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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.

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.

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.

Geometry for q-exponential families is studied in this paper. A q-exponential family is a set of probability distributions, which is a natural generalization of the standard exponential family. A q-exponential family has information geometric structure and a dually flat structure. To describe these relations, generalized conformal structures for statistical manifolds are studied in this paper. As an application of geometry for q-exponential families, a geometric generalization of statistical inference is also studied.

We give a survey on geometry of statistical manifolds in terms of estimating functions. A statistical model naturally has a statistical manifold structure. In particular, a q-exponential family which is a generalization of an exponential family admits several statistical manifold structures. An estimating function can be regarded as a tangent vector of a statistical model, and it gives rise to dualistic structures on a statistical manifold. In this paper, we construct statistical manifold structures on statistical models and divergence functions from the viewpoint of estimating functions. We also study geometry of nonintegrable estimating functions.

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.

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.

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.

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.

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 $A$.

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 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.

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.

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