Transmission electron microscope (TEM) images of mixed-layer illite/smectite (I/S) from Gulf Coast shales obtained earlier by the authors have been reexamined by comparing them with the calculated images of G. D. Guthrie and D. R. Veblen. Ordered two-layer periodicity was not detected in the 1750- and 2450-m depth samples, for which X-ray powder diffraction (XRD) showed 20% and 40% illite randomly interstratified in I/S, respectively. Two-layer periodicities that occur in images of the 5500-m depth sample were inferred to reflect ordered I/S. XRD data for the same sample imply the presence of 80% illite in RI-ordered I/S. The two-layer periodicities were observed in slightly overfocused images, consistent with the image calculations of Guthrie and Veblen, with strong dark fringes inferred to correspond to smectite interlayers. Two-layer periodicities were observed only in small domains of a few of the images, consistent with the requirement of special orientation of layers, which varies continuously over a wide range. The lack of more frequent observations of ordered periodicities in TEM images may reflect the lack of the special observation conditions and chemical heterogeneity of illite and smectite layers. Ordered mixed-layering may exist in those specimens for which XRD indicates such ordering, in contrast to the previous interpretation of the authors.

We show that for a Salem number $\beta $ of degree d, there exists a positive constant $c(d)$ where $\beta ^m$ is a Parry number for integers m of natural density $\ge c(d)$. Further, we show $c(6)>1/2$ and discuss a relation to the discretized rotation in dimension $4$.

According to a conjecture by Yang, if $f(z)f^{(k)}(z)$ is a periodic function, where $f(z)$ is a transcendental entire function and $k$ is a positive integer, then $f(z)$ is also a periodic function. We propose related questions, which can be viewed as difference or differential-difference versions of Yang’s conjecture. We consider the periodicity of a transcendental entire function $f(z)$ when differential, difference or differential-difference polynomials in $f(z)$ are periodic. For instance, we show that if $f(z)^{n}f(z+\unicode[STIX]{x1D702})$ is a periodic function with period $c$, then $f(z)$ is also a periodic function with period $(n+1)c$, where $f(z)$ is a transcendental entire function of hyper-order $\unicode[STIX]{x1D70C}_{2}(f)<1$ and $n\geq 2$ is an integer.

Periodicity in nematode egg excretion may be of evolutionary origin as it can favour dispersal of the eggs in the environment. We investigated whether egg excretion by Heterakis gallinarum shows a repeatable pattern of periodicity. The faecal egg concentration and total number of eggs excreted within 4-h intervals were significantly affected by the sampling time within 1 day, but remained unaffected by the sampling day or interaction effects. By contrast, the total number of eggs excreted within 24 h did not differ among the 4 days of the study, collectively indicating repeatable egg excretion patterns. Both host feces and parasite egg excretion increased from night to late afternoon, followed by a decrease in the evening, resulting in higher egg excretion during daytime than the dark period. Feces excretion and worm fecundity showed overlapping diurnal rhythms with similarly timed phases, suggesting the existence of synchronicity between the host feces and nematode egg excretion patterns. We conclude that egg excretion by H. gallinarum is synchronized with host feces excretion and is higher during the daytime than during the dark period. This overlaps with the maximum activity of the day-active host and allows a maximal dispersal of the eggs in the environment.

Active sun is characterized by compelling short-lived flash of solar eruption like solar flare, coronal mass ejections (CMEs), high-speed solar winds and solar energetic particles along with colossal release of energy and mass. This paper proposes a new method to evaluate solar wind parameters and geomagnetic indices based on wavelet analysis during the solar flares. The crucial role of IMF-Bz (interplanetary magnetic field) is examined for the two solar flares events. The key result obtained from our study is substantial dependence of solar flare intensity on IMF-Bz together with solar wind velocity. We also observed the duration of solar flares and their effect on ionospheric and ground based parameters.

Understanding how seasonal patterns change from year to year is important for the management of infectious disease epidemics. Here, we present a mathematical formalization of the application of complex demodulation, which has previously only been applied in an exploratory manner in the context of infectious diseases. This method extracts the changing amplitude and phase from seasonal data, allowing comparisons between the size and timing of yearly epidemics. We first validate the method using synthetic data that displays the key features of epidemic data. In particular, we analyse both annual and biennial synthetic data, and explore the effect of delayed epidemics on the extracted amplitude and phase. We then demonstrate the usefulness of complex demodulation using national notification data for influenza in Australia. This method clearly highlights the higher number of notifications and the early peak of the influenza pandemic in 2009. We also identify that epidemics that peaked later than usual generally followed larger epidemics and involved fewer overall notifications. Our analysis establishes a role for complex demodulation in the study of seasonal epidemiological events.

