On the extremal compatible linear connection of a generalized Berwald manifold

Generalized Berwald manifolds are Finsler manifolds admitting linear connections such that the parallel transports preserve the Finslerian length of tangent vectors (compatibility condition). It is known (Vincze in J AMAPN 21:199–204, 2005) that such a linear connection must be metrical with respect to the averaged Riemannian metric given by integration of the Riemann-Finsler metric on the indicatrix hypersurfaces. Therefore the linear connection (preserving the Finslerian length of tangent vectors) is uniquely determined by its torsion. If the torsion is zero then we have a classical Berwald manifold. Otherwise, the torsion is some strange data we need to express in terms of the intrinsic quantities of the Finsler manifold. The paper presents the idea of the extremal compatible linear connection of a generalized Berwald manifold by minimizing the pointwise length of its torsion tensor. It is uniquely determined because the number of the Lagrange multipliers is equal to the number of the equations for the compatibility of the linear connection with the Finslerian metric. Using the reference element method, the extremal compatible linear connection can be expressed in terms of the canonical data as well. It is an intrinsic algorithm to check the existence of compatible linear connections on a Finsler manifold because it is equivalent to the existence of the extremal compatible linear connection.

Multiplicative connections and their Lie theory

We define and study multiplicative connections in the tangent bundle of a Lie groupoid. Multiplicative connections are linear connections satisfying an appropriate compatibility with the groupoid structure. Our definition is natural in the sense that a linear connection on a Lie groupoid is multiplicative if and only if its torsion is a multiplicative tensor in the sense of Bursztyn–Drummond [Lie theory of multiplicative tensors, Mat. Ann. 375 (2019) 1489–1554, arXiv:1705.08579] and its geodesic spray is a multiplicative vector field. We identify the obstruction to the existence of a multiplicative connection. We also discuss the infinitesimal version of multiplicative connections in the tangent bundle, that we call infinitesimally multiplicative (IM) connections and we prove an integration theorem for IM connections. Finally, we present a few toy examples.

Learning Impulsive Pinning Control of Complex Networks

In this paper, we present an impulsive pinning control algorithm for discrete-time complex networks with different node dynamics, using a linear algebra approach and a neural network as an identifier, to synthesize a learning control law. The model of the complex network used in the analysis has unknown node self-dynamics, linear connections between nodes, where the impulsive dynamics add feedback control input only to the pinned nodes. The proposed controller consists of the linearization for the node dynamics and a reorder of the resulting quadratic Lyapunov function using the Rayleigh quotient. The learning part of the control is done with a discrete-time recurrent high order neural network used for identification of the pinned nodes, which is trained using an extended Kalman filter algorithm. A numerical simulation is included in order to illustrate the behavior of the system under the developed controller. For this simulation, a 20-node complex network with 5 different node dynamics is used. The node dynamics consists of discretized versions of well-known continuous chaotic attractors.

METHOD FOR IDENTIFYING NON-LINEAR RELATIONSHIPS BETWEEN INDICATORS OF POPULATION LIFE QUALITY IN THE RUSSIAN FEDERATION REGIONS AND CHILDREN’S DEATH IN FIRES

В статье рассмотрено применение метода выявления значимости и важности нелинейных связей показателей качества жизни населения в регионах Российской Федерации и показателей гибели/травматизма детей на пожарах. Показано, что система нелинейных связей существенно более сложная, чем система линейных связей. The article considers the application of the method for identifying significance and importance of nonlinear relationships between the indicators of population life quality in the Russian Federation regions and the indicators of children’s death in fires. It is shown that the system of nonlinear connections is significantly more complex than the system of linear connections.

Metallic Kähler and nearly metallic Kähler manifolds

In this paper, we construct metallic Kähler and nearly metallic Kähler structures on Riemannian manifolds. For such manifolds with these structures, we study curvature properties. Also, we describe linear connections on the manifold which preserve the associated fundamental 2-form and satisfy some additional conditions and present some results concerning them.

