相关论文: Approximations for the natural logarithm from sole…
Certain geometric approximations such as the widely used traditional shallow-atmosphere, spherical-geoid (TSA-SG) and the deep-atmosphere, spherical-geoid (DA-SG) approximations boil down to the specification of a spatial metric tensor. In…
Horn functions form a subclass of Boolean functions and appear in many different areas of computer science and mathematics as a general tool to describe implications and dependencies. Finding minimum sized representations for such functions…
Linear combinations of translations of a single Gaussian, e^{-x^2}, are shown to be dense in L^2(R). Two algorithms for determining the coefficients for the approximations are given, using orthogonal Hermite functions and least squares.…
We show that the normal form of the Taylor expansion of a $\lambda$-term is isomorphic to its B\"ohm tree, improving Ehrhard and Regnier's original proof along three independent directions. First, we simplify the final step of the proof by…
The article describes the structural and algorithmic relations between Cartesian trees and Lyndon Trees. This leads to a uniform presentation of the Lyndon table of a word corresponding to the Next Nearest Smaller table of a sequence of…
We combine different techniques to extract information about the logarithmic contributions to the two-body conservative dynamics within the post-Newtonian (PN) approximation of General Relativity. The logarithms come from the conservative…
A common measure of a function's complexity is the count of its stationary points. For complicated functions, this count grows exponentially with the volume and dimension of their domain. In practice, the count is averaged over a class of…
Why do natural and interesting sequences often turn out to be log-concave? We give one of many possible explanations, from the viewpoint of "standard conjectures". We illustrate with several examples from combinatorics.
Consider a probability measure supported by a regular geodesic ball in a manifold. For any p larger than or equal to 1 we define a stochastic algorithm which converges almost surely to the p-mean of the measure. Assuming furthermore that…
In this note, given a regular Courant algebroid, we compute its group of automorphisms relative to a dissection. We also propose an infinitesimal version and recover examples of the literature.
We write out relations between the base of natural logarithms ($e$), the ratio of the circumference of a circle to its diameter ($\pi$), the golden ratios ($\Phi_p$) of the additive $p$-sequences, and the ratio of the diagonal of a square…
A general Archimedean spiral lattice is a Delone set in the relative distance if and only if its rotation angle is badly approximable.
There are known constructions for some regular polygons, usually inscribed in a circle, but not for all polygons - the Gauss-Wantzel Theorem states precisely which ones can be constructed. The constructions differ greatly from one polygon…
Approximation by polynomials on a triangle is studied in the Sobolev space $W_2^r$ that consists of functions whose derivatives of up to $r$-th order have bounded $L^2$ norm. The first part aims at understanding the orthogonal structure in…
We establish a natural correspondence between (the equivalence classes of) cubic solutions of an eiconal type equation and (the isomorphy classes of) cubic Jordan algebras.
The standard method for the propagation of errors, based on a Taylor series expansion, is approximate and frequently inadequate for realistic problems. A simple and generic technique is described in which the likelihood is constructed…
The relative algebraic monodromy of abelian logarithms (defined as the kernel of a map between algebraic monodromy groups attached to an abelian scheme with and without a section) was computed in \cite{A1}: under natural assumptions, this…
Contours may be viewed as the 2D outline of the image of an object. This type of data arises in medical imaging as well as in computer vision and can be modeled as data on a manifold and can be studied using statistical shape analysis.…
In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, logarithmic means, etc. Inequalities involving logarithmic mean with differences among other means are presented
The paper gives a wide range, uniform, local approximation of symmetric binomial distribution. The result clearly shows how one has to modify the the classical de Moivre--Laplace normal approximation in order to give an estimate at the tail…