We study the reduction in a $\lambda$ -calculus derived from Moggi’s computational one, which we call the computational core. The reduction relation consists of rules obtained by orienting three monadic laws. Such laws, in particular associativity and identity, introduce intricacies in the operational analysis. We investigate the central notions of returning a value versus having a normal form and address the question of normalizing strategies. Our analysis relies on factorization results.

For numerical semigroups with a specified list of (not necessarily minimal) generators, we describe the asymptotic distribution of factorization lengths with respect to an arbitrary modulus. In particular, we prove that the factorization lengths are equidistributed across all congruence classes that are not trivially ruled out by modular considerations.

A Nikishin–Maurey characterization is given for bounded subsets of weak-type Lebesgue spaces. New factorizations for linear and multilinear operators are shown to follow.

We analyze domination properties and factorization of operators in Banach spaces through subspaces of $L^{1}$-spaces. Using vector measure integration and extending classical arguments based on scalar integral bounds, we provide characterizations of operators factoring through subspaces of $L^{1}$-spaces of finite measures. Some special cases involving positivity and compactness of the operators are considered.

The elasticity of an atomic integral domain is, in some sense, a measure of how far the domain is from being a half-factorial domain. We consider the relationship between the elasticity of a domain R and the elasticity of its polynomial ring R[x]. For example, if R has at least one atom, a sufficient condition for the polynomial ring R[x] to have elasticity 1 is that every non-constant irreducible polynomial f ∈ R[x] be irreducible in K[x]. We will determine the integral domains R whose polynomial rings satisfy this condition.

It is well known that the factorization properties of a domain are reflected in the structure of its group of divisibility. The main theme of this paper is to introduce a topological/graph-theoretic point of view to the current understanding of factorization in integral domains. We also show that connectedness properties in the graph and topological space give rise to a generalization of atomicity.

In this paper we analyse the structure of a finite group of minimal order among the finite non-supersoluble groups possessing a triple factorization by supersoluble subgroups of pairwise relatively prime indices. As an application we obtain some sufficient conditions for a triple factorized group by supersoluble subgroups of pairwise relatively prime indices to be supersoluble. Many results appear as consequences of our analysis.

We consider the conventional techniques of vision robot system calibration where camera parameters and robot hand–eye parameters are computed separately, i.e., first performing camera calibration and then carrying out hand–eye calibration based on the calibrated parameters of cameras. In this paper we propose a joint algorithm that combines the camera calibration and the hand–eye calibration together. The proposed algorithm gives the solutions of the cameras' parameters and the hand–eye parameters simultaneously by using nonlinear optimization. Both simulations and real experiments show the superiority of our algorithm. We also apply our algorithm in the real application of the robot-assisted surgical system, and very good results have been obtained.

This paper provides a comprehensive description of a new method of factorization for the Coriolis/centripetal matrix. In the past three decades, studies on dynamics have rapidly developed through the efforts of many researchers in the field of mechanics. While direct methods for deriving the Coriolis/centripetal matrix are well known and have been widely used in the last century, the entries of this matrix were always obtained by means of the Christoffel symbols of first kind. Startling techniques for deriving dynamic equations of robot manipulators first appeared about 30 years ago. Since then, much has been done to refine and develop the method, but it is still a highly active field of research, with many outstanding problems, both theoretical and in applications. This work presents, in a unitary frame and from a new perspective, the main concepts and results of one of the most fascinating aspects of mechanics, namely the factorization of structures, and offers the reader another point of view concerning a possible way to approach the Coriolis/centripetal matrix. It aims to study a theory of representation for such a matrix based on an elegant method of fundamental matrices. The paper is intended to be self-contained by presenting complete properties emerging from these novel structures. This work is useful not only to researchers in mechanics, but also to control engineers who are interested in learning some of the mechanical modeling. Toward this end, the paper provides numerical examples, as well as practical adaptive applications for modern designers to use at the system level.

The question of counting minimal factorizations of permutations into transpositions that act transitively on a set has been studied extensively in the geometrical setting of ramified coverings of the sphere and in the algebraic setting of symmetric functions.

It is natural, however, from a combinatorial point of view to ask how such results are affected by counting up to equivalence of factorizations, where two factorizations are equivalent if they differ only by the interchange of adjacent factors that commute. We obtain an explicit and elegant result for the number of such factorizations of permutations with precisely two factors. The approach used is a combinatorial one that rests on two constructions.

We believe that this approach, and the combinatorial primitives that have been developed for the “cut and join” analysis, will also assist with the general case.

Let $G$ be a $\sigma$-compact, locally compact group and $\mathcal I$ be a closed 2-sided ideal with finite codimension in $L^1(G)$. It is shown that there are a closed left ideal ${\mathcal L}$ having a right bounded approximate identity and a closed right ideal ${\mathcal R}$ having a left bounded approximate identity such that ${\mathcal I} = {\mathcal L} + {\mathcal R}$. The proof uses ideas from the theory of boundaries of random walks on groups. 2000 Mathematics Subject Classification: primary 43A20; secondary 42A85, 43A07, 46H10, 46H40, 60B11.

A group is said to be factorizable if it has a finite number of abelian subgroups, H1, H2, … Hn, such that G = H1H2 … Hn. It is shown that, if G is a factorizable or connected locally compact group, then every derivation from L1 (G) to an arbitrary L1 (G)-bimodule X is continuous.