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... that this equation is solvable iff z2 - (k2 - 4)z/2 = +4 is solvable. The latter equation has an obvious solution, namely {z9 y)= (k, 1) . So we have solutions of a2 - kab + b2 = 1 for every k, not just fc = 3. When k = 3, we have only the solutions given by the Theorem of §3, but when k - 4 we have ...
... that this equation is solvable iff z2 - (k2 - 4)z/2 = +4 is solvable. The latter equation has an obvious solution, namely {z9 y)= (k, 1) . So we have solutions of a2 - kab + b2 = 1 for every k, not just fc = 3. When k = 3, we have only the solutions given by the Theorem of §3, but when k - 4 we have ...
New Variational-Lagrangian Thermodynamics of Viscous Fluid Mixtures with Thermomolecular Diffusion
... procedure has been extended to open systems by expressing this virtual work in terms of mass flow across an open cell (Biot r977a). The object of this paper is to apply the principle of virtual dissipation to fluid mixtures with thermomolecular diffusion, and to derive directly by a variational proc ...
... procedure has been extended to open systems by expressing this virtual work in terms of mass flow across an open cell (Biot r977a). The object of this paper is to apply the principle of virtual dissipation to fluid mixtures with thermomolecular diffusion, and to derive directly by a variational proc ...
Space-time fractional derivative operators
... In the continuous time random walk, the size of the particle jumps can depend on the waiting time between jumps. For these models, the limiting particle distribution is governed by a fractional differential equation involving coupled space-time fractional derivative operators [3, 19]. This paper dev ...
... In the continuous time random walk, the size of the particle jumps can depend on the waiting time between jumps. For these models, the limiting particle distribution is governed by a fractional differential equation involving coupled space-time fractional derivative operators [3, 19]. This paper dev ...
Partial differential equation
In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. (A special case are ordinary differential equations (ODEs), which deal with functions of a single variable and their derivatives.) PDEs are used to formulate problems involving functions of several variables, and are either solved by hand, or used to create a relevant computer model.PDEs can be used to describe a wide variety of phenomena such as sound, heat, electrostatics, electrodynamics, fluid flow, elasticity, or quantum mechanics. These seemingly distinct physical phenomena can be formalised similarly in terms of PDEs. Just as ordinary differential equations often model one-dimensional dynamical systems, partial differential equations often model multidimensional systems. PDEs find their generalisation in stochastic partial differential equations.