Insufficient weed control is a major constraint to adoption of reduced-tillage practices for organic grain production. Tillage, cover crop management, and crop planting date are factors that influence emergence periodicity and growth potential of important weed species in these systems. We assessed two hairy vetch cover crop management practices, disk-kill and roll-kill, across a range of corn planting dates from early May to late June in three experiments in Beltsville, MD. Patterns of seed dormancy, emergence, and early weed growth were determined for overseeded populations of common ragweed, giant foxtail, and smooth pigweed, three important species in the Mid-Atlantic states that represent early to late emergence. Common ragweed emergence was lowest and dormancy was highest of the three species across all planting dates. Giant foxtail emergence was higher than the other species in roll-killed hairy vetch and included a significant number of seeds that germinated before rolling operations in late June. Smooth pigweed had the highest emergence and lowest dormancy in disk-killed hairy vetch in June. Individual giant foxtail plant weight was higher in roll-killed than disk-killed hairy vetch in 2 of 3 yr, whereas that of smooth pigweed plants was higher in disk-killed than roll-killed vetch in 2 of 3 yr. Giant foxtail was the dominant species in roll-killed hairy vetch (averaged 79% of total weed biomass at corn silking), probably because of early germination and establishment before rolling operations. Smooth pigweed was the dominant species in disk-killed hairy vetch at June planting dates (averaged 77% of total weed biomass), probably because of high growth rates under warm conditions in tilled soil. This research demonstrated that cover crop management practices and the timing of planting operations can shift the dominant species of weed communities in organic farming systems and must be considered in long-term weed management planning.

Knowing when weed species are likely to emerge can aid in developing effective integrated weed management programs. When using nonresidual herbicides such as glyphosate for weed control, treatment timing is critical. This study characterized the emergence patterns of common lambsquarters, common sunflower, common waterhemp, eastern black nightshade, ivyleaf morningglory, shattercane, and woolly cupgrass in soybean, in relation to common glyphosate application timings. Approximately 90% or more of common lambsquarters, common sunflower, and common waterhemp seedlings emerged before the end of May, both in 2000 and 2001. Both ivyleaf morningglory and shattercane emerged from late April to mid-August, allowing these species to avoid glyphosate applications timed to prevent early-season weed competition. Avoidance through periodicity in emergence underscores the importance of integrating multiple tactics to ensure that difficult to manage weeds are not selected for in this management system.

Data from multiple ice and sediment cores in the North Atlantic show that Marine Oxygen Isotope Stage 3 (MIS 3) was characterized by recurring millennial-scale variations in climate, but the periodic behavior of the well-known millennial-scale variations, Heinrich events and Dansgaard–Oeschger events, is uncertain. We use oxygen isotope values from the Greenland Ice Sheet Project 2 (GISP2) and North Greenland Ice Core Project (NGRIP) ice cores and estimated sea-surface temperature derived from a Bermuda Rise marine sediment core as climate proxies to assess the periodic behavior of Heinrich events and Dansgaard–Oeschger events using Lomb–Scargle spectral decomposition and continuous time autoregressive models. We find that continuous time autoregressive models produce less variable estimates of periodicity for Heinrich events than Lomb–Scargle methods. Heinrich events during MIS 3 are periodic with an estimated periodicity of 6.29–6.49 ka in the GISP 2 ice core, 6.71–6.76 ka in the marine sediment core, and 7.89–8.23 ka in the NGRIP core. There is insufficient evidence from these data to conclude that Dansgaard–Oeschger events exhibit a single periodicity during MIS 3. We also find that the periodic behavior of millennial-scale variations depends on the observational time frame.

Let $P$ be a finitely generated cancellative abelian monoid. A $P$-graph ${\rm\Lambda}$ is a natural generalization of a $k$-graph. A pullback of ${\rm\Lambda}$ is constructed by pulling it back over a given monoid morphism to $P$, while a pushout of ${\rm\Lambda}$ is obtained by modding out its periodicity, which is deduced from a natural equivalence relation on ${\rm\Lambda}$. One of our main results in this paper shows that, for some $k$-graphs ${\rm\Lambda}$, ${\rm\Lambda}$ is isomorphic to the pullback of its pushout via a natural quotient map, and that its graph $\text{C}^{\ast }$-algebra can be embedded into the tensor product of the graph $\text{C}^{\ast }$-algebra of its pushout and $\text{C}^{\ast }(\text{Per}\,{\rm\Lambda})$. As a consequence, in this case, the cycline algebra generated by the standard generators corresponding to equivalent pairs is a maximal abelian subalgebra, and there is a faithful conditional expectation from the graph $\text{C}^{\ast }$-algebra onto it.

As an application of our papers in hermitian K-theory, in favourable cases we prove the periodicity of hermitian K-groups with a shorter period than previously obtained. We also compute the homology and cohomology with field coeffcients of infinite orthogonal and symplectic groups of specific rings of integers in a number field.

An algorithm is corrected here that was presented as Theorem 2 in [Š. Holub, RAIRO-Theor. Inf. Appl. 40 (2006) 583–591]. It is designed to calculate the maximum length of a nontrivial word with a given set of periods.