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

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

Adaptive survey designs for sampling rare and clustered populations

Designing an efficient large-area survey is a challenge, especially in environmental science when many populations are rare and clustered. Adaptive and unequal probability sampling designs are appealing when populations are rare and clustered because survey effort can be targeted to subareas of high interest. For example, higher density subareas are usually of more interest than lower density areas. Adaptive and unequal probability sampling offer flexibility for designing a long-term survey because they can accommodate changes in survey objectives, changes in underlying environmental habitat, and changes in species-habitat models. There are many different adaptive sampling designs including adaptive cluster sampling, two-phase stratified sampling, two-stage sequential sampling, and complete allocation stratified sampling. Sample efficiency of these designs can be very high compared with simple random sampling. Large gains in efficiency can be made when survey effort is targeted to the subareas of the study site where there are clusters of individuals from the underlying population. These survey methods work by partitioning the study area in some way, into strata, or primary sample units, or in the case of adaptive cluster sampling, into networks. Survey effort is then adaptively allocated to the strata or primary unit where there is some indication of higher species counts. Having smaller, and more numerous, strata improves efficiency because it allows more effective targeting of the adaptive, second-phase survey effort

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

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

Towards a Model-Independent Low Momentum Nucleon-Nucleon Interaction

We provide evidence for a high precision model-independent low momentum nucleon-nucleon interaction. Performing a momentum-space renormalization group decimation, we find that the effective interactions constructed from various high precision nucleon-nucleon interaction models, such as the Paris, Bonn, Nijmegen, Argonne, CD Bonn and Idaho potentials, are identical. This model-independent low momentum interaction, called V_{low k}, reproduces the same phase shifts and deuteron pole as the input potential models, without ambiguous assumptions on the high momentum components, which are not constrained by low energy data and lead to model-dependent results in many-body applications. V_{low k} is energy-independent and does not necessitate the calculation of the Brueckner G matrix.Comment: 12 pages, 5 figures, minor changes and additions, to appear in Phys. Lett.

Do we know the mass of a black hole? Mass of some cosmological black hole models

Using a cosmological black hole model proposed recently, we have calculated the quasi-local mass of a collapsing structure within a cosmological setting due to different definitions put forward in the last decades to see how similar or different they are. It has been shown that the mass within the horizon follows the familiar Brown-York behavior. It increases, however, outside the horizon again after a short decrease, in contrast to the Schwarzschild case. Further away, near the void, outside the collapsed region, and where the density reaches the background minimum, all the mass definitions roughly coincide. They differ, however, substantially far from it. Generically, we are faced with three different Brown-York mass maxima: near the horizon, around the void between the overdensity region and the background, and another at cosmological distances corresponding to the cosmological horizon. While the latter two maxima are always present, the horizon mass maxima is absent before the onset of the central singularity.Comment: 11 pages, 8 figures, revised version, accepted in General Relativity and Gravitatio