We investigate the following two problems on a hermitian form Φ over an algebraic number field: (1) classification of Φ over the ring of algebraic integers; (2) hermitian Diophantine equations. The same types of problems for quadratic forms were treated in the author’s previous articles. Here we discuss the hermitian case. Problem (2) concerns an equation ξΦ · ξ = Ψ , where Φ and Ψ represent he...

We introduce the concept of (EA) property and occasional w-compatibility for hybrid pair F : X × X → 2 (X) and f : X → X. We also introduce common (EA) property for two hybrid pairs F, G : X → 2 (X) and f, g : X → X. We establish some common coupled fixed point theorems for two hybrid pairs of mappings under φ-ψ contraction on noncomplete metric spaces. An example is also given to validate our ...

We show that for any pair φ and ψ of contradictory formulas of dependence logic there is a formula θ of the same logic such that φ ≡ θ and ψ ≡ ¬θ. This generalizes a result of J. Burgess [2].

We show that to every recursive total continuous functional Φ there is a representative Ψ of Φ in the hierearchy of partial continuous functionals such that Ψ is S1 − S9 computable over the hierarchy of partial continuous functionals. Equivalently, the representative Ψ will be PCF -definable over the partial continuous functionals, where PCF is Plotkin’s programming language for computable func...

in this paper direct proofs of some common fixed point results for two and three mappings under weak contractive conditions are given. some of these results are improved by using different arguments of control functions. examples are presented showing that some generalizations cannot be obtained and also that our results are distinct from the existing ones.

We study certain properties and conjuctures on the composition of the arithmetic functions σ, φ, ψ, where σ is the sum of divisors function, φ is Euler’s totient, and ψ is Dedekind’s function.

In the Article, we did not take into account the entanglement swapping that can be caused by eavesdropping efforts. Due to entanglement swapping, in Group 2 of Table 3 and Group 3 of Table 4, the initial states will never lead to a measurement outcome by Eve Ψ Ψ + − 13 24 and Ψ Φ − − 13 24 . Similarly, if after Eve’s measurement Bob performs a measurement using an incorrect sequence, this will ...

In evolutionary biology, it is common to study how various entities evolve together, for example, how parasites coevolve with their host, or genes with their species. Coevolution is commonly modelled by considering certain maps or reconciliations from one evolutionary tree P to another H, all of which induce the same map φ between the leaf-sets of P and H (corresponding to present-day associati...

We find solutions for quantum Class A Bianchi models of the form Ψ = W e ±Φ generalizing the results obtained by Moncrief and Ryan in standard quantum cosmology. For the II and IX Bianchi models there are other solu-tions˜Φ 2 , ˜ Φ 9 to the Hamilton-Jacobi equation for which Ψ is necessarely zero, in contrast with solutions found in supersymmetric quantum cosmology.