相关论文: Approximations for the natural logarithm from sole…

To any rooted tree, we associate a sequence of numbers that we call the logarithmic factorials of the tree. This provides a generalization of Bhargava's factorials to a natural combinatorial setting suitable for studying questions around…

The semi-classical approximation is an explicit formula of mathematical physics for the sum of Feynman diagrams with a single circuit.In this paper, we study the same problem in the setting of modular operads (see dg-ga/9408003); instead of…

Lueck expressed the Gromov norm of a knot complement in terms of an infinite series that can be computed from a presentation of the fundamental group of the knot complement. In this note we show that Lueck's formula, applied to torus knots,…

For any root system corresponding to a semisimple simply-laced Lie algebra a logarithmic CFT is constructed. Characters of irreducible representations were calculated in terms of theta functions.

The amoeba of a Laurent polynomial is the image of the corresponding hypersurface under the coordinatewise log absolute value map. In this article, we demonstrate that a theoretical amoeba approximation method due to Purbhoo can be used…

The aim of this paper is to present an efficient numerical procedure to approximate the generalized Abel's integral equations of the first and second kinds. For this reason, the Taylor polynomials and the collocation method are applied.…

We study approximations of theories both in general context and with respect to some natural classes of theories. Some kinds of approximations are considered, connections with finitely axiomatizable theories and minimal generating sets of…

A correspondence between the orbits of a system of 2 complex, homogeneous, polynomial ordinary differential equations with real coefficients and those of a polygonal billiard is displayed. This correspondence is general, in the sense that…

We explore an algorithm for approximating roots of integers, discuss its motivation and derivation, and analyze its convergence rates with varying parameters and inputs. We also perform comparisons with established methods for approximating…

Semiclassical approximations often involve the use of stationary phase approximations. This method can be applied when $\hbar$ is small in comparison to relevant actions or action differences in the corresponding classical system. In many…

An estimate on the number of distinct relative periodic orbits around a stable relative equilibrium in a Hamiltonian system with continuous symmetry is given. This result constitutes a generalization to the Hamiltonian symmetric framework…

We introduce the notion of an arithmetic matroid, whose main example is given by a list of elements of a finitely generated abelian group. In particular we study the representability of its dual, providing an extension of the Gale duality…

The metric properties of the set in which random variables take their values lead to relevant probabilistic concepts. For example, the mean of a random variable is a best predictor in that it minimizes the standard Euclidean distance or…

Log-atomic numbers are surreal numbers whose iterated logarithms are monomials, and consequently have a trivial expansion as transseries. Presenting surreal numbers as sign sequences, we give the sign sequence formula for log-atomic…

A graph-theoretic method, simpler than existing ones, is used to characterize the minimal set of monomial generators for the integral closure of any algebra of polynomials generated by quadratic monomials. The toric ideal of relations…

Given a real cubic function $f(x)$ with three roots, take an equilateral triangle $ABC$, the projections of which vertices are the roots of $f(x)$. There is a folklore fact that the vertical lines through the extrema of $f(x)$ are tangent…

In this paper the double-sided Taylor's approximations are studied. A short proof of a well-known theorem on the double-sided Taylor's approximations is introduced. Also, two new theorems are proved regarding the monotonicity of such…

These notes present an approach to obtaining monoid operations which are compatible with a given family of mappings in the sense that the mappings become left translations in the monoid. This can be applied to various situations such as the…

Polygonalization of any smooth billiard boundary can be carried out in several ways. We show here that the semiclassical description depends on the polygonalization process and the results can be inequivalent. We also establish that…

Algebraic theories, sometimes called equational theories, are syntactic notions given by finitary operations and equations, such as monoids, groups, and rings. There is a well-known category-theoretic treatment of them that algebraic…