Different protocols for calibrating electron pair distribution function (ePDF) measurements are explored and described for quantitative studies on nanomaterials. It is found that the most accurate approach to determine the camera length is to use a standard calibration sample of Au nanoparticles from the National Institute of Standards and Technology. Different protocols for data collection are...

It is shown that the Boolean center of complemented elements in a bounded integral residuated lattice characterizes direct decompositions. Generalizing both Boolean products and poset sums of residuated lattices, the concepts of poset product, Priestley product and Esakia product of algebras are defined and used to prove decomposition theorems for various ordered algebras. In particular, we sho...

The transport of L-sets along an L-relation R is considered, with L any residuated lattice, sometimes with further properties as to be a frame or an MV-algebra. Pairs of powerset operators related to R are considered and their basic properties are studied in a comprehensive discussion including some results already known. A few examples and suggestions for application and further development ar...

We extend the lattice embedding of the axiomatic extensions of the positive fragment of intuitionistic logic into the axiomatic extensions of intuitionistic logic to the setting of substructural logics. Our approach is algebraic and uses residuated lattices, the algebraic models for substructural logics. We generalize the notion of the ordinal sum of two residuated lattices and use it to obtain...

The aim of this work is to show that the universal theory R of real closed fields [1] is interpretable in the equational theory of LPi1/2-algebras [2,3,6,7,8], and viceversa. Since R enjoys quantifier elimination, we will obtain that the full theory of R is interpretable in LPi1/2. This will also yield that any function definable in R is definable in LPi1/2. As a consequence of this constructio...

We propose a cheap micropayment scheme based on reasonable requirements. It is exible in the sense that many security options are possible depending on the policy of the involved participants. We avoid large data storage, heavy computations. The scheme is software based for the user and hardware based for the service provider. Possibilities of having software-based solution for both are also pr...

Proof theory can provide useful tools for tackling problems in algebra. In particular, Gentzen systems admitting cut-elimination have been used to establish decidability, complexity, amalgamation, admissibility, and generation results for varieties of residuated lattices corresponding to substructural logics. However, for classes of algebras bearing some family resemblance to groups, such as la...