TWISTED DOUBLING INTEGRALS FOR BRYLINSKI–DELIGNE EXTENSIONS OF CLASSICAL GROUPS

We explain how to develop the twisted doubling integrals for Brylinski–Deligne extensions of connected classical groups. This gives a family of global integrals which represent Euler products for this class of nonlinear extensions.

Nonlinear extensions of gravitating dyons: from NUT wormholes to Taub-Bolt instantons

Recent work has shown the existence of a unique nonlinear extension of electromagnetism which preserves conformal symmetry and allows for the freedom of duality rotations. Moreover, black holes and gravitational waves have been found to exist in this nonlinearly extended electrovacuum. We generalise these dyonic black holes in two major ways: with the relaxation of their horizon topology and with the inclusion of magnetic mass. Motivated by recent attention to traversable wormholes, we use this new family of Taub-NUT spaces to construct AdS wormholes. We explore some thermodynamic features by using a semi-classical approach. Our results show that a phase transition between the nut and bolt configurations arises in a similar way to the Maxwellian case.

On Polynomial Recursive Sequences

We study the expressive power of polynomial recursive sequences, a nonlinear extension of the well-known class of linear recursive sequences. These sequences arise naturally in the study of nonlinear extensions of weighted automata, where (non)expressiveness results translate to class separations. A typical example of a polynomial recursive sequence is bn = n!. Our main result is that the sequence un = nn is not polynomial recursive.

A Combined Entropy/Phase-Field Approach to Gravity

Terms related to gradients of scalar fields are introduced as scalar products into the formulation of entropy. A Lagrange density is then formulated by adding constraints based on known conservation laws. Applying the Lagrange formalism to the resulting Lagrange density leads to the Poisson equation of gravitation and also includes terms being related to curvature of space. The formalism further leads to terms possibly explaining nonlinear extensions known from modified Newtonian dynamics approaches. The article concludes with a short discussion of the presented methodology and provides an outlook on other phenomena, which might be tackled using this new approach.

On the Predictive Content of Nonlinear Transformations of Lagged Autoregression Residuals and Time Series Observations

Although many macroeconomic time series are assumed to follow nonlinear processes, nonlinear models often do not provide better predictions than their linear counterparts. Furthermore, nonlinear models easily become very complex and difficult to estimate. The aim of this study is to investigate whether simple nonlinear extensions of autoregressive processes are able to provide more accurate forecasting results than linear models. Therefore, simple autoregressive processes are extended by means of nonlinear transformations (quadratic, cubic, sine, exponential functions) of lagged time series observations and autoregression residuals. The proposed forecasting models are applied to a large set of macroeconomic and financial time series for 10 European countries. Findings suggest that these models, including nonlinear transformation of lagged autoregression residuals, are able to provide better forecasting results than simple linear models. Thus, it may be possible to improve the forecasting accuracy of linear models by including nonlinear components. This is especially true for time series that are positively tested for nonlinear characteristics and longer forecast horizons.

Polynomial Extensions of the Weyl C*-Algebra

We introduce higher order (polynomial) extensions of the unique (up to isomorphisms) nontrivial central extension of the Heisenberg algebra, which can be concretely realized as sub-Lie algebras of the polynomial algebra generated by the creation and annihilation operators in the Schrödinger representation. The simplest nontrivial of these extensions (the quadratic one) is isomorphic to the Galilei algebra, widely studied in quantum physics. By exponentiation of this representation we construct the corresponding polynomial analogue of the Weyl [Formula: see text]-algebra and compute the polynomial Weyl relations. From this we deduce the explicit form of the composition law of the associated nonlinear extensions of the 1-dimensional Heisenberg group. The above results are used to calculate a simple explicit form of the vacuum characteristic functions of the nonlinear field operators of the Galilei algebra, as well as of their moments. The corresponding measures turn out to be an interpolation family between Gaussian and Meixner, in particular Gamma.