In the slice Hardy space over unit ball of quaternions, we introduce hyperbolic backward shift operator $$\mathcal S_a$$ with decomposition process $$\begin{aligned} f=e_a\langle f, e_a\rangle +B_{a}*\mathcal S_a \end{aligned}$$ where $$e_a$$ denotes normalized Szegö kernel and $$ B_a Blaschke factor. Iterating above process, a corresponding maximal selection principle gives rise to adaptive Fo...

The quaternionic valued functions of a variable, often referred to as slice regular functions, has been studied extensively due the large number generalized results theory one complex variable. Recently, several global properties these found such Borel–Pompieu formula and Stokes’ Theorem from study differential operator, see González-Cervantes González-Campos (Complex Var Ellipt Equ 66(5):1–10,...

XOR-AND Graphs (XAGs) are an enrichment of the classical AND-Inverter (AIGs) with XOR nodes. In particular, XAGs networks composed by ANDs, XORs, and inverters. Besides several emerging technologies applications, often exploited in cryptography-related applications based on multiplicative complexity a Boolean function. The function is minimum number AND gates (i.e., multiplications) that suffic...

This article presents SLAM, an Automatic Solver for Lexical Metaphors like “déshabiller* une pomme” (to undress* an apple). SLAM calculates a conventional solution for these productions. To carry on it, SLAM has to intersect the paradigmatic axis of the metaphorical verb “déshabiller*”, where “peler” (“to peel”) comes closer, with a syntagmatic axis that comes from a corpus where “peler une pom...

* Correspondence: [email protected] College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China Full list of author information is available at the end of the article Abstract In this article, we introduce and consider a new system of general nonconvex variational inequalities defined on uniformly prox-regular sets. We establish the equivalence b...