In [5] it is shown how a model for the logic of constructible duality is a symmetric monoidal closed category with products, that is, a model of linear logic. Remarkably, Nelson’s strong negation∼ behaves as linear duality ⊥. We compare it with some previous results from [4] regarding stable models in a linear logic setting, and suggest some further lines to explore. 1. From Ncd to linear logic...

In this paper, we consider the concept of Ω-distance on a complete, partially ordered G-metric space and prove a fixed point theorem for (ψ, φ)-Weak contraction. Then, we present some applications in integral equations. c ©2013 All rights reserved.

In this paper, we define a new contractive mapping called fuzzy (φ,ψ)-contraction in fuzzy metric space and prove a fixed point theorem for this type of mapping. Finally, an example is given to illustrate the main result of this paper. Mathematics Subject Classification: 54E70; 47H25

Let (φ, ψ) be an (m,n)-valued pair of maps φ, ψ : X ( Y , where φ is an m-valued map and ψ is n-valued, on connected finite polyhedra. A point x ∈ X is a coincidence point of φ and ψ if φ(x) ∩ ψ(x) 6= ∅. We define a Nielsen coincidence number N(φ : ψ) which is a lower bound for the number of coincidence points of all (m,n)-valued pairs of maps homotopic to (φ, ψ). We calculate N(φ : ψ) for all ...

and Applied Analysis 3 Theorem3. Letφ, ψ∈H∞(T) orφ,ψ ∈ H(T), the following statements are equivalent: (1.1) U φ and U ψ commute; (1.2) U φ and U ψ essentially commute; (1.3) φ(zk)ψ(z) = φ(z)ψ(z); (1.4) there exist scalars α andβ, not both zero, such that αφ+ βψ = 0. Nowwe start to study the commutativity of two kth-order slant Toeplitz operators with harmonic symbols. Proposition4. Letφ(z)=∑n p...

The Front Cover shows a protein backbone segment with its characteristic degrees of freedom, the dihedral angles φ and ψ. Exploiting angular dependencies cross-correlated spin relaxation experiments (background), (φ,ψ)-distributions (front left) in Human Ubiquitin are characterized by means newly developed Maximum Entropy routine (equation). More information can be found Article Clemens Kauffma...

Muskens presents in Meaning and Partiality a semantics of possibly contradictory beliefs and other propositional attitudes. We propose a different partial logic based on a few key equalities for the connectives and with four values (truth, falsehood, and undefinedness with negative and positive polarity; only the first truth value is designated). Aim and Scope In logical semantics the grammar a...

Proof: (R ⊂ κ(G, s)). Let I ⊂ M(G, s) be a nonempty ideal. Fix ψ ∈ I. Given σ ∈ R, there exists a sandpile φ such that σ = (φ + ψ)◦ by defintion. Since I is an ideal, this implies that σ ∈ I. Hence R ⊂ I. We conclude that R ⊂ ⋂ I ideal of M(G,s) I = κ(G, s). (κ(G, s) ⊂ R). Recall that R 6= ∅. Since κ(G, s) is the minimal ideal of M(G, s), it is enough to show that R is an ideal. Consider σ ∈ R ...

In this short note we prove two results about medial quasigroups. First, let φ and ψ be binary operations defined by multiplication, left and right division in a medial quasigroup. Then φ and ψ are mutually medial, i.e. φ(ψ(a, b), ψ(c, d)) = ψ(φ(a, c), φ(b, d)). Second, four points a, b, c, d in an idempotent medial quasigroup form a parallelogram if and only if d = (a / b)(b \ c).