Related papers: Melnikov-Arnold integrals and optimal normal forms
Starting from the parametric representation of a Feynman diagram, we obtain it's well defined value in dimensional regularisation by changing the integrals over parameters into contour integrals. That way we eventually arrive at a…
Miniaturized optical resonators with spatial dimensions of the order of the wavelength of the trapped light offer prospects for a variety of new applications like quantum processing or construction of meta-materials. Light propagation in…
A generalized matrix-pencil approach is proposed for the estimation of complex exponential components with segmented signal samples, which is very efficient and provides super-resolution estimations. It is applicable to the signals sampled…
We prove mixed-norm estimates for circular averages with respect to $\alpha$-dimensional fractal measures on $\mathbb{R}^2$, using circle tangency bounds when $\alpha \in (0,1]$ and a $\delta$-discretized slicing lemma for fractals when…
We consider small polynomial deformations of integrable systems of the form $dF=0$, $F\in\mathbb{C}[x,y]$ and the first nonzero term $M_\mu$ of the displacement function $\Delta(t,\epsilon)=\sum_{i=\mu}M_i(t)\epsilon^i$ along a cycle…
We develop a Melnikov method for volume-preserving maps with codimension one invariant manifolds. The Melnikov function is shown to be related to the flux of the perturbation through the unperturbed invariant surface. As an example, we…
We study exact, volume-preserving diffeomorphisms that have heteroclinic connections between a pair of normally hyperbolic invariant manifolds. We develop a general theory of lobes, showing that the lobe volume is given by an integral of a…
We introduce a class of Monte Carlo estimators that aim to overcome the rapid growth of variance with dimension often observed for standard estimators by exploiting the target's independence structure. We identify the most basic…
Additive regression models have a long history in multivariate nonparametric regression. They provide a model in which each regression function depends only on a single explanatory variable allowing to obtain estimators at the optimal…
We extend a systematic renormalization procedure for quantum field theory to include particle masses and present several applications. We use a Hamiltonian formulation and light-front quantization because this may produce a convergent…
One considers Hilbert space valued measures on the Borel sets of a compact metric space. A natural numerical valued integral of vector valued continuous functions with respect to vector valued functions is defined. Using this integral,…
The mass splittings of hyperons including the isospin splittings are calculated with $O(\ms^2)$ and $O(\ms \dm)$ accuracy respectively within the semibosonized SU(3)-NJL model. The pattern of the isospin splittings is not spoiled by the…
The generalized minimal subtraction scheme for ultraviolet renormalization (Kuznetsov and Tkachov, 1988) is fine-tuned with applications in mind. The resulting $\text{MS}^4$ scheme obviates extraneous regularizations and renders momentum…
Radiative-recoil corrections to hyperfine splitting in muonium of orders $\alpha(Z\alpha)(m/M)^2E_F$ and $(Z^2\alpha)(Z\alpha)(m/M)^2E_F$ are calculated. These corrections are of the second order in the small electron-muon mass ratio. An…
We represent the coordinate ring of algebraic hulls (which are generalizations of the Malcev completions of nilpotent groups for solvable groups) of solvmanifolds $G/\Gamma$ by using Miller's exponential iterated integrals (which are…
In recent work, we initiated a research program aimed at the systematic investigation of quantum superintegrable systems describing the interaction of two non-relativistic spin-$1/2$ particles in three-dimensional Euclidean space. In that…
Recent results of Kahle and Miller give a method of constructing primary decompositions of binomial ideals by first constructing "mesoprimary decompositions" determined by their underlying monoid congruences. Monoid congruences (and…
Sensitivity analysis (SA) is a procedure for studying how sensitive are the output results of large-scale mathematical models to some uncertainties of the input data. The models are described as a system of partial differential equations.…
We calculate the maximum Lyapunov exponent of the motion in the separatrix map's chaotic layer, along with calculation of its width, as functions of the adiabaticity parameter $\lambda$. The separatrix map is set in natural variables; and…
Our main purpose is to give multiple examples for using the available implementations for computing the normalization of an affine ring, computing the minimial generators of the normalization as an algebra over the original ring and…