On Symmetric Brackets Induced by Linear Connections

In this note, we discuss symmetric brackets on skew-symmetric algebroids associated with metric or symplectic structures. Given a pseudo-Riemannian metric structure, we describe the symmetric brackets induced by connections with totally skew-symmetric torsion in the language of Lie derivatives and differentials of functions. We formulate a generalization of the fundamental theorem of Riemannian geometry. In particular, we obtain an explicit formula of the Levi-Civita connection. We also present some symmetric brackets on almost Hermitian manifolds and discuss the first canonical Hermitian connection. Given a symplectic structure, we describe symplectic connections using symmetric brackets. We define a symmetric bracket of smooth functions on skew-symmetric algebroids with the metric structure and show that it has properties analogous to the Lie bracket of Hamiltonian vector fields on symplectic manifolds.

ONE SIZE DOES NOT FIT ALL — LEADER–MEMBER EXCHANGE AND INNOVATIVENESS

Individual-level innovativeness is widely acknowledged to be critical to the success of an organisation’s innovation, and understanding the related nuances is therefore important. The goal of this study is to add to existing knowledge on how managerial characteristics influence employee innovativeness. Specifically, we address the role of leader–member exchange (LMX) in predicting the three components of employee innovative work behaviour (IWB) — idea generation, idea promotion, and idea implementation. LMX denotes the quality of the relationship between an employee and his/her immediate supervisor and is a significant predictor of many employee attitudes and behaviours. Studies examining the direct and joint effects of LMX and other organisational characteristics on employee creativity and employee IWB have shown the LMX construct has a significant effect on employee innovativeness. However, a more nuanced view on the effects of LMX on the various components of IWB — idea generation, idea promotion, and idea implementation — is missing. Moreover, most research to date on LMX and innovation has focused on the potential linear connections between LMX and employee innovation-related outcomes, leaving the possible opportunities associated with low-quality LMX under-explored. This is a shortcoming, as a growing body of literature demonstrates that, under specific conditions, not only high but also low-quality LMX can be conducive for various employee outcomes. Analysing survey data collected from 93 employees of a knowledge-intensive service company, our study shows U-shaped and linear relationships between LMX and varying components of IWB. We further test an earlier presented assumption that perceived organisational support for innovation may emerge as a powerful contextual condition in relationships between employee innovativeness and its antecedents. We find that LMX and organisational support for innovation have a joint positive effect on the components of employee IWB. These findings extend innovation management theorising and provide advice for managers.

Influence of Modelling Assumptions on the Seismic Risk of Industrial Precast Concrete Structures

This research evaluates the influence of different modelling assumptions on the global and local seismic risk assessment of code-conforming precast reinforced concrete buildings, specifically single-story industrial buildings. In particular the modelling of the system mass, the overhead crane, the beam-to-column and roof-to-beam connections and the cladding system are investigated. For this purpose, a case study resembling a new industrial building designed in accordance with the current Italian building code was selected. Typical dowel beam-to-column connections were considered and the influence of various modelling strategies investigated: perfect hinges, linear elastic connections and non-linear connections with a degrading hysteretic force-displacement model which was calibrated from available data on experimental tests. Three different types of roof-to-beam connections were investigated removing the assumption of rigid diaphragm, namely hot-rolled, cold-formed and socket welded connections. Initially, simplified planar models of single frames were considered to evaluate the influence of the different modelling strategies, then 3D models of the entire building were analyzed. Multiple-stripe non-linear dynamic time history analyses allowed to evaluate displacements, drifts, deformations and ultimate curvatures of the main elements and connections for various intensity measure levels. The seismic risk was assessed in terms of failure rate considering the collapse of both the columns and of the connections. The results show that the beam-to-column connections fail right after reaching yielding due to their low displacement ductility, leading to the loss of support of the beam and therefore increasing the collapse rate of the investigated structural typology.