We discuss continuous duality transformations and the properties of classical theories with invariant interactions between electromagnetic fields and matter. The case of scalar fields is treated in some detail. Special discrete elements of the continuous group are shown to be related to the Legendre transformation with respect to the field strengths. Contribution to the Proceedings of the Newto...

We construct an induced gravity (pregeometry) where both the Newton constant and the cosmological constant appear as integration constants in solving field equations. By adding the kinetic terms of ghosts and antighosts, an action of the induced gravity is transformed to a topological field theory. Moreover, by solving field equations of the topological field theory in the FRW universe, we find...

We present an Altered Jacobian Newton Iterative Method for solving nonlinear elliptic problems. Effectiveness of the proposed method is demonstrated through numerical experiments. Comparison of our method with Newton Iterative Method is also presented. Convergence of the Newton Iterative Method is highly sensitive to the initialization or initial guess. Reported numerical work shows the robustn...

in this paper, we present a full newton step feasible interior-pointmethod for circular cone optimization by using euclidean jordanalgebra. the search direction is based on the nesterov-todd scalingscheme, and only full-newton step is used at each iteration.furthermore, we derive the iteration bound that coincides with thecurrently best known iteration bound for small-update methods.

Quasi-Newton methods have played a prominent role, over many years, in the design of effective practical methods for the numerical solution of nonlinear minimization problems and in multi-dimensional zero-finding. There is a wide literature outlining the properties of these methods and illustrating their performance [e.g., [8]]. In addition, most modern optimization libraries house a quasi-Newt...

In this paper, we investigate the convergence behaviour of a class of regularized Newton methods for the solution of nonlinear inverse problems. In order to keep the overall numerical effort as small as possible, we propose to solve the linearized equations by certain semiiterative regularization methods, in particular, iterations with optimal speed of convergence. Our convergence rate analysis...

The rediscovery of the rhetorical tradition in the past thirty years has transformed the study of early modern authors like Montaigne and Pascal. The categories of traditional literary history, like originality, influence, predecessors, and followers, are now seen as inadequate when it comes to explaining how Montaigne and Pascal thought of themselves as authors and how they understood the proc...

Abstract: This paper proposes a one-to-one mapping between the coefficients of continuous-time (s-domain) and discrete-time (z-domain) IIR transfer functions such that the s-domain numerator/denominator coefficients can be uniquely mapped to the z-domain numerator/denominator coefficients, and vice versa. The one-to-one mapping provides a firm basis for proving the inverses of the so-called gen...

The cycle-preserving symmetries for the nine two-dimensional real spaces of constant curvature are collectively obtained within a Cayley–Klein framework. This approach affords a unified and global study of the conformal structure of the three classical Riemannian spaces as well as of the six relativistic and non-relativistic spacetimes (Minkowskian, de Sitter, anti-de Sitter, both Newton–Hooke ...

Gauss–Legendre quadrature formulas have excellent convergence properties when applied to integrals ∫ 1 0 f(x) dx with f ∈ C∞[0, 1]. However, their performance deteriorates when the integrands f(x) are in C∞(0, 1) but are singular at x = 0 and/or x = 1. One way of improving the performance of Gauss–Legendre quadrature in such cases is by combining it with a suitable variable transformation such ...