Congruence Relations Mod 2 For (2 x 4^t + 1)-Colored Partitions

Let p_r(n) denote the difference between the number of r-colored partitions of n into an even number of distinct parts and into an odd number of distinct parts. Inspired by proofs involving modular forms of the Hirschhorn-Sellers Conjecture, we prove a similar congruence for p_r(n). Using the Jacobi Triple Product identity, we discover a much stricter congruence for p_3(n)

neuropeptidergic acral dysesthesia

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Urease Activity in a Kentucky Bluegrass Turf

The components of a turfgrass ecosystem, including plants, an intervening layer of thatch and the underlying soil, influence the fate of topically applied urea fertilizer. The loss of urea N by ammonia volatilization may be governed by the rate of urea hydrolysis. The main objective of this study was to determine the extent of urease activity associated with turfgrass plant tissue, thatch, and the underlying soil. This information may help elucidate the mechanism of ammonia loss following urea application. Because a turfgrass stand frequently possesses an extensive thatch layer that may serve as the primary plant growth medium, additional objectives included: i) determining the effects of air drying and seasonal variation on the activity of urease in thatch; ii) determining the variability in thatch urease activity by analyzing multiple field samples; and iii) determining the variation of urease activity within a thatch profile. Turfgrass clippings, thatch, and underlying Flanagan silt loam soil (Aquic Argiudoll) samples were taken from a field-grown Kentucky bluegrass (Poa pratensis L.) turf in either September 1980 or March 1981. On a dry weight basis, urease activity was 18 to 30 times higher from turfgrass clippings and thatch than from soil. Air drying thatch increased urease activity by 20 % over moist samples while air drying soil samples had no apparent effect. Greenhouse incubation of winter-dormant thatch samples increased urease activity 40 %, presumably in response to the duration of increased temperature. Thatch urease activity varied between sampling sites but still remained extremely high compared to soil activity. Within each thatch sample (1 X 1 X 2 cm), urease activity was highest in the upper 1.0 cm of the profile. It was concluded that thatch urease activity was variable in nature depending upon seasonal conditions which contrasts sharply with extremely stable soil urease activities. These findings suggest that, because of the high level of urease in thatch, ammonia volatilization will occur from most urea-treated turfgrass stands, regardless of the type of underlying soil unless the urea is thoroughly washed into the soil

Real-Time Monitoring of the Yeast Intracellular State During Bioprocesses With a Toolbox of Biosensors

Industrial fermentation processes strive for high robustness to ensure optimal and consistent performance. Medium components, fermentation products, and physical perturbations may cause stress and lower performance. Cellular stress elicits a range of responses, whose extracellular manifestations have been extensively studied; whereas intracellular aspects remain poorly known due to lack of tools for real-time monitoring. Genetically encoded biosensors have emerged as promising tools and have been used to improve microbial productivity and tolerance toward industrially relevant stresses. Here, fluorescent biosensors able to sense the yeast intracellular environment (pH, ATP levels, oxidative stress, glycolytic flux, and ribosome production) were implemented into a versatile and easy-to-use toolbox. Marker-free and efficient genome integration at a conserved site on chromosome X of Saccharomyces cerevisiae strains and a commercial Saccharomyces boulardii strain was developed. Moreover, multiple biosensors were used to simultaneously monitor different intracellular parameters in a single cell. Even when combined together, the biosensors did not significantly affect key physiological parameters, such as specific growth rate and product yields. Activation and response of each biosensor and their interconnection were assessed using an advanced micro-cultivation system. Finally, the toolbox was used to screen cell behavior in a synthetic lignocellulosic hydrolysate that mimicked harsh industrial substrates, revealing differences in the oxidative stress response between laboratory (CEN.PK113-7D) and industrial (Ethanol Red) S. cerevisiae strains. In summary, the toolbox will allow both the exploration of yeast diversity and physiological responses in natural and complex industrial conditions, as well as the possibility to monitor production processes