A bidirectional transformation (BX) keeps a pair of interrelated models synchronized. Symmetric BXs are those for which neither model in the pair fully determines the other. We build two algebraic frameworks for symmetric BXs, with one correctly implementing the other, and both being delta-based generalizations of known state-based frameworks. We identify two new algebraic laws—weak undoability...

In a recent paper, Bruinier and Ono prove that the coefficients of certain weight −1/2 harmonic Maass forms are traces of singular moduli for weak Maass forms. In particular, for the partition function p(n), they prove that p(n) = 1 24n− 1 · ∑ Pp(αQ), where Pp is a weak Maass form and αQ ranges over a finite set of discriminant −24n + 1 CM points. Moreover, they show that 6 · (24n − 1) · Pp(αQ)...

in this paper, let $l$ be a completeresiduated lattice, and let {bf set} denote the category of setsand mappings, $lf$-{bf pos} denote the category of $lf$-posets and$lf$-monotone mappings, and $lf$-{bf cslat}$(sqcup)$, $lf$-{bfcslat}$(sqcap)$ denote the category of $lf$-completelattices and $lf$-join-preserving mappings and the category of$lf$-complete lattices and $lf$-meet-preserving mapping...

It is studied how taking the inverse image by a sliding block code affects the syntactic semigroup of a sofic subshift. Two independent approaches are used: ζ-semigroups as recognition structures for sofic subshifts, and relatively free profinite semigroups. A new algebraic invariant is obtained for weak equivalence of sofic subshifts, by determining which classes of sofic subshifts naturally d...

Coupled transformations occur in software evolution when multiple artifacts must be modified in such a way that they remain consistent with each other. An important example involves the coupled transformation of a data type, its instances, and the programs that consume or produce it. Previously, we have provided a formal treatment of transformation of the first two: data types and instances. Th...

In this article, the energy stability of a one-field fictitious domain method is proved and validated by numerical tests in two and three dimensions. The distinguishing feature of this method is that it only solves for one velocity field for the whole fluid-structure domain; the interactions remain decoupled until solving the final linear algebraic equations. To achieve this the finite element ...

Randomization tests are based on a re-randomization of existing data to gain data-dependent critical values that lead exact hypothesis under special circumstances. However, it is not always possible re-randomize in accordance with the physical randomization from which have been obtained. As consequence, statistical typically cannot control type I error probability if available sample overly lar...