Chords are a declarative synchronisation construct based on the Join calculus, available in the programming language Cω. Compared with synchronisation constructs in most imperative languages, chords promise development of programs that are more succinct, easier to read, and easier to reason about. However, to our knowledge, chords have no formal model in an object-oriented setting. In this pape...

A well-known result of Ladner says that the satissability problem for K45, KD45, and S5 is NP-complete. This result implicitly assumes that there are innnitely many primitive propositions in the language; it is easy to see that the satissability problem for these logics becomes linear time if there are only nitely many primitive propositions in the language. By way of contrast, we show that the...

J.-L. Krivine introduced the AF2 type system in order to obtain programs (λterms) which calculate functions, by writing demonstrations of their totalities. We present in this paper two results of completness for some types of AF2 and for many notions of reductions. These results generalize a theorem of R. Labib-Sami established in the system F of J.-Y. Girard. Résumé. J.-L. Krivine a introduit ...

we study different completeness definitions for two categories of lattice-valued cauchy spaces and the relations between these definitions. we also show the equivalence of a so-called completion axiom and the existence of a completion.

in this paper, we present legendre wavelet method to obtain numerical solution of a singular integro-differential equation. the singularity is assumed to be of the cauchy type. the numerical results obtained by the present method compare favorably with those obtained by various galerkin methods earlier in the literature.

We explore properties of Cauchy-Stieltjes families that have no counterpart in exponential families. We relate the variance function of the iterated Cauchy-Stieltjes family to the pseudo-variance function of the initial Cauchy-Stieltjes family. We also investigate when the domain of means can be extended beyond the ”natural domain”.

Γ-ultrametric spaces are spaces which satisfy all the axioms of an ultrametric space except that the distance function takes values in a complete lattice Γ instead of R≥0. Γ-ultrametric spaces have been extensively studied as a way to weaken the notion of an ultrametric space while still providing enough structure to be useful (see for example [17], [18], [8]). The many uses of Γ-ultrametric sp...

Recently, K. Kamano studied sums of products of Bernoulli numbers including poly-Bernoulli numbers. A relation among these sums was given, and an explicit expression of sums of two products was also given, reduced to the famous Euler’s formula. The concept of poly-Cauchy numbers is given by the author as a generalization of the classical Cauchy number and an analogue of poly-Bernoulli number. I...

We develop the basic elements of a Cauchy theory on the complex Levi-Civita field, which constitutes the smallest algebraically closed nonArchimedean extension of the complex numbers. We introduce a concept of analyticity based on differentiation, and show that it leads to local expandability in power series. We show that analytic functions can be integrated over suitable piecewise smooths path...

We study different completeness definitions for two categories of lattice-valued Cauchy spaces and the relations between these definitions. We also show the equivalence of a so-called completion axiom and the existence of a completion.