Interaction nets are graph rewriting systems which are a generalisation of proof nets for classical linear logic. The linear chemical abstract machine (CHAM) is a term rewriting system which corresponds to classical linear logic, via the Curry-Howard isomorphism. We can obtain a textual calculus for interaction nets which is surprisingly similar to linear CHAM based on the multiplicative fragme...

This work deals with semantics of programming languages (or equivalently, thanks to Curry-Howard isomorphism, with semantics of proofs). We introduce a framework in which both static semantics (Ehrhard’s hypercoherences) and dynamic semantics (Hyland-Ong’s games), can be presented. The work is carried in a multiplicative subsystem of Laurent’s polarized linear logic with weakening. Like Böhm tr...

We prove that for no nontrivial ordered abelian group G, the ordered power series field R((G)) admits an exponential, i.e. an isomorphism between its ordered additive group and its ordered multiplicative group of positive elements, but that there is a nonsurjective logarithm. For an arbitrary ordered field k, no exponential on k((G)) is compatible, that is, induces an exponential on k through t...

We considers how a particular kind of graph corresponds to multiplicative intuitionistic linear logic formula. The main feature of the graphical notation is that it absorbs certain symmetries between conjunction and implication. We look at the basic definitions and present details of an implementation in the functional programming language Standard ML. This provides a functional approach to gra...

Wheeling: A Diagrammatic Analogue of the Duflo Isomorphism We construct and prove a diagrammatic version of the Duflo isomorphism between the invariant subalgebra of the symmetric algebra of a Lie algebra and the center of the universal enveloping algebra. This version implies the original for metrized Lie algebras (Lie algebras with an invariant non-degenerate bilinear form). As an application...

Given a finite group [Formula: see text], we study certain regular subgroups of the permutations which occur in classification theories two types algebraic objects: skew left braces with multiplicative isomorphic to text] and Hopf–Galois structures admitted by Galois extension fields text]. We questions when such yield or involving Hopf algebras. In particular, show that some cases isomorphism ...

there are several kinds of hyperrings, for example, krasnerhyperrings, multiplicative hyperring, general hyperrings and$h_v$-rings. in a multiplicative hyperring, the multiplication isa hyperoperation, while the addition is a binary operation. in this paper, the notion of derivation on multiplicative hyperrings is introduced and some related properties are investigated. {bf keywords:} multiplic...

Consistency is an important issue that causes wide public concern of decision makers in the decision-making process. The lack consistency preference relations results a vague solution. main goal this paper to achieve consistent intuitionistic multiplicative relation using graphical approach. We have proposed two different approaches for (IMPR). In first approach, we propose algorithm IMPR by cy...

Let p be a prime number and let n an integer not divisible by such that every group of order np has normal subgroup p. (This holds in particular for p>n.) Under these hypotheses, we obtain one-to-one correspondence between the isomorphism classes braces size set pairs (Bn,[τ]), where Bn runs over [τ] morphisms from multiplicative to Zp⁎ under certain equivalence relation. This gives classificat...

‎We extend the notion of approximately multiplicative to approximately n-multiplicative maps between locally multiplicatively convex algebras and study some properties of these maps‎. ‎‎W‎e prove that every approximately n-multiplicative linear functional on a functionally continuous locally multiplicatively convex algebra is continuous‎. ‎We also study the relationship between approximately mu...