Some identities on derangement and degenerate derangement polynomials

In combinatorics, a derangement is a permutation that has no fixed points. The number of derangements of an n-element set is called the n-th derangement number. In this paper, as natural companions to derangement numbers and degenerate versions of the companions we introduce derangement polynomials and degenerate derangement polynomials. We give some of their properties, recurrence relations and identities for those polynomials which are related to some special numbers and polynomials.Comment: 12 page

Identifying a Window of Vulnerability during Fetal Development in a Maternal Iron Restriction Model

It is well acknowledged from observations in humans that iron deficiency during pregnancy can be associated with a number of developmental problems in the newborn and developing child. Due to the obvious limitations of human studies, the stage during gestation at which maternal iron deficiency causes an apparent impairment in the offspring remains elusive. In order to begin to understand the time window(s) during pregnancy that is/are especially susceptible to suboptimal iron levels, which may result in negative effects on the development of the fetus, we developed a rat model in which we were able to manipulate and monitor the dietary iron intake during specific stages of pregnancy and analyzed the developing fetuses. We established four different dietary-feeding protocols that were designed to render the fetuses iron deficient at different gestational stages. Based on a functional analysis that employed Auditory Brainstem Response measurements, we found that maternal iron restriction initiated prior to conception and during the first trimester were associated with profound changes in the developing fetus compared to iron restriction initiated later in pregnancy. We also showed that the presence of iron deficiency anemia, low body weight, and changes in core body temperature were not defining factors in the establishment of neural impairment in the rodent offspring

A combined multi-technique in situ approach used to probe the stability of iron molybdate catalysts during redox cycling

A setup combining a number of techniques (WAXS, XANES and UV–Vis) has been used to probe the stability of an iron molybdate catalyst during redox cycling. The catalyst was first reduced under anaerobic methanol/helium conditions, producing formaldehyde and then regenerated using air. Although in this test-case the catalyst and conditions differ from that of a commercial catalyst bed we demonstrate how such a setup can reveal new information on catalyst materials. In particular we observe the formation of two phases during reduction; one which we propose to be an oxygen deficient ‘pseudo-molybdate phase’, the other a molybdenum carbide-like phase, both produced as oxygen is removed from the catalyst. Standard in situ techniques could detect such transient phases, however, the information from multiple techniques, allows us to more accurately identify the nature of these materials and to carry out appropriate complementary ex situ measurements to aid in the analysis. This and similar setups therefore offer a way to more quickly and accurately observe reaction pathways within a catalyst, which may for example, result in the deactivation of the material by different routes to those observed previously. Additionally, the specific combination of these techniques with on-line mass spectrometry, allows us to monitor the activity of the catalyst surface and here observe that different catalytic mechanisms may occur during different stages of the redox process. Therefore this setup should allow for the observation of many novel variations in a catalyst’s reactivity, leading to the improvement of current and development of new materials