Premorphisms are monotonic mappings between partially ordered monoids where the morphism condition φ(xy) = φ(x)φ(y) is relaxed into the condition φ(xy) ≤ φ(x)φ(y). Their use in place of morphisms has recently been advocated in situations where classical algebraic recognizability collapses. With languages of overlapping tiles, an extension of classical recognizability by morphisms, called quasi-...

The problem of finding a maximum clique in a graph is prototypical for many clustering and similarity problems; however, in many real-world scenarios, the classical problem of finding a complete subgraph needs to be relaxed to finding an almost complete subgraph, a so-called quasi-clique. In this work, we demonstrate how two previously existing definitions of quasi-cliques can be unified and ho...

Numerical simulation of the high order derivatives based on the sampling data is an important and basic problem in numerical approximation, especially for solving the differential equations numerically. The classical method is the divided difference method. However, it has been shown strongly unstable in practice. Actually, it can only be used to simulate the lower order derivatives in applicat...

In previous work we have established that a particular quasi-classical theoretical viewpoint about the nature of gravitation in galaxy discs provides extremely high concordance (comparable with MOND) with the observed dynamics in optical discs. In this paper, we consider the possibility that the optical disc and the flat radio disc represent distinct dynamical regions which are inherently descr...

If A is a finite alphabet, U ⊂ Z, and μU is a probability measure on A that “looks like” the marginal projection of a stationary stochastic process on A D , then can we “extend” μU to such a process? Under what conditions can we make this extension ergodic, (quasi)periodic, or (weakly) mixing? After surveying classical work on this problem when D = 1, we provide some sufficient conditions and s...

‎In this work‎, ‎we introduce the concept of classical 2-absorbing secondary modules over a commutative ring as a generalization of secondary modules and investigate some basic properties of this class of modules‎. ‎Let $R$ be a commutative ring with‎ ‎identity‎. ‎We say that a non-zero submodule $N$ of an $R$-module $M$ is a‎ ‎emph{classical 2-absorbing secondary submodule} of $M$ ...

We create a new family of Banach spaces, the James–Schreier spaces, by amalgamating two important classical Banach spaces: James’ quasi-reflexive Banach space on the one hand and Schreier’s Banach space giving a counterexample to the Banach–Saks property on the other. We then investigate the properties of these James–Schreier spaces, paying particular attention to how key properties of their ‘a...

Mittelstaedt has defined the class of quasi-implicative lattices and shown that an ortholattice (orthocomplemented lattice) is quasi-implicative exactly if it is orthomodular (quasi-modular). He has also shown that the quasi-implication operation is uniquely determined by the quasi-implicative conditions. One of Mittelstaedt's conditions, however, seems to lack immediate intuitive motivation. C...