Epimorphisms in varieties of subidempotent residuated structures

A commutative residuated lattice A is said to be subidempotent if the lower bounds of its neutral element e are idempotent (in which case they naturally constitute a Brouwerian algebra A*). It is proved here that epimorphisms are surjective in a variety K of such algebras A (with or without involution), provided that each finitely subdirectly irreducible algebra B in K has two properties: (1) B is generated by lower bounds of e, and (2) the poset of prime filters of B* has finite depth. Neither (1) nor (2) may be dropped. The proof adapts to the presence of bounds. The result generalizes some recent findings of G. Bezhanishvili and the first two authors concerning epimorphisms in varieties of Brouwerian algebras, Heyting algebras and Sugihara monoids, but its scope also encompasses a range of interesting varieties of De Morgan monoids

South Africans’ susceptibility to phishing attacks

PURPOSE : The purpose of the study is to assess the phishing susceptibility of individuals in South Africa, across industries related to financial services, education, legal services, and fraud- and forensic businesses. DESIGN/METHODOLOGY/APPROACH : This was an empirical, quantitative research study that collected anonymised data on simulated phishing attacks, using a survey. The results were statistically analysed to identify factors that were significantly related to the phishing score generated. FINDINGS : This was the first South African study to develop a phishing susceptibility score. The following demographic categories demonstrated a higher likelihood of phishing susceptibility: the legal industry; Gen Z and Alpha; females; and participants with matric as the highest educational level. The only two variables that were found to be significantly related to the phishing susceptibility score were gender (with females more susceptible) and the variable relating to prior reporting of phishing attacks (rendering such reporters less susceptible). RESEARCH LIMITATIONS/IMPLICATIONS : The data collected from the online survey represents the perceptions of the individual respondents. The results of this research are valuable, not only to the participants in this study but also to organisations within other industries, as it highlights phishing susceptibility risks. ORIGINALITY/VALUE : This study provides insight into factors influencing phishing susceptibility. For future research purposes, this study could be replicated within other industries in South Africa.https://journals.co.za/journal/sajaarhj2024AuditingNon

Semilinear De Morgan monoids and epimorphisms

DATA AVAILABILITY : Data sharing not applicable to this article as datasets were neither generated nor analysed.A representation theorem is proved for De Morgan monoids that are (i) semilinear, i.e., subdirect products of totally ordered algebras, and (ii) negatively generated, i.e., generated by lower bounds of the neutral element. Using this theorem, we prove that the De Morgan monoids satisfying (i) and (ii) form a variety—in fact, a locally finite variety. We then prove that epimorphisms are surjective in every variety of negatively generated semilinear De Morgan monoids. In the process, epimorphism-surjectivity is established for several other classes as well, including the variety of all semilinear idempotent commutative residuated lattices and all varieties of negatively generated semilinear Dunn monoids. The results settle natural questions about Beth-style definability for a range of substructural logics.The Operational Programme Research, Development and Education of the Ministry of Education, Youth and Sports of the Czech Republic, the EU and in part by the National Research Foundation of South Africa. Open access funding provided by University of Pretoria.https://link.springer.com/journal/12hj2024Mathematics and Applied MathematicsNon

Varieties of De Morgan monoids : covers of atoms

The variety DMM of De Morgan monoids has just four minimal subvarieties. The join-irreducible covers of these atoms in the subvariety lattice of DMM are investigated. One of the two atoms consisting of idempotent algebras has no such cover; the other has just one. The remaining two atoms lack nontrivial idempotent members. They are generated, respectively, by 4{element De Morgan monoids C4 and D4, where C4 is the only nontrivial 0{generated algebra onto which nitely subdirectly irreducible De Morgan monoids may be mapped by non-injective homomorphisms. The homomorphic pre-images of C4 within DMM (together with the trivial De Morgan monoids) constitute a proper quasivariety, which is shown to have a largest subvariety U. The covers of the variety V(C4) within U are revealed here. There are just ten of them (all nitely generated). In exactly six of these ten varieties, all nontrivial members have C4 as a retract. In the varietal join of those six classes, every subquasivariety is a variety|in fact, every nite subdirectly irreducible algebra is projective. Beyond U, all covers of V(C4) [or of V(D4)] within DMM are discriminator varieties. Of these, we identify in nitely many that are nitely generated, and some that are not. We also prove that there are just 68 minimal quasivarieties of De Morgan monoids.The European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant, RVO 67985807 and by the CAS-ICS postdoctoral fellowship, the National Research Foundation of South Africa and DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), South Africa.https://www.cambridge.org/core/journals/review-of-symbolic-logic2021-06-01am2021Mathematics and Applied Mathematic

