Singly generated quasivarieties and residuated structures

A quasivariety K of algebras has the joint embedding property (JEP) iff it is generated by a single algebra A. It is structurally complete iff the free countably generated algebra in K can serve as A. A consequence of this demand, called "passive structural completeness" (PSC), is that the nontrivial members of K all satisfy the same existential positive sentences. We prove that if K is PSC then it still has the JEP, and if it has the JEP and its nontrivial members lack trivial subalgebras, then its relatively simple members all belong to the universal class generated by one of them. Under these conditions, if K is relatively semisimple then it is generated by one K-simple algebra. It is a minimal quasivariety if, moreover, it is PSC but fails to unify some finite set of equations. We also prove that a quasivariety of finite type, with a finite nontrivial member, is PSC iff its nontrivial members have a common retract. The theory is then applied to the variety of De Morgan monoids, where we isolate the sub(quasi)varieties that are PSC and those that have the JEP, while throwing fresh light on those that are structurally complete. The results illuminate the extension lattices of intuitionistic and relevance logics

Multiple Conclusion Rules in Logics with the Disjunction Property

We prove that for the intermediate logics with the disjunction property any basis of admissible rules can be reduced to a basis of admissible m-rules (multiple-conclusion rules), and every basis of admissible m-rules can be reduced to a basis of admissible rules. These results can be generalized to a broad class of logics including positive logic and its extensions, Johansson logic, normal extensions of S4, n-transitive logics and intuitionistic modal logics

∗\ast-SDYM Fields and Heavenly Spaces. I. ∗\ast-SDYM equations as an integrable system

It is shown that the self-dual Yang-Mills (SDYM) equations for the $\ast$-bracket Lie algebra on a heavenly space can be reduced to one equation (the \it master equation\rm). Two hierarchies of conservation laws for this equation are constructed. Then the twistor transform and a solution to the Riemann-Hilbert problem are given.Comment: 25 page

Mutations in Radial Spoke Head Genes and Ultrastructural Cilia Defects in East-European Cohort of Primary Ciliary Dyskinesia Patients

Primary ciliary dyskinesia (PCD) is a rare (1/20,000), multisystem disease with a complex phenotype caused by the impaired motility of cilia/flagella, usually related to ultrastructural defects of these organelles. Mutations in genes encoding radial spoke head (RSPH) proteins, elements of the ciliary ultrastructure, have been recently described. However, the relative involvement of RSPH genes in PCD pathogenesis remained unknown, due to a small number of PCD families examined for mutations in these genes. The purpose of this study was to estimate the involvement of RSPH4A and RSPH9 in PCD pathogenesis among East Europeans (West Slavs), and to shed more light on ultrastructural ciliary defects caused by mutations in these genes. The coding sequences of RSPH4A and RSPH9 were screened in PCD patients from 184 families, using single strand conformational polymorphism analysis and sequencing. Two previously described (Q109X; R490X) and two new RSPH4A mutations (W356X; IVS3_2–5del), in/around exons 1 and 3, were identified; no mutations were found in RSPH9. We estimate that mutations in RSPH4A, but not in RSPH9, are responsible for 2–3% of cases in the East European PCD population (4% in PCD families without situs inversus; 11% in families preselected for microtubular defects). Analysis of the SNP-haplotype background provided insight into the ancestry of repetitively found mutations (Q109X; R490X; IVS3_2–5del), but further studies involving other PCD cohorts are required to elucidate whether these mutations are specific for Slavic people or spread among other European populations. Ultrastructural defects associated with the mutations were analyzed in the transmission electron microscope images; almost half of the ciliary cross-sections examined in patients with RSPH4A mutations had the microtubule transposition phenotype (9+0 and 8+1 pattern). While microtubule transposition was a prevalent ultrastructural defect in cilia from patients with RSPH4A mutations, similar defects were also observed in PCD patients with mutations in other genes

Impact of Prison Status on HIV-Related Risk Behaviors

Baseline data were collected to evaluate the effectiveness of interventions on completion of the hepatitis A and B vaccine series among 664 sheltered and street-based homeless adults who were: (a) homeless; (b) recently (<1 year) discharged from prison; (c) discharged 1 year or more; and (d) never incarcerated. Group differences at baseline were assessed for socio–demographic characteristics, drug and alcohol use, sexual activity, mental health and public assistance. More than one-third of homeless persons (38%) reported prison time and 16% of the sample had been recently discharged from prison. Almost half of persons who were discharged from prison at least 1 year ago reported daily use of drugs and alcohol over the past 6 months compared to about 1 in 5 among those who were recently released from prison. As risk for HCV and HIV co-infection continues among homeless ex-offenders, HIV/HCV prevention efforts are needed for this population