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Integrability Formulas. Part I

Bo LiNa Ma — 2010

Formalized Mathematics

In this article, we give several differentiation and integrability formulas of special and composite functions including the trigonometric function, and the polynomial function.

Approximation of a Martensitic Laminate with Varying Volume Fractions

Bo LiMitchell Luskin — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

We give results for the approximation of a laminate with varying volume fractions for multi-well energy minimization problems modeling martensitic crystals that can undergo either an orthorhombic to monoclinic or a cubic to tetragonal transformation. We construct energy minimizing sequences of deformations which satisfy the corresponding boundary condition, and we establish a series of error bounds in terms of the elastic energy for the approximation of the limiting macroscopic deformation and...

Simple Continued Fractions and Their Convergents

Bo LiYan ZhangArtur Korniłowicz — 2006

Formalized Mathematics

The article introduces simple continued fractions. They are defined as an infinite sequence of integers. The characterization of rational numbers in terms of simple continued fractions is shown. We also give definitions of convergents of continued fractions, and several important properties of simple continued fractions and their convergents.

Difference and Difference Quotient. Part II

Bo LiYanping ZhuangXiquan Liang — 2008

Formalized Mathematics

In this article, we give some important properties of forward difference, backward difference, central difference and difference quotient and forward difference, backward difference, central difference and difference quotient formulas of some special functions [11].MML identifier: DIFF 2, version: 7.8.09 4.97.1001

Generators for algebras dense in L p -spaces

Alexander J. IzzoBo Li — 2013

Studia Mathematica

For various L p -spaces (1 ≤ p < ∞) we investigate the minimum number of complex-valued functions needed to generate an algebra dense in the space. The results depend crucially on the regularity imposed on the generators. For μ a positive regular Borel measure on a compact metric space there always exists a single bounded measurable function that generates an algebra dense in L p ( μ ) . For M a Riemannian manifold-with-boundary of finite volume there always exists a single continuous function that generates...

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