The linearization of complex ordinary differential equations is studied by extending Lie’s criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations implies the linearizability of systems of partial differential equations corresponding to those complex ordinary differential equations. The invertible comp...

We construct multimonopole solutions containing N−1 distinct fundamental monopoles in SU(N) gauge theory. When the gauge symmetry is spontaneously broken to U(1)N−1, the monopoles are all massive, and we show that the fields can be written in terms of elementary function for all values of the monopole positions and phases. In the limit of unbroken U(1) × SU(N − 2) × U(1) symmetry, the configura...

While home services is a fast growing industry, little attention has been given to the management of its workforce. In particular, the productivity of home-service technicians depends not only on efficiently routing from customer-to-customer, but also the management of their skillsets. This paper introduces a model of technician routing that explicitly models individualized, experience-based le...

The main aim of this study is to construct an explicit form of an analytic solution of a multidimensional difference equation. To this end, we present a nonlinear Cournot duopoly model with unimodal reaction functions, show that its dynamical system is double logistic when the production externalities involved get stronger, and then give a constructive proof of the existence of an analytic solu...

An unconditionally stable alternating direction explicit scheme (ADE) to solve the one-dimensional unsteady convection-diffusion equation was developed by J. Xie, Z. Lin and J. Zhou in [6]. Aside from being explicit and unconditionally stable, the method is straightforward to implement. In this paper we show extensions of this scheme to higher-dimensions of the convection-diffusion equation sub...

We introduce a mathematical framework for the analysis of the input–output dynamics of externally driven memristors. We show that, under general assumptions, their dynamics comply with a Bernoulli differential equation and hence can be nonlinearly transformed into a formally solvable linear equation. The Bernoulli formalism, which applies to both chargeand flux-controlled memristors when either...

This paper proposes a new modeling and solution method that is relatively simple yet powerful enough to handle complex multi-physics problems. The new methodology is based on a combination of cellular automata, finite difference, and analytical analysis concepts. The basic idea is to construct a cascading sequence of simple, explicit rules of evolution, rather than attempt to solve complicated ...

In shallow water propagation the steeper ray angles are weakened most by boundary losses. Regarding the sound intensity as a continuous function of angle it can be converted into a function of travel time to reveal the multipath pulse shape received from a remote source (one-way path) or a target (two-way path). The closed-form isovelocity pulse shape is extended here to the case of upward or d...

An improved technique for matching the asymptotic solutions of non-linear differential equations is presented and successfully applied to the three-dimensional atmospheric skip trajectories. The classical method of matched asymptotic expansions (MAE) is generally applied to two-point-boundary value problems. When we apply the MAE method to initial value problems, due to error propagation, the r...