Abstract. We develop the theories of the strong commutator, the rectangular commutator, the strong rectangular commutator, as well as a solvability theory for the nonmodular TC commutator. These theories are used to show that each of the following sets of statements are equivalent for a variety V of algebras.(I) (a) V satisfies a nontrivial congruence identity. throughout V. We prove that a residually small variety that satisfies a congruence identity is congruence modular. IntroductionThis monograph is concerned with the relationships between Maltsev conditions, commutator theories and the shapes of congruence lattices in varieties of algebras. Shapes of Congruence LatticesCarl F. Gauss, in [23], introduced the notationwhich is read as "a is congruent to b modulo m", to mean that the integers a and b have the same remainder upon division by the integer modulus m, equivalently that a − b ∈ mZ. As the notation suggests, congruence modulo m is an equivalence relation on Z. It develops that congruence modulo m is compatible with the ring operations of Z, and that the only equivalence relations on Z that are compatible with the ring operations are congruences modulo m for m ∈ Z. Richard Dedekind conceived of a more general notion of "integer", which nowadays we call an ideal in a number ring. Dedekind extended the notation (1.1) towhere a, b ∈ C and µ ⊆ C; (1.2) is defined to hold if a − b ∈ µ. Dedekind called a subset µ ⊆ C a module if it could serve as the modulus of a congruence, i.e., if this relation of congruence modulo µ is an equivalence relation on C. This happens precisely when µ is closed under subtraction. For Dedekind, therefore, a "module" was an additive subgroup of C. The set of Dedekind's modules is closed under the operations of intersection and sum. These two operations make the set of modules into a lattice. Dedekind proposed and investigated the problem of determining the identities of this lattice (the "laws of congruence arithmetic"). In 1900, in [13], he published the discovery that if α, β, γ ⊆ C are modules, then (1.3) α ∩ (β + (α ∩ γ)) = (α ∩ β) + (α ∩ γ).

Forty-eight apple trees infected by 'Candidatus Phytoplasma mali' were examined using single-strand conformation polymorphism (SSCP) and sequence analysis of a variable hflB gene fragment and the immunodominant membrane protein-encoding imp gene. SSCP analysis of polymerase chain reaction-amplified hflB gene fragments revealed diverse profiles, differing in number and position of the bands. The 'Ca. P. mali' content of a single infected apple tree was termed an accession. Cloning of fragments from accessions that yielded fewer bands resulted in clone populations showing uniform or moderately polymorphic SSCP patterns and largely homogenous nucleotide sequences. In contrast, inserts from accessions yielding more bands were heterogeneous and formed two to four distinct groups of profiles. DNA fragments from such accessions were diverse and clustered distantly when subjected to phylogenetic analysis, mostly as two homogenous groups plus one or a few other sequences. Similar results were obtained upon imp gene examination. The collective data indicate that accessions exhibiting more complex patterns were composed of two or three distinct 'Ca. P. mali' strains. There is evidence that multiple infections are of pathological relevance due to strain interactions leading to shifts in the populations. In triply infected trees of one accession, no specific symptoms were induced by the presence of two of the strains. The rare appearance of pronounced symptoms was associated with a separate strain that possessed a unique SSCP profile and a unique hflB sequence. The two mild strains from this apple accession also induced only mild symptoms on periwinkle and tobacco and occurred specifically in one of these plants.

We develop a new centrality concept and apply it to solve certain outstanding problems about ÿnite algebras. In particular, we describe all ÿnite algebras of ÿnite complexity and all ÿnite strongly abelian algebras which generate residually small varieties.

The aim of this study was to perform a preformulation study of dexamethasone (DXM)-loaded nanostructured lipid carriers (NLCs) for ocular use. Lipid screening was applied to find the most suitable solid and liquid lipids and surfactant for the NLC formulation. The visual observation was proved with XRD measurements for the establishment of the soluble state of DXM. Thermoanalytical measurements indicated that the most relevant depression of the crystallinity index could be ensured when using a 7:3 solid lipid:oil ratio. In order to optimize the NLC composition, a 23 full factorial experimental design was used. It was established that each independent factor (lipid, DXM, and surfactant concentration) had a significant effect on the particle size while in the case of entrapment efficiency, the DXM and surfactant concentrations were significant. Lower surfactant and lipid concentrations could be beneficial because the stability and the entrapment efficacy of NLCs were more favorable. The toxicity tests on human cornea cells indicated good ophthalmic tolerability of NLCs. The in vitro drug release study predicted a higher concentration of the solute DXM on the eye surface while the Raman mapping penetration study on the porcine cornea showed a high concentration of nanocarriers in the hydrophylic stroma layer.

The results of an earlier empirical research study on modifying ‘step-by-step’ instructions to practical activities requiring one or more steps of the experiments to be designed by students initiated a longitudinal study to investigate the effectiveness of the approach for younger students and over a period of time. The longitudinal study that followed took the form of a four year research project that began in September 2016. Over 900 students have been involved. All were 12–13 years old in the beginning of the study. Each year they spend six lessons carrying out practical activities using worksheets we provide. This paper reports the findings of the first year, when the participating classes were allocated to one of three groups. Group 1 was the control group. Students simply followed the step-by-step instructions. Groups 2 and 3 were experimental groups. Group 2 students not only followed the same instructions, but also had to complete experimental design tasks on paper. Group 3 students followed the same instructions, but one or more steps were incomplete and students were required to design these steps. The impact of the intervention on the students’ experimental design skills, disciplinary content knowledge and attitude toward chemistry is measured by structured tests. After the first school year of the project it was clear that the type of instruction only had a weak significant positive effect on the results of the Group 2 students’ disciplinary content knowledge. No significant effect of the intervention could be detected on the changes in the students’ grades and attitudes toward the subject, which only seemed to depend on the ranking of their schools. This paper provides the interesting details of the results of the first year (pilot) of the research and discusses changes to the approach that have been made for the remaining three years of the project.