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In two-dimensional space-time, point particles can experience a geometric, dimension-specific gravity force, which modifies the usual geodesic equation of motion and provides a link between the cosmological constant and the vacuum…
We describe recent nonlinear analytic approximation tools in the classical setting of Hardy spaces in the upper half plane and show how to transfer them to the higher dimensional real setting of harmonic functions in upper half spaces. It…
Using Maxwell's mental imagery of a tube of fluid motion of an imaginary fluid, we derive his equations $\operatorname{curl} \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}$, $\operatorname{curl} \mathbf{H} = \frac{\partial…
We show how a $d$-stress on a piecewise-linear realization of an oriented (non-simplicial, in general) $d$-manifold in \rd naturally induces stresses of lower dimensions on this manifold, and discuss implications of this construction to the…
The actions of the ``$R=T$'' and string-inspired theories of gravity in (1+1) dimensions are generalized into one single action which is characterized by two functions. We discuss differing interpretations of the matter stress-energy…
Large contributions to the near closure of the Universe and to the acceleration of its expansion are due to the gravitation of components of the stress-energy tensor other than its mass density. To familiarise astronomers with the…
A theory of gravity in $d+1$ dimensions is dynamically generated from a theory in $d$ dimensions. As an application we show how $N$ dynamically coupled gravity theories can reduce the effective Planck mass.
A powerful procedure is presented for calculating the Casimir attraction between plane parallel multilayers made up of homogeneous regions with arbitrary magnetic and dielectric properties by use of the Minkowski energy-momentum tensor. The…
Persistence diagrams are two-dimensional plots that summarize the topological features of functions and are an important part of topological data analysis. A problem that has received much attention is how deal with sets of persistence…
Estimating the coefficient functionals on various classes of holomorphic functions traditionally forms an important field of geometric complex analysis and its mathematical and physical applications. These coefficients reflect fundamental…
The two-dimensional transient problem that is studied concerns a semi-infinite crack in an isotropic solid comprising an infinite strip and a half-plane joined together and having the same elastic constants. The crack propagates along the…
The left-invariant sub-Riemannian problem on the group of motions of a plane is considered. Sub-Riemannian geodesics are parametrized by Jacobi's functions. Discrete symmetries of the problem generated by reflections of pendulum are…
A series of stationary principles are developed for dynamical systems by formulating the concept of mixed convolved action, which is written in terms of mixed variables, using temporal convolutions and fractional derivatives. Dynamical…
This study presents an analytical investigation of stress distributions in square-shaped elastic bodies subjected to concentrated compressive loads under uniaxial and biaxial conditions. By employing the Airy stress function method, we…
Using the mathematical theory of shape calculus as tool, we perform a rigorous investigation of the virtual work principle for the computation of electromagnetic forces in static settings. The main goal is to shed light on the widely held…
We consider infinite weighted graphs $G$, i.e., sets of vertices $V$, and edges $E$ assumed countable infinite. An assignment of weights is a positive symmetric function $c$ on $E$ (the edge-set), conductance. From this, one naturally…
We give estimates for the convolution product of an arbitrary number of endlessly continuable functions. This allows us to deal with nonlinear operations for the corresponding resurgent series, e.g. substitution into a convergent power…
Based on the connection between Tsallis nonextensive statistics and fractional dimensional space, in this work we have introduced, with the aid of Verlinde's formalism, the Newton constant in a fractal space as a function of the…
The probabilistic satisfiability of a logical expression is a fundamental concept known as the partition function in statistical physics and field theory, an evaluation of a related graph's Tutte polynomial in mathematics, and the…
As a first step toward realizing a dynamical system that evolves while spontaneously determining its own rule for time evolution, function dynamics (FD) is analyzed. FD consists of a functional equation with a self-referential term, given…