequency of Euler–Bernoulli single nanobeams based on Eringen’s nonlocal elasticity theory are investigated. Cantilever nanobeams with attached sprung masses were subjected to compressed concentrated and distributed follower forces. The parameter that determines the direction of nonconservative follower forces was given the positive and negative values, therefore, sub-tangential and super-tangential load were analyzed. The stability analysis is based on dynamical stability criterion and was carried out using a numerical algorithm for solving segmental nanobeams with many boundary conditions. The presented algorithm is based on the exact solutions of motion equations which are derived from equilibrium conditions for each separated segment of the nanobeam. Two comparison studies are conducted to ensure the validity and accuracy of the presented algorithm. The excellent agreement of critical load for Beck’s nano-column on Winkler foundation observed was confirmed as reported by other researchers. The effect of different values of the nonlocality parameter, tangency coefficient, spring stiffness coefficient, location of sprung mass and the greater number of attached sprung masses on a critical load of nanobeams compressed by nonconservative load are discussed. One of the presented results shows that significant differences between local and nonlocal theory appear when the beam subjected to follower forces loses its stability by flutter.

Risk measures for multivariate financial positions are studied in a utility-based framework. Under a certain incomplete preference relation, shortfall and divergence risk measures are defined as the optimal values of specific set minimization problems. The dual relationship between these two classes of multivariate risk measures is constructed via a recent Lagrange duality for set optimization. In particular, it is shown that a shortfall risk measure can be written as an intersection over a family of divergence risk measures indexed by a scalarization parameter. Examples include set-valued versions of the entropic risk measure and the average value at risk. As a second step, the minimization of these risk measures subject to trading opportunities is studied in a general convex market in discrete time. The optimal value of the minimization problem, called the market risk measure, is also a set-valued risk measure. A dual representation for the market risk measure that decomposes the effects of the original risk measure and the frictions of the market is proved.

In this note, we define four main categories of conservative flows: (a) those in which the dissipation is identically zero, (b) those in which the dissipation depends on the state of the system and is zero on average as a consequence of the orbits being bounded, (c) those in which the dissipation depends on the state of the system and is zero on average, but for which the orbit need not be bounded and a different proof is required, and (d) those in which the dissipation depends on the initial conditions and cannot be determined from the equations alone. We introduce a new 3D conservative jerk flow to serve as an example of the first two categories and show what might be the simplest examples for each category. Also, we categorize some of the existing known systems according to these definitions.

The present paper studies continuity of generalized entropy functions and relative entropies defined using the notion of a deformed logarithmic function. In particular, two distinct definitions of relative entropy are discussed. As an application, all considered entropies are shown to satisfy Lesche's stability condition. The entropies of Tsallis' non-extensive thermostatistics are taken as examples.

This paper presents the nonlinear analysis of functionally graded curved panels under high temperature supersonic gas flows. The aerothermoelastic governing equations are determined via Hamilton's variational principle. The von Karman nonlinear strain–displacement relations are used to account for large deflections. The material properties are assumed to be temperature-dependent and varying through the thickness direction according to a power law distribution in terms of the volume fractions of the constituent components. The panel is assumed to be infinitely long and simply supported. The Galerkin method is applied to convert the partial differential governing equation into a set of ordinary differential equations and the resulting system of nonlinear equations is solved through a numerical integration scheme. The effects of volume fraction index, curved panel height-rise, and aerodynamic pressure, in conjunction with the applied thermal loading, on the dynamical behavior of the panel are investigated. Regular and chaotic motions regime are determined through bifurcation analysis using Poincaré maps of maximum panel deflection, panel time history, phase-space and frequency spectra as qualitative tools, while Lyapunov's exponents and dimension are used as quantitative tools.

In this paper, flutter and divergence instabilities of functionally graded porous plate strip reinforced with graphene nanoplatelets in supersonic flow and subjected to an axial loading are studied. The graphene nanoplatelets are distributed in the matrix either uniformly or non-uniformly along the thickness direction. Four graphene nanoplatelets distribution patterns namely, Patterns A through D are considered. Based on the modified Halpin–Tsai micromechanics model and the rule of mixture, the effective material properties of functionally graded plate strip reinforced with graphene nanoplatelets are obtained. The aerodynamic pressure is considered in accordance with the quasi-steady supersonic piston theory. To transform the governing equations of motion to a general eigenvalue problem, the Galerkin method is employed. The flutter aerodynamic pressure and stability boundaries are determined by solving standard complex eigenvalue problem. The effects of graphene nanoplatelets distributions, graphene nanoplatelets weight fraction, geometry of graphene nanoplatelets, porosity coefficient and porosity distributions on the flutter and divergence instabilities of the system are studied. The results show that the plate strip with symmetric distribution pattern (stiffness in the surface areas) and GPLs pattern A predict the highest stable area. The flutter and divergence regions decrease as the porosity coefficient increases. Besides, the critical aerodynamic loads increase by adding a small amount of GPL to the matrix.

In this paper we provide a framework for the study of isoperimetric problems in finitely generated groups, through a combinatorial study of universal covers of compact simplicial complexes. We show that, when estimating filling functions, one can restrict to simplicial spheres of particular shapes, called “round” and “unfolded”, provided that a bounded quasi-geodesic combing exists. We prove that the problem of estimating higher dimensional divergence as well can be restricted to round spheres. Applications of these results include a combinatorial analogy of the Federer–Fleming inequality for finitely generated groups.

