Abstract: We present theoretical properties of the log-concave maximum likelihood estimator of a density based on an independent and identically distributed sample in R. Our study covers both the case where the true underlying density is log-concave, and where this model is misspecified. We begin by showing that for a sequence of log-concave densities, convergence in distribution implies much s...

Let L = −∆+ V be a Schrödinger operator on R, d ≥ 3, where V is a nonnegative function, V 6= 0, and belongs to the reverse Hölder class RHd/2. The purpose of this paper is three-fold. First, we prove a version of the classical theorem of Jones and Journé on weak∗-convergence in H L(R ). Secondly, we give a bilinear decomposition for the product space H L(R )×BMOL(R). Finally, we study the commu...

An implementation of a component-free symbolic vector algebra in Aldor is presented. This package provides two powerful functions: simplification of vector expressions and the proof of vector identities. The implementation benefits greatly from Aldor’s strong typing, which allows several simplification problems that have defeated previous implementations to be solved.

Object-oriented data models are receiving wide attention since they provide expressive abstraction mechanisms to model naturally and directly both structural and behavioral aspects of complex databases applications. In an objectoriented data model, a database is modeled in terms of objects grouped in classes, organized into subclasses hierarchies. Moreover, associations between entities are mod...

The goal of the Mathemagix project is to develop a new and free software for computer algebra and computer analysis, based on a strongly typed and compiled language. In this paper, we focus on the underlying type system of this language, which allows for heavy overloading, including parameterized overloading with parameters in so called “categories”. The exposition is informal and aims at givin...

We propose a semantic model of PAF!, a proof assistant dedicated to program verification focused on the functional fragment of ML. In particular, we model the strong typing predicate, specific to the PAF! system. From the semantic correctness of the system, we prove the consistency of the formalism, as well as the termination property for all strongly typed programs (as defined in the system). ...

We examine the problem of how to ensure behavioral consistency of an object-oriented system after its schema has been updated. The problem is viewed from the perspective of both the strongly typed and the untyped language model. Solutions are compared in both models using C++ and CLOS as examples.

Scientists and engineers must ensure that physical equations are dimensionally consistent, but existing programming languages treat all numeric values as dimensionless. This paper extends a strongly-typed programming language with a notion of dimension type. Our approach improves on previous proposals in that dimension types may be polymorphic. Furthermore, any expression which is typable in th...

Given a graph H on vertex set {1, 2, · · · , n} and a function f : [0, 1] → R, define ‖f‖H := ∣∣∣∣∣ ∫ ∏ ij∈E(H) f(xi, xj)dμ |V (H)| ∣∣∣∣∣ 1/|E(H)| , where μ is the Lebesgue measure on [0, 1]. We say that H is norming if ‖·‖H is a semi-norm. A similar notion ‖·‖r(H) is defined by ‖f‖r(H) := ‖|f |‖H and H is said to be weakly norming if ‖·‖r(H) is a norm. Classical results show that weakly normin...

Fibonacci is an object-oriented database programming language characterized by static and strong typing and by new mechanisms for modelling databases in terms of objects with roles, classes and associations. A brief introduction to the language is provided to present those features which are particularly suited to modelling complex databases. Examples of the use of Fibonacci are given with refe...