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A characterization of relative weak mixing in W∗-dynamical systems in terms of a relatively independent joining is proven.

By using the Darboux formula obtained as a generalization of the Taylor formula, we deduce some Jensen–Ostrowski-type inequalities. The applications to quadrature rules and f-divergence measures (specifically, for higher-order ...

We develop analogs of exponential and trigonometric functions (including the basic exponential function) and derive their fundamental properties: addition formula, positivity, reciprocal and fundamental relations of ...

We present a network-based framework for simulating systemic risk that considers shock propagation in banking systems. In particular, the framework allows the modeller to reflect a top-down framework where a shock to one ...

We consider the fraction of nodes that default in large, stochastic, inhomogeneous financial networks following an initial shock to the system. Results for deterministic sequences of networks are generalized to stochastic ...

A new barycentric spectral domain decomposition methods algorithm for solving partial integro-differential models is described. The method is applied to European and butterfly call option pricing problems under a class of ...

We prove that any correspondence (multi-function) mapping a metric space into a Banach space that satisfies a certain pointwise Lipschitz condition, always has a continuous selection that is pointwise Lipschitz on a dense ...

The bifurcation analysis of a continuous n‐dimensional nonlinear dynamical system with a nonhyperbolic equilibrium point is done by using the main theorem in the work of Castillo‐Chavez and Song. We derive an analog of ...

This is a brief exposition of dynamic systems approaches that form the basis for linear implicit evolution equations with some indication of interesting applications. Examples in in nite-dimensional dissipative systems ...