A data-driven procedure is developed to compute the optimal map between two conditional probabilities $$\rho (x|z_{1},\ldots ,z_{L})$$ and $$\mu (y|z_{1},\ldots , known only through samples depending on a set of covariates $$z_{l}$$ . The tested synthetic data from ACIC Data Analysis Challenge 2017 it applied non-uniform lightness transfer images. Exactly solvable examples simulations are perfo...

Note that the intersection property in Theorem A is equivalent to saying that NL(P ) is a p-group. Also, since this property is clearly independent of the choice of P in Sylp(G), it is clear that L is characteristic in G. Our interest in this characteristic subgroup was motivated by the following. Theorem B. Suppose that G is p-solvable and let L be the largest normal subgroup of G such that L∩...

1. Introduction. Recall that a field extension F ⊆ L is said to be a radical extension if it is possible to write L = F [α], where α ∈ L is an element with α n ∈ F for some positive integer n. More generally, an extension F ⊆ L is a repeated radical extension if there exist intermediate fields L i with F = L 0 ⊆ L 1 ⊆ · · · ⊆ L r = L and such that each field L i is a radical extension of L i−1 ...

One-dimensional three-body Schrödinger equation is studied, with binding mediated by the power-law two-body long-range attraction V (x) = αx in superposition with a short-range repulsion V (x) = β/x (plus, possibly, further subdominant power-law components). Such an unsolvable and non-separable generalization of Calogero model (where one had L = K = 2) is shown to become separable and solvable ...

We found that the two–dimensional Schrödinger equation for 3 electrons in an homogeneous magnetic field (perpendicular to the plane) and a parabolic scalar confinement potential (frequency ω 0) has exact analytical solutions in the limit, where the expectation value of the center of mass vector R is small compared with the average distance between the electrons. These analytical solutions exist...

Three sets of exactly solvable one-dimensional quantum mechanical potentials are presented. These are shape invariant potentials obtained by deforming the radial oscillator and the trigonometric/hyperbolic Pöschl-Teller potentials in terms of their degree l polynomial eigenfunctions. We present the entire eigenfunctions for these Hamiltonians (l = 1, 2, . . .) in terms of new orthogonal polynom...

An exponent β which characterises non-equilibrium coarsening processes is calculated in a deterministic solvable model of coarsening for a 1D q-state Potts system. We study how the fraction of sites P which have never changed their state, scale with the characteristic domain length 〈l〉. β is defined by P ∼ 〈l〉β−1. We propose a new model of coarsening that prevents correlations from developing b...

In order to guarantee that the optimal motif is found, traditional pattern-driven approaches perform an exhaustive search over all candidate motifs of length l. We develop an improved pattern-driven algorithm that takes O(4lk) time, where k is the number of sequences in the sample and l is the motif length, which is independent of the length of each sequence n for large enough l and saving a fa...

An exponent β which characterises non-equilibrium coarsening processes is calculated in a deterministic solvable model of coarsening for a 1D q-state Potts system. We study how the fraction of sites P which have never changed their state, scale with the characteristic domain length 〈l〉. β is defined by P ∼ 〈l〉β−1. We propose a new model of coarsening that prevents correlations from developing b...