Apollonian gaskets are formed by repeatedly filling the gaps between three mutually tangent circles with further tangent circles. In this paper we give explicit formulas for the the limiting pair correlation and the limiting nearest neighbor spacing of centers of circles from a fixed Apollonian gasket. These are corollaries of the convergence of moments that we prove. The input from ergodic the...

life style and life expectancy of inhabitants have been affected by the increase of particulate matter 10 micrometers or less in diameter (pm10) in cities and this is why maximum pm10 concentrations have received extensive attention. an early notice system for pm10 concentrations necessitates an accurate forecasting of the pollutant. in the current study an artificial neural network was used t...

On the hyperbolic space, we give spectrum of Laplacian acting on trace free symmetric tensors fields any rank.

In the present investigation, the magnetohydrodynamic Falkner-Skan flow of tangent hyperbolic nanofluids over a stretching/shrinking wedge with variable suction, internal heat generation/absorption and chemical reaction with activation energy have been scrutinized. Nanofluid model is composed of “Brownian motion’’ and “Thermophoresis’’. Transformed non-dimensional coupled non-linear equations a...

In the paper, authors find series expansions and identities for positive integer powers of inverse (hyperbolic) sine tangent, composite incomplete gamma function with hyperbolic sine, in terms first kind Stirling numbers, apply a newly established expansion to derive closed-form formula specific partial Bell polynomials representation generalized logsine function, deduce combinatorial involving...

We introduce index systems, a tool for studying isolated invariant sets of dynamical systems that are not necessarily hyperbolic. The mapping of the index systems mimics the expansion and contraction of hyperbolic maps on the tangent space, and they may be used like Markov partitions to generate symbolic dynamics. Every continuous dynamical system satisfying a weak form of expansiveness possess...

In this paper we prove the persistence of hyperbolic invariant tori in generalized Hamiltonian systems, which may admit a distinct number of action and angle variables. The systems under consideration can be odd dimensional in tangent direction. Our results generalize the well-known results of Graff and Zehnder in standard Hamiltonians. In our case the unperturbed Hamiltonian systems may be deg...

We prove that there are only finitely many closed hyperbolic 3-manifolds with injectivity radius and first eigenvalue of the Laplacian bounded below whose fundamental groups can be generated by a given number of elements.

An explicit construction of a geodesic flow-invariant distribution lying in the discrete series of weight 2k isotopic component is found, using techniques from representation theory of SL2(R). It is found that the distribution represents an AC measure on the unit tangent bundle of the hyperbolic plane minus an explicit singular set. Finally, via an averaging argument, a geodesic flow-invariant ...