Multiple correlation sequences not approximable by nilsequences

We show that there is a measure-preserving system $(X,\mathscr {B}, \mu , T)$ together with functions $F_0, F_1, F_2 \in L^{\infty }(\mu )$ such that the correlation sequence $C_{F_0, F_1, F_2}(n) = \int _X F_0 \cdot T^n F_1 \cdot T^{2n} F_2 \, d\mu $ is not an approximate integral combination of $2$ -step nilsequences.

Boundary Layer Theory: New Analytical Approximations with Error and Lambert Functions for Flat Plate without/with Suction

In this work, we investigated the problem of the boundary layer suction on a flat plate with null incidence and without pressure gradient. There is an analytical resolution using the Bianchini approximate integral method. This approximation has been achieved by Lambert or Error functions for boundary layer profiles with uniform suction, even in the case without suction. Based on these new laws, we brought out analytical expressions of several boundary layer features. This gives a necessary data to suction effect modeling for boundary layer control. To recommend our theoretical results, we numerically studied the boundary layer suction on a porous flat plate equipped with trailing edge flap deflected to 40°. We showed that this flap moves the stagnation point on the upper surface, resulting to avoid the formation of the laminar bulb of separation. Good agreement was obtained between the new analytical laws, the numerical results (CFD Fluent), and the literature results.

Physical layer security in hybrid TPSR two-way half-duplex relaying networks over rayleigh fading channel: non-zero secrecy probability analysis

In this paper, we proposed and investigated the Hybrid TPSR Two-Way Half-Duplex (HD) Relaying Communication Networks Over Rayleigh Fading Channel in the presence of the Eavesdropper (E). The system model consists of two sources A and B communicate with each other with helping of intermediate Relay (R). For the system performance analysis, we analyzed and derived the exact and approximate integral-form of the system Non-zero secrecy probability (NZSP) in the case that the E uses the MRC (maximal ratio combining) technique. In addition, the effect of the main system parameters on the system performance is investigated. Finally, all the research results are convinced by the Monte Carlo Simulation. This paper can provide a novel recommendation for relaying communication network manufacture.In this paper, we proposed and investigated the Hybrid TPSR Two-Way Half-Duplex (HD) Relaying Communication Networks Over Rayleigh Fading Channel in the presence of the Eavesdropper (E). The system model consists of two sources A and B communicate with each other with helping of intermediate Relay (R). For the system performance analysis, we analyzed and derived the exact and approximate integral-form of the system Non-zero secrecy probability (NZSP) in the case that the E uses the MRC (maximal ratio combining) technique. In addition, the effect of the main system parameters on the system performance is investigated. Finally, all the research results are convinced by the Monte Carlo Simulation. This paper can provide a novel recommendation for relaying communication network manufacture.

Approximate solutions to one-phase Stefan-like problems with space-dependent latent heat

The work in this paper concerns the study of different approximations for one-dimensional one-phase Stefan-like problems with a space-dependent latent heat. It is considered two different problems, which differ from each other in their boundary condition imposed at the fixed face: Dirichlet and Robin conditions. The approximate solutions are obtained by applying the heat balance integral method (HBIM), the modified HBIM and the refined integral method (RIM). Taking advantage of the exact analytical solutions, we compare and test the accuracy of the approximate solutions. The analysis is carried out using the dimensionless generalised Stefan number (Ste) and Biot number (Bi). It is also studied the case when Bi goes to infinity in the problem with a convective condition, recovering the approximate solutions when a temperature condition is imposed at the fixed face. Some numerical simulations are provided in order to assert which of the approximate integral methods turns out to be optimal. Moreover, we pose an approximate technique based on minimising the least-squares error, obtaining also approximate solutions for the classical Stefan problem.

Numerical Methods for Transverse Vibration Analysis of Straight Euler and Timoshenko Beams

This paper presents a short review of numerical methods used for lateral vibration analysis in the case of straight Euler and Timoshenko beams. A particular integral method is described with more details. This approximate integral method is based on the use of flexibility influence functions (Green’s functions). It leads to a matrix formulation and to an eigenvalue problem for vibration analysis. The presented approach is able to estimate separately the shear effects and the rotary inertia effects and also the combined effects. Simple numerical examples are also presented for comparisons with analytical and finite elements results. The results show good agreement.

A new dynamically self-consistent version of the Besançon Galaxy model

Context. Dynamically self-consistent galactic models are necessary for analysing and interpreting star counts, stellar density distributions, and stellar kinematics in order to understand the formation and the evolution of our Galaxy. Aims. We modify and improve the dynamical self-consistency of the Besançon Galaxy model in the case of a stationary and axisymmetric gravitational potential. Methods. Each stellar orbit is modelled by determining a Stäckel approximate integral of motion. Generalised Shu distribution functions (DFs) with three integrals of motion are used to model the stellar distribution functions. Results. This new version of the Besançon model is compared with the previous axisymmetric BGM2014 version and we find that the two versions have similar densities for each stellar component. The dynamically self-consistency is improved and can be tested by recovering the forces and the potential through the Jeans equations applied to each stellar distribution function. Forces are recovered with an accuracy better than one per cent over most of the volume of the Galaxy.

The effects on neutral variability of recurrent selective sweeps and background selection

ABSTRACTLevels of variability and rates of adaptive evolution may be affected by hitchhiking, the effect of selection on evolution at linked sites. Hitchhiking can be caused either by selective sweeps or by background selection, involving the spread of new favorable alleles or the elimination of deleterious mutations, respectively. Recent analyses of population genomic data have fitted models where both these processes act simultaneously, in order to infer the parameters of selection. Here, we investigate the consequences of relaxing a key assumption of some of these studies – that the time occupied by a selective sweep is negligible compared with the neutral coalescent time. We derive a new expression for the expected level of neutral variability in the presence of recurrent selective sweeps and background selection. We also derive approximate integral expressions for the effects of recurrent selective sweeps. The accuracy of the theoretical predictions was tested against multilocus simulations, with selection, recombination and mutation parameters that are realistic for Drosophila melanogaster. In the presence of crossing over, there is approximate agreement between the theoretical and simulation results. We show that the observed relations between the rate of crossing over and the level of synonymous site diversity and rate of adaptive evolution in Drosophila are probably mainly caused by background selection, whereas selective sweeps and population size changes are needed to produce the observed distortions of the site frequency spectrum.