In order to explain the present accelerated expansion of the Universe, suggested by the measurements of high redshifts supernovae[2] [3], we consider that presently, at cosmological scales, classical General Relativity (GR) is not valid. Instead of changing the right hand side of Einstein’s equations by introducing some new negative pressure fluid, we modify its left hand side according to phys...

In order to explain the present accelerated expansion of the Universe, suggested by the measurements of high redshifts supernovae[2] [3], we consider that presently, at cosmological scales, classical General Relativity (GR) is not valid. Instead of changing the right hand side of Einstein’s equations by introducing some new negative pressure fluid, we modify its left hand side according to phys...

1. Write the formula for the Liouville measure Λ on the unit tangent bundle T 1 H n. Prove that Λ is invariant under the actions by Isom(H n) and the geodesic flow g t on T 1 H n. 2. Let δ be a geodesic in the hyperbolic space H n and let π : H n → δ denote the nearest point projection map. Suppose that for some x, y ∈ H n and some r > 0 we have d(x, δ), d(y, δ) ≥ r. Prove that d(π(x), π(y)) ≤ ...

We show that noncompact simply connected harmonic manifolds with volume density Θ p (r) = sinh n−1 r is isometric to the real hyperbolic space and noncompact simply connected Kähler harmonic manifold with volume density Θ p (r) = sinh 2n−1 r cosh r is isometric to the complex hyperbolic space. A similar result is also proved for Quaternionic Kähler manifolds. Using our methods we get an alterna...

Solutions, in terms of special functions, of all wave equations uxx − utt = V (x)u(t, x), characterised by eight inequivalent time independent potentials and by variables separation, have been found. The real valueness and the properties of the solutions produced by computer algebra programs are not always manifest and in this work we provide ready to use solutions. We discuss especially the po...

In this paper, we study the error behavior of nonequispaced fast Fourier transform (NFFT). This approximate algorithm is mainly based on convenient choice a compactly supported window function. Here consider continuous Kaiser--Bessel, $\exp$-type, $\sinh$-type, and $\cosh$-type functions with same support shape parameter. We present novel explicit estimates for NFFT such function derive rules o...