相关论文: The dual horospherical Radon transform for polynom…
The p-adic valuation of a polynomial can be given by its valuation tree. This work describes the 2-adic valuation tree of the general degree 2 polynomial in 2 variables.
In this paper we study a probabilistic framework for Radon partitions, where our points are chosen independently from the $d$-dimensional normal distribution. For every point set we define a corresponding Radon polytope, which encodes all…
We obtain an exact formula for the Fourier transform of multiradial functions, i.e., functions of the form $\Phi(x)=\phi(|x_1|, \dots, |x_m|)$, $x_i\in \mathbf R^{n_i}$, in terms of the Fourier transform of the function $\phi$ on $\mathbf…
We present an explicit branching formula for the six-parameter Macdonald-Koornwinder polynomials with hyperoctahedral symmetry.
In this work we consider the Conical Radon Transform, which integrates a function on $\R^n$ over families of circular cones. Transforms of this type are known to arise naturally as models of Compton camera imaging and single-scattering…
In this paper we propose a new version of differential transform method (we shall call this method as $\alpha$-parameterized differential transform method), which differs from the traditional differential transform method in calculating…
The Doppler spectrum estimation of a weather radar signal in a classic way can be made by two methods, temporal one based in the autocorrelation of the successful signals, whereas the other one uses the estimation of the power spectral…
The leading-order hadronic vacuum polarization contribution to the hyperfine splitting of true muonium is reevaluated in two ways. The first considers a more complex pionic form factor and better estimates of the perturbative QCD…
Here, we find the characteristics polynomial of normalized Laplacian of a tree. The coefficients of this polynomial are expressed by the higher order general Randi\'c indices for matching, whose values depend on the structure of the tree.…
In this paper we present an algorithmic procedure that transforms, if possible, a given system of ordinary or partial differential equations with radical dependencies in the unknown function and its derivatives into a system with polynomial…
In this paper we focus on r-geometric polynomials, r-exponential polynomials and their harmonic versions. It is shown that harmonic versions of these polynomials and their generalizations are useful to obtain closed forms of some series…
- An algorithm for calculating the radiation field of a charged point particle performing a spiral motion in an infinite cylindrical waveguide with a multilayer side wall is found. The number of layers and their filling is arbitrary. The…
The ring of dual numbers over a ring $R$ is $R[\alpha] = R[x]/(x^2)$, where $\alpha$ denotes $x+(x^2)$. For any finite commutative ring $R$, we characterize null polynomials and permutation polynomials on $R[\alpha]$ in terms of the…
We present an algorithm for computing a holonomic system for a definite integral of a holonomic function over a domain defined by polynomial inequalities. If the integrand satisfies a holonomic difference-differential system including…
This study provides an exact solution to Chandrasekhar's H function for isotropic scattering. The H function, which is governed by a nonlinear integral equation, plays a central role in radiative transfer theory. To facilitate the solution,…
We develop a tree method for multidimensional q-Hahn polynomials. We define them as eigenfunctions of a multidimensional q-difference operator and we use the factorization of this operator as a key tool. Then we define multidimensional…
Inversion of Radon transforms is the mathematical foundation of many modern tomographic imaging modalities. In this paper we study a conical Radon transform, which is important for computed tomography taking Compton scattering into account.…
We compute the factorization homology of a polynomial algebra over a compact and closed manifold with trivialized tangent bundle up to weak equivalence in a new way. This calculation is based on the model of a graph complex and an explicit…
The Funk-Radon transform assigns to a function defined on the unit sphere its integrals along all great circles of the sphere. In this paper, we consider a frame decomposition of the Funk-Radon transform, which is a flexible alternative to…
We develop integral geometry for non-compactly causal symmetric spaces. We define a complex horospherical transform and, for some cases, identify it with a Cauchy type integral.