A basic problem that confronts the standard cosmological models is the problem of Initial Singularity characterised by infinite material density, infinite temperature and infinite spacetime curvature. The inevitable existence of such a phase of the universe may be considered to be one of the major drawbacks of Einstein’s field equations. To some extent inflation models ameliorate this. In the p...

Bayesian inference is a vital tool for consistent manipulation of the uncertainty that is present in many military scenarios. However, in some highly complex environments, it is hard to write down an analytic form for the likelihood function that underlies Bayesian inference. Approximate Bayesian computation (ABC) algorithms address this difficulty by enabling one to proceed without analyticall...

By applying Mawhin’s continuation theorem of coincidence degree theory and some skills of inequalities, sufficient conditions are obtained for the existence of at least four positive almost periodic solutions to two species parasitical system with impulsive effects and harvesting terms. Key–Words: Almost periodic solutions; Parasitical system; Coincidence degree; Harvesting term; Time delay; Im...

We study the sedimentation of two identical but nonspherical particles sedimenting in a Stokesian fluid. Experiments and numerical simulations reveal periodic orbits wherein the bodies mutually induce an in-phase rotational motion accompanied by periodic modulations of sedimentation speed and separation distance. We term these "tumbling orbits" and find that they appear over a broad range of bo...

In this short note we consider wave equations with a periodic in time dissipation and discuss the effect of parametric resonance in the framework of energy estimates. The approach is based on a treatment for a generalized Mathieu equation related to the periodic dissipation term.

Variational theories of double-porosity models can be derived by homogenization of high-contrast periodic media (see [12]). Typically, we have one or more strong phases (i.e., uniformly elliptic energies on periodic connected domains) and a weak phase with a small ellipticity constant, coupled with some lower-order term. In the simplest case of quadratic energies, this amounts to considering en...

With the help of the coincidence degree and the related continuation theorem, we explore the existence of at least two periodic solutions of a delayed ratio-dependent predator-prey system with exploited term. Some easily verifiable sufficient criteria are established for the existence of at least two positive periodic solutions.

By using Mawhin’s continuation theorem of coincidence degree theory, we establish the existence of 2 positive periodic solutions for n species non-autonomous Lotka-Volterra competition systems with harvesting terms. An example is given to illustrate the effectiveness of our results. Keywords—Positive periodic solutions; Lotka-Volterra competition system; Coincidence degree; Harvesting term.

Nutrition influences sleep. Drinking a glass of warm milk in the evening has been a long term tradition in several cultures. Although most of these reports are anecdotal, several milk components have been associated with sleep, such as tryptophan, bioactive peptides and magnesium. The widest researched dairy component in relation to sleep is tryptophan. Tryptophan is the precursor of serotonin....