In a recent paper (Diversity in Monoids, Czech. Math. J. 62 (2012), 795–809), the last two authors introduced and developed the monoid invariant “diversity” and related properties “homogeneity” and “strong homogeneity”. We investigate these properties within the context of inside factorial monoids, in which the diversity of an element counts the number of its different almost primary components. Inside factorial monoids are characterized via diversity and strong homogeneity. A new invariant complementary to diversity, height, is introduced. These two invariants are connected with the well-known invariant of elasticity.
Let $M$ be a (commutative cancellative) monoid. A nonunit element $q\in M$ is called almost primary if for all $a,b\in M$, $q\mid ab$ implies that there exists $k\in \mathbb {N}$ such that $q\mid a^k$ or $q\mid b^k$. We introduce a new monoid invariant, diversity, which generalizes this almost primary property. This invariant is developed and contextualized with other monoid invariants. It naturally leads to two additional properties (homogeneity and strong homogeneity) that measure how far an almost primary element is from being primary. Finally, as an application the authors consider factorizations into almost primary elements, which generalizes the established notion of factorization into primary elements.
Firing properties of single neurons in the nervous system have been recognized to be determined by their intrinsic ion channel dynamics and extrinsic synaptic inputs. Previous studies have suggested that dendritic structures exhibit significant roles in the modulation of somatic firing behavior in neurons. Following these studies, we show that finite information transmission delay between dendrite and soma can also influence the somatic firings in neurons. Our investigation is based on a two-compartment model which can approximately reproduce the firing activity of cortical pyramidal neurons. The obtained simulation results indicate that under subthreshold stimulus, spontaneous fast spiking activity is induced by large values of time delay, while for suprathreshold stimulus, regular bursting, chaotic firing and fast spiking can be observed under different time delays. More importantly, the transition mode between these diverse firing patterns with the variation of delay shows a period-doubling phenomenon under certain stimulus intensity. Consequently, our model results can not only illustrate the influential roles of internal time delay in the generation of a diversity of neuronal firing patterns, but also provide us with frameworks for investigating the impacts of internal time delay on the firing properties of many other neurons in the nervous system.
Two hundred and seventeen captive great apes (150 chimpanzees, Pan troglodytes; 14 bonobos, Pan paniscus; 53 western gorillas, Gorilla gorilla) and 20 personnel from thirteen European zoos and two African sanctuaries were sampled and examined in order to determine the occurrence of Enterocytozoon bieneusi and species of Encephalitozoon in faecal specimens and to compare the epidemiological situation between zoos and sanctuaries. Microsporidia were detected at all sampling sites. Sequence analyses of ITS amplicons generated by using microsporidia-specific primers determined the presence of microsporidia in 87 samples including 13 humans; since two cases of simultaneous occurrence of Encephalitozoon cuniculi and Enterocytozoon bieneusi were identified, 89 full-length ITS sequences were obtained, namely 78 Encephalitozoon cuniculi genotype I, five E. cuniculi genotype II, two E. hellem 1A and four Enterocytozoon bieneusi. No Encephalitozoon intestinalis-positive samples were identified. This is the first report of Encephalitozoon species and Enterocytozoon bieneusi genotypes in captive great apes kept under various conditions and the first record of natural infection with E. hellem in great apes. A comparison of zoos and sanctuaries showed a significantly higher prevalence of microsporidia in sanctuaries (P<0.001), raising a question about the factors affecting the occurrence of microsporidia in epidemiologically and sanitarily comparable types of facilities.
Předkládaný článek přináší stručný průřez problematiky studia taxonomie štírů rodu Euscorpius. Evropským štírům byla věnována pozornost již od poloviny 18. století. Po bezmála 250 letech zkoumání se tento rod stále nedočkal vyřešení otázky své komplikované taxonomie. Zdá se ovšem, že současné studie kombinující morfologické, genetické a cytogenetické znaky mohou být klíčem pro odhalení skutečné druhové diverzity., This article briefly summarizes the last two and a half centuries of taxonomic research into the European genus of scorpions commonly known as small wood scorpions (Euscorpius). Despite the fact that taxonomists have been focusing on this genus since the mid-18th century, their taxonomy is not yet sufficiently resolved. However, present studies seem to be on the right track, and looking into a combination of morphological, genetic and cytogenetic features may hold the key to revealing the true diversity of the species., and Jana Plíšková.
We study solvability of equations of the form $x^n=g$ in the groups of order automorphisms of archimedean-complete totally ordered groups of rank 2. We determine exactly which automorphisms of the unique abelian such group have square roots, and we describe all automorphisms of the general ones.
In some economic or social division problems, we may encounter uncertainty of claims, that is, a certain amount of estate has to be divided among some claimants who have individual claims on the estate, and the corresponding claim of each claimant can vary within a closed interval or fuzzy interval. In this paper, we classify the division problems under uncertainty of claims into three subclasses and present several division schemes from the perspective of axiomatizations, which are consistent with the classical bankruptcy rules in particular cases. When claims of claimants have fuzzy interval uncertainty, we settle such type of division problems by turning them into division problems under interval uncertainty.