In 1958 J. Lambek introduced a calculus L of syntactic types and defined an equivalence relation on types: “x ≡ y means that there exists a sequence x = x1, . . . , xn = y (n ≥ 1), such that xi → xi+1 or xi+1 → xi (1 ≤ i < n)”. He pointed out that x ≡ y if and only if there is join z such that x → z and y → z. This paper gives an effective characterization of this equivalence for the Lambek cal...

martindale proved that under some conditions every multiplicative isomorphism between two rings is additive. in this paper, we extend this theorem to a larger class of mappings and conclude that every multiplicative $(alpha, beta)-$derivation is additive.

This paper shows that the synoptic variability of zonal and meridional midlatitude Pacific and Southern Ocean sea surface winds can be well described by a univariate stochastic dynamical system directly derived from data. The method used to analyze blended Quick Scatterometer (QuikSCAT)–NCEP winds is a general method to estimate drift and diffusion coefficients of a continuous stationary Markov...

We present the logic of bunched implications, BI, in which a multiplicative (or linear) and an additive (or intuitionistic) implication live side-by-side. The propositional version of BI arises from an analysis of the proof-theoretic relationship between conjunction and implication, and may be viewed as a merging of intuitionistic logic and multiplicative, intuitionistic linear logic. The predi...

We extend the multiplicative fragment of linear logic with a non-commutative connective (called before), which, roughly speaking, corresponds to sequential composition. This lead us to a calculus where the conclusion of a proof is a Partially Ordered MultiSET of formulae. We rstly examine coherence semantics, where we introduce the before connective, and ordered products of formulae. Secondly w...

In this paper we investigate multiplicative noise models in the context of continuous optimization. We illustrate how some intrinsic properties of the noise model imply the failure of reasonable search algorithms for locating the optimum of the noiseless part of the objective function. Those findings are rigorously investigated on the (1 + 1)-ES for the minimization of the noisy sphere function...

a model for missing data in mixed binary and continuous responses, which can be used on cross-sectional data, is presented. in this model response indicator for the binary response can be dependent on the continuous response. a closed form for the likelihood is found. for data with a complicated pattern of missing responses some new residuals are also proposed. the model of multiplicative heter...