Sums and differences of four k-th powers

We prove an upper bound for the number of representations of a positive integer $N$ as the sum of four $k$-th powers of integers of size at most $B$, using a new version of the Determinant method developed by Heath-Brown, along with recent results by Salberger on the density of integral points on affine surfaces. More generally we consider representations by any integral diagonal form. The upper bound has the form $O_{N}(B^{c/\sqrt{k}})$, whereas earlier versions of the Determinant method would produce an exponent for $B$ of order $k^{-1/3}$ in this case. Furthermore, we prove that the number of representations of a positive integer $N$ as a sum of four $k$-th powers of non-negative integers is at most $O_{\epsilon}(N^{1/k+2/k^{3/2}+\epsilon})$ for $k \geq 3$, improving upon bounds by Wisdom.Comment: 18 pages. Mistake corrected in the statement of Theorem 1.2. To appear in Monatsh. Mat

The Xp10 bacteriophage protein P7 inhibits transcription by the major and major variant forms of the host RNA polymerase via a common mechanism

The σ factor is a functionally obligatory subunit of the bacterial transcription machinery, the RNA polymerase. Bacteriophage-encoded small proteins that either modulate or inhibit the bacterial RNAP to allow the temporal regulation of bacteriophage gene expression often target the activity of the major bacterial σ factor, σ70. Previously, we showed that during Xanthomonas oryzae phage Xp10 infection, the phage protein P7 inhibits the host RNAP by preventing the productive engagement with the promoter and simultaneously displaces the σ70 factor from the RNAP. In this study, we demonstrate that P7 also inhibits the productive engagement of the bacterial RNAP containing the major variant bacterial σ factor, σ54, with its cognate promoter. The results suggest for the first time that the major variant form of the host RNAP can also be targeted by bacteriophage-encoded transcription regulatory proteins. Since the major and major variant σ factor interacting surfaces in the RNAP substantially overlap, but different regions of σ70 and σ54 are used for binding to the RNAP, our results further underscore the importance of the σ–RNAP interface in bacterial RNAP function and regulation and potentially for intervention by antibacterials

Movement of Coconut Crabs, Birgus latro, in a Rainforest Habitat in Vanuatu

Patterns of movement in the coconut crab, Birgus latro (L.), were studied using mark-recapture and radio-tracking techniques at a number of sites in the rainforest regions of eastern Santo, Republic of Vanuatu (South Pacific). Movement was assessed both for crabs caught and released in one place (indigenous) and for crabs caught and then released at a new location (introduced). Recapture rates in eastern Santo were very small ( < I%), whereas on the small islet sites (area <2 ha) the rate approached 20%. There were no significant relationships between distance moved and either time at liberty or size of the individuals for introduced crabs. But for indigenous crabs, size of individual was negatively correlated with distance moved. Recapture rates of introduced and indigenous crabs were similar , but introduced crabs moved significantly further from their point of release. Almost all radio-tagged crabs moved from their point of release; smaller crabs tended to move further. On eastern Santo, only two of five radio-tagged crabs were located again ; both had moved over 250-m away from their release point. On the islet sites, all radiotagged crabs were found again at least once; some of these returned to a number of different sites, indicating that B. latro seems to be able to home to particular locations. Nonetheless, dispersal of animals from an area, at least after handling, is a common feature

Investigation of the Effect of Biodiesel Blends on Fuel Injection Pumps based on Vibration and Pressure Measurements

Amongst alternative fuels for diesel-engine application, biodiesel is very attractive because it is biodegradable, an environmentally-friendly and sustainable source that can meet future energy demands. However, there are few published studies of the impact of biodiesel fuel and its blends on fuel injection pumps (FIPs). This study will investigate the influence of biodiesels derived from waste cooking oils with incremental blends of B10, B20, B30, B40 and B100. The FIP in this study is a rotary type attached to a four-cylinder, four-stroke direct injection, turbocharged diesel engine. Vibration and pressure measurements were made on the FIP. The results show the peak pressure close to the pump increases slightly the higher the proportion of biodiesel because of increased viscosity, density and bulk modulus of the fuel. Low frequency vibration increased as the proportion of biodiesel increased. These results demonstrate an increase in dynamic load on the pump components. However, high frequency vibration levels are lowest for the blends B10, B20 and B30, which may be helpful for improving the service life of the delivery

A Study on the Parallelization of Terrain-Covering Ant Robots Simulations

Agent-based simulation is used as a tool for supporting (time-critical) decision making in differentiated contexts. Hence, techniques for speeding up the execution of agent-based models, such as Parallel Discrete Event Simulation (PDES), are of great relevance/benefit. On the other hand, parallelism entails that the final output provided by the simulator should closely match the one provided by a traditional sequential run. This is not obvious given that, for performance and efficiency reasons, parallel simulation engines do not allow the evaluation of global predicates on the simulation model evolution with arbitrary time-granularity along the simulation time-Axis. In this article we present a study on the effects of parallelization of agent-based simulations, focusing on complementary aspects such as performance and reliability of the provided simulation output. We target Terrain Covering Ant Robots (TCAR) simulations, which are useful in rescue scenarios to determine how many agents (i.e., robots) should be used to completely explore a certain terrain for possible victims within a given time. © 2014 Springer-Verlag Berlin Heidelberg

Glycerol valorization: dehydration to acrolein over silica-supported niobia catalysts

The catalytic dehydration of glycerol to acrolein is investigated over silica-supported niobia catalysts in a continuous fixed-bed gas-phase reactor. Various supported niobia catalysts are prepared and characterized using surface analysis and spectroscopic methods (XRD, UV–Vis, XPS, N2 adsorption), as well as with ammonia adsorption microcalorimetry. Good results are obtained with initial glycerol conversions of over 70% and with 50–70% selectivity to acrolein. We investigate the influence of changing the catalyst acid strength by varying the niobia content and catalyst calcination temperature. Glycerol conversion and acrolein selectivity depend on the surface acid strength. Catalyst deactivation by coking is also observed, but simple oxidative treatment in air restores the activity of the catalysts completely

On some problems involving Hardy's function

Some problems involving the classical Hardy function $$Z(t) := \zeta(1/2+it)\bigl(\chi(1/2+it)\bigr)^{-1/2}, \quad \zeta(s) = \chi(s)\zeta(1-s)$$ are discussed. In particular we discuss the odd moments of $Z(t)$, the distribution of its positive and negative values and the primitive of $Z(t)$. Some analogous problems for the mean square of $|\zeta(1/2+it)|$ are also discussed.Comment: 15 page