In this article, a simple and cost-effective method to create patterned nanoindentations on Al surface via mold-assisted chemical etching process is demonstrated. This report shows the reaction-diffusion method which formed nanoscale shallow etch pits by the absorption/liberation behaviors of chemical etchant in poly(dimethylsiloxane) stamp. During subsequent anodization, it was possible to obt...

(Note that the Craig interpolation theorem is the special case of Chang's theorem in which Q19,.., Qn are all universal quantifiers.) Chang also raised the question [2, Remark (k)] as to whether the Lopez-Escobar interpolation theorem [6] for the infinitary language L.1. possesses a similar generalization. In this paper, we show that the answer to Chang's question is affirmative and, moreover, ...

Let Γ be a (not necessarily finite) structure with a finite relational signature. We prove that deciding whether a given existential positive sentence holds in Γ is in LOGSPACE or complete for the class CSP(Γ )NP under deterministic polynomial-time many-one reductions. Here, CSP(Γ )NP is the class of problems that can be reduced to the constraint satisfaction problem of Γ under non-deterministi...

There is a striking convergence between Burgers turbulence and the continuous spontaneous localization [CSL] model of quantum mechanics. In this paper, we exploit this analogy showing the similarities in the physics of these two apparently unrelated problems. It is hoped that the kind of analogy we introduce here may lead to important developments in both areas.

Recently, Dassow et al. connected partial words and regular languages. Partial words are sequences in which some positions may be undefined, represented with a “hole” symbol . If we restrict what the symbol can represent, we can use partial words to compress the representation of regular languages. Doing so allows the creation of so-called -DFAs which are smaller than the DFAs recognizing the o...

Lukasiewicz' infinite-valued logic L has been used by a number of authors to study reasoning with vague, "fuzzy", or uncertain statements ([5], [2], [11], [12]). Scott and, more recently, Katz have also argued that L is appropriate for the logic of degrees of error or degrees of approximation to the truth ([6], p. 421 and [4], p. 773). The aim of this note is to show that L is not appropriate f...

Assume T is superstable, Φ(x) is a formula over ∅, Q = Φ(M∗) is countable and KQ = {M : M is countable and Φ(M) = Q}. We investigate models in KQ assuming KQ has the prime model property. We prove some corollaries on the number of models inKQ. We show an example of an ω-stable T and Q with KQ having exactly 3 models. First we fix the general set-up. Throughout, T is a countable complete theory ...

This paper investigates the word problem for inverse monoids generated by a set Γ subject to relations of the form e = f , where e and f are both idempotents in the free inverse monoid generated by Γ. It is shown that for every fixed monoid of this form the word problem can be solved both in linear time on a RAM as well as in deterministic logarithmic space, which solves an open problem of Marg...