Epimorphisms, definability and cardinalities

We characterize, in syntactic terms, the ranges of epimorphisms in an arbitrary class of similar first-order structures (as opposed to an elementary class). This allows us to strengthen a result of Bacsich, as follows: in any prevariety having at most s non-logical symbols and an axiomatization requiring at most m variables, if the epimorphisms into structures with at most m+s+ℵ0 elements are surjective, then so are all of the epimorphisms. Using these facts, we formulate and prove manageable ‘bridge theorems’, matching the surjectivity of all epimorphisms in the algebraic counterpart of a logic ⊢ with suitable infinitary definability properties of ⊢, while not making the standard but awkward assumption that ⊢ comes furnished with a proper class of variables.The European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 689176 (project “Syntax Meets Semantics: Methods, Interactions, and Connections in Substructural logics”). The first author was also supported by the Project GA17-04630S of the Czech Science Foundation (GAČR). The second author was supported in part by the National Research Foundation of South Africa (UID 85407). The third author was supported by the DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), South Africa.http://link.springer.com/journal/112252020-02-07hj2019Mathematics and Applied Mathematic

Singly generated quasivarieties and residuated structures

Please read abstract in the article.H2020 Marie Skłodowska-Curie Actions; DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), South Africa and National Research Foundation of South Africa.https://onlinelibrary.wiley.com/journal/15213870hj2021Mathematics and Applied Mathematic

Ultra-conformal drawn-on-skin electronics for multifunctional motion artifact-free sensing and point-of-care treatment

An accurate extraction of physiological and physical signals from human skin is crucial for health monitoring, disease prevention, and treatment. Recent advances in wearable bioelectronics directly embedded to the epidermal surface are a promising solution for future epidermal sensing. However, the existing wearable bioelectronics are susceptible to motion artifacts as they lack proper adhesion and conformal interfacing with the skin during motion. Here, we present ultra-conformal, customizable, and deformable drawn-on-skin electronics, which is robust to motion due to strong adhesion and ultra-conformality of the electronic inks drawn directly on skin. Electronic inks, including conductors, semiconductors, and dielectrics, are drawn on-demand in a freeform manner to develop devices, such as transistors, strain sensors, temperature sensors, heaters, skin hydration sensors, and electrophysiological sensors. Electrophysiological signal monitoring during motion shows drawn-on-skin electronics' immunity to motion artifacts. Additionally, electrical stimulation based on drawn-on-skin electronics demonstrates accelerated healing of skin wounds. Designing efficient wearable bioelectronics for health monitoring, disease prevention, and treatment, remains a challenge. Here, the authors demonstrate an ultra-conformal, customizable and deformable drawn-on-skin electronics which is robust to motion artifacts and resistant to physical damage

Epimorphisms in varieties of subidempotent residuated structures

Please read abstract in the article.The European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant agreement No 689176 (project “Syntax Meets Semantics: Methods, Interactions, and Connections in Substructural logics”). The first author was also supported by the project CZ.02.2.69/0.0/0.0/17_050/0008361, OPVVV MŠMT, MSCA-IF Lidské zdroje v teoretické informatice. The second author was supported in part by the National Research Foundation of South Africa (UID 85407). The third author was supported by the DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), South Africa.https://link.springer.com/journal/12hj2022Mathematics and Applied Mathematic

Epimorphisms in varieties of subidempotent residuated structures

Please read abstract in the article.The European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant agreement No 689176 (project “Syntax Meets Semantics: Methods, Interactions, and Connections in Substructural logics”). The first author was also supported by the project CZ.02.2.69/0.0/0.0/17_050/0008361, OPVVV MŠMT, MSCA-IF Lidské zdroje v teoretické informatice. The second author was supported in part by the National Research Foundation of South Africa (UID 85407). The third author was supported by the DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), South Africa.https://link.springer.com/journal/12hj2022Mathematics and Applied Mathematic

Varieties of De Morgan monoids : minimality and irreducible algebras

Please read abstract in the article.The first author acknowledges project CZ.02.2.69/0.0/0.0/17_050/0008361, OPVVV MŠMT, MSCA-IF Lidské zdroje v teoretické informatice, and project GJ15-07724Y of the Czech Science Foundation.The European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 689176 (project “Syntax Meets Semantics: Methods, Interactions, and Connections in Substructural logics”).http://www.elsevier.com/locate/jpaa2020-07-01hj2018Mathematics and Applied Mathematic