Let $A$ be a reduced ring containing $\mathbb{Q}$ and let ${\xi }_1,{\xi }_2$ be commuting locally nilpotent derivations of $A$. In this paper, we give an algorithm to decide the local nilpotency of derivations of the form $\xi =a_1{\xi }_1+a_2{\xi }_2$, where $a_1,a_2$ are elements in $A$.

The paper deals with a three-dimensional problem on natural vibrations and stability of thin-walled cylindrical shells with arbitrary cross sections, containing a quiescent or flowing ideal compressible fluid. The motion of compressible non-viscous fluid is described by a wave equation, which together with the impermeability condition and corresponding boundary conditions is transformed using the Bubnov–Galerkin method. A mathematical formulation of the problem of thin-walled structure dynamics has been developed based on the variational principle of virtual displacements. Simulation of shells with arbitrary cross sections is performed under the assumption that a curvilinear surface is approximated to sufficient accuracy by a set of plane rectangular elements. The strains are calculated using the relations of the theory of thin shells based on the Kirchhoff–Love hypothesis. The developed finite element algorithm has been employed to investigate the influence of the fluid level, the ratio of the ellipse semi-axes and types of boundary conditions on the eigenfrequencies, vibration modes and the boundary of hydroelastic stability of thin-walled circular and elliptical cylindrical shells interacting with a quiescent or flowing fluid.

The effective mass m_eff of the Pauli–Fierz Hamiltonian with ultraviolet cutoff Λ and the bare mass m in non-relativistic quantum electrodynamics (QED) with spin ½ is investigated. Analytic properties of m_eff in coupling constant e are shown. Let us set . The explicit form of constant a₂(Λ/m) depending on Λ/m is given. It is shown that the spin interaction enhances the effective mass and that there exist strictly positive constants c₁ and c₂ such that

Presented herein is a modified Galerkin discretization procedure for determining the qualitative dynamic behavior of elastic cantilevers with internal damping under partial follower step loading at their tips. For this strong nonlinear nonconservative system, the scheme proposed makes use of basic functions that are a product of nonlinear corrections of approximate linear shape functions. These corrected modes are computed in a way that all the nonlinear nonhomogeneous boundary conditions of the actual problem are satisfied throughout the motion. Numerical results obtained using a two-mode approach are found to be in very good qualitative agreement with the finite element results presented in the literature, not only in the vicinity of the critical states, but also in remote unstable domains. The effect of variation of initial conditions is also investigated and the advantages of the proposed procedure compared with conventional ones are discussed. Further research is required for establishing its capabilities and the range of its applicability for a broader class of nonconservative dynamic problems.

CNN templates for image processing and pattern formation are derived from neural field equations, advection equations and reaction–diffusion equations by discretizing spatial integrals and derivatives. Many useful CNN templates are derived by this approach. Furthermore, self-organization is investigated from the viewpoint of divergence of vector fields.

In the first part of this paper, elastostatic stability of cracked conservative flanged concrete beam-columns has been analyzed. Using the derived expression for the lateral stiffness under constant axial force, their elastodynamic stability is investigated in this second part. As expected, the instantaneous values of the stiffness and the damping coefficients of the lumped-mass underdamped SDOF nonlinear structures are found to depend upon the vibration amplitude. The natural frequency has been found to vanish at the two critical axial loads defined in the first part. For axial load exceeding the second critical value, the concrete beam-columns in the second equilibrium state are shown to exhibit loss of dynamic stability by divergence. Depending upon the initial conditions, the phase plane has been partitioned into dynamically stable and unstable regions. Under harmonic excitations, the nonlinear dynamical systems exhibit subharmonic resonances and jump phenomena. Loss of dynamic stability has been predicted for some ranges of damping ratio as well as of peak sinusoidal force and forcing frequency. Sensitivity of dynamic stability to the initial conditions and the sense of the peak sinusoidal force have also been predicted. The theoretical significance and the methodology adopted in this paper are also discussed.

A method of constructing (finitely generated and projective) right module structure on a finitely generated projective left module over an algebra is presented. This leads to a construction of a first-order differential calculus on such a module which admits a hom-connection or a divergence. Properties of integrals associated to this divergence are studied, in particular the formula of integration by parts is derived. Specific examples include inner calculi on a non-commutative algebra, the Berezin integral on the supercircle and integrals on Hopf algebras.

In this work the notion of divergence of elementary cellular automata is introduced and it is analyzed from a cryptographic point of view. Specifically, the balancedness and propagation characteristics are analyzed.

Load balancing, which redistributes dynamic workloads across computing nodes within cloud to improve resource utilization, is one of the main challenges in cloud computing system. Most existing rule-based load balancing algorithms failed to effectively fuse load data of multi-class system resources. The strategies they used for balancing loads were far from optimum since these methods were essentially performed in a combined way according to load state. In this work, a fuzzy clustering method with feature weight preferences is presented to overcome the load balancing problem for multi-class system resources and it can achieve an optimal balancing solution by load data fusion. Feature weight preferences are put forward to establish the relationship between prior knowledge of specific cloud scenario and load balancing procedure. Extensive experiments demonstrate that the proposed method can effectively balance loads consisting of multi-class system resources.

Taking into account the generalized uncertainty principle (GUP), we calculate the entropy of a scalar field in a Kerr spacetime. Different to previous work, we have used an new equation of the density of quantum states, which arises from the modified commutation relation . The divergence in the brick wall model is removed, without the cutoff.

The emergence of complexity is investigated from the viewpoint of the energy balance property and the divergence property of reaction–diffusion cellular neural networks.