Note: This is a only a draft version, so there could be flaws. If you find any errors, please do send email to [email protected]. A more thorough version would be available soon in this space. In this chapter, we introduce the all important notion of pure strategy Nash equilibrium. We provide several examples to illustrate this notion. We show that pure strategy Nash equilibrium may not ex...

This paper describes a new method for increasing the number and the volume of hexahedral and prism elements in a hexdominant mesh by topological transformations. The method takes as input a hex-dominant mesh consisting of hexahedrons, prisms, pyramids and tetrahedrons and modifies the mesh to increase the number and the volume of hexahedrons and prisms while maintaining the relaxed conformity c...

When Newton’s method is applied to find the maximal symmetric solution of a discrete algebraic Riccati equation (DARE), convergence can be guaranteed under moderate conditions. In particular, the initial guess does not need to be close to the solution. The convergence is quadratic if the Fréchet derivative is invertible at the solution. When the closed-loop matrix has eigenvalues on the unit ci...

The paper studies the Bardeen{Cooper{Schrieeer energy gap equation at nite temperatures. When the kernel is positive representing a phonon-dominant phase in a superconductor, the existence and uniqueness of a gap solution is established in a class which contains solutions obtainable from bounded domain approximations. The critical temperatures that characterize superconducting-normal phase tran...

In this paper we rigorously derive stochastic amplitude equations for a rather general class of SPDEs with quadratic nonlinearities forced by small additive noise. Near a change of stability we use the natural separation of time-scales to show that the solution of the original SPDE is approximated by the solution of an amplitude equation, which describes the evolution of dominant modes. Our res...

The carbon-13 spin-lattice relaxation times (T1) of glycine have been measured as a function of pD and concentration. Contrary to previously reported findings, no significant dependence was observed on either pD or concentration. In addition, the T1 values reported here are much longer than those published earlier. The discrepancies arise from the presence of paramagnetic impurities in the earl...

This paper presents a formal modeling paradigm that is callable from C, the dominant language for embedded systems programming, for message passing APIs that provides reasonable assurance that the model correctly captures intended behavior. The model is a suitable reference solution for the API, and it supports putative what-if queries over API scenarios for behavior exploration, reproducibilit...

A novel high-order approach to numerical modeling of semiconductor devices is presented. The new method is a combination of the classical Fourier-series Galerkin procedure, a special matrix calculus, and fast numerical pseudospectral techniques. The proposed algorithm renders the exact solution (machine precision) of the semiconductor equations in closed form of a trigonometric polynomial. The ...