The symmetries in a neighbourhood of a gray value image are modelled by conjugate harmonic function pairs. These are shown to be a suitable curve linear coordinate pair, in which the model represents a neighbourhood. In this representation the image parts, which are symmetric with respect to the chosen function pair, have iso-gray value curves which are simple lines or parallel line patterns. T...

In this paper, we introduce a Liouville action for harmonic diffeomorphism from compact Riemann surface to hyperbolic of genus $g\ge 2$. We derive the variational formula diffeomorphisms when source surfaces vary with fixed target surface.

All models in Law and Economics use punishment functions (PF) that incorporates a trade-off between probability of detection, p, and punishment, F . Suppose society wishes to minimize the total costs of enforcement and damages from crime, T (p, F ). For a given p, an optimal punishment function (OPF) determines an F that minimizes T (p, F ). A popular and tractable PF is the hyperbolic punishme...

The progressive application of non-linear loads in distribution systems (DS) increases current harmonics flow in DS's apparatuses, especially distribution transformers (DTs). Since DTs' operating temperature rises due to the harmonics flow, their loading should be reduced such that the hot spot temperature (HST) is preserved under its permissible value. This means that DTs' available capacity i...

In this paper, first the space of hyperbolic tangent functions is introduced and then the universal approximator property of this space is proved. In fact, by using this space, any nonlinear continuous function can be uniformly approximated with any degree of accuracy. Also, as an application, this space of functions is utilized to design feedback control for a nonlinear dynamical system.

Perturbative quantum field theory for the Ising model at the three-loop level yields a tetrahedral Feynman diagram C(a, b) with masses a and b and four other lines with unit mass. The completely symmetric tetrahedron CTet ≡ C(1, 1) has been of interest from many points of view, with several representations and conjectures having been given in the literature. We prove a conjectured exponentially...

Assume that $p\in [1,\infty ]$ and $u=P_{h}[\phi ]$, where $\phi \in L^{p}(\mathbb{S}^{n-1},\mathbb{R}^n)$ $u(0) = 0$. Then we obtain the sharp inequality $\lvert u(x) \rvert \le G_p(\lvert x )\lVert \phi \rVert_{L^{p}}$ for some smooth function $G_p$ vanishing at $0$. Moreover, an explicit form of constant $C_p$ in $\lVert Du(0)\rVert C_p\lVert \rVert \rVert_{L^{p}}$. These two results general...

the electronic absorption spectral line shape of a diatomic molecule with harmonic potential curves is calculated using the time correlation function formalism. both the equilibrium shift and the frequency shift of the two linking electronic states ate taken into account. the spectrum is also calculated using the cumulated expansion which is related to the correlation function of the time-depen...