in this paper, an effective technique is proposed to determine thenumerical solution of nonlinear volterra-fredholm integralequations (vfies) which is based on interpolation by the hybrid ofradial basis functions (rbfs) including both inverse multiquadrics(imqs), hyperbolic secant (sechs) and strictly positive definitefunctions. zeros of the shifted legendre polynomial are used asthe collocatio...

This note is a brief summary of my talk that I gave at RIMS workshop “Complex Analysis and Topology of Discrete Groups and Hyperbolic Spaces.” See [4] for detail. If a group G has a finite K(G, 1) and does not contain any Baumslag–Solitar groups, is G hyperbolic? (See [1].) This is one of the most famous questions on hyperbolic groups. Probably, many people expect that the answer is negative, a...

In arid and semi-arid environments, groundwater plays a significant role in the ecosystem. In the last decades, groundwater levels have decreased due to the increasing demand for water, weak irrigation management and soil damage. For the effective management of groundwater, it is important to model and predict fluctuations in groundwater levels. In this study, groundwater table in Kashan plain ...

We discuss selected topics of current research interest in the theory of dynamical systems, with emphasis on dimension theory, multifractal analysis, and quantitative recurrence. The topics include the quantitative versus the qualitative behavior of Poincaré recurrence, the product structure of invariant measures and return times, the dimension of invariant sets and invariant measures, the comp...

Let Γ be a Fuchsian group of the first kind acting on the hyperbolic upper half plane H, and let M = Γ\H be the associated finite volume hyperbolic Riemann surface. If γ is parabolic, there is an associated (parabolic) Eisenstein series, which, by now, is a classical part of mathematical literature. If γ is hyperbolic, then, following ideas due to Kudla-Millson, there is a corresponding hyperbo...

‎Einstein‎, ‎M"{o}bius‎, ‎and Proper Velocity gyrogroups are relativistic gyrogroups that appear as three different realizations of the proper Lorentz group in the real Minkowski space-time $bkR^{n,1}.$ Using the gyrolanguage we study their gyroharmonic analysis‎. ‎Although there is an algebraic gyroisomorphism between the three models we show that there are some differences between them‎. ‎Our...

In a recent paper, we verifed a conjecture of Mej́ıa and Pommerenke that the extremal value for the Schwarzian derivative of a hyperbolically convex function is realized by a symmetric hyperbolic “strip” mapping. There were three major steps in the verification: first, a variational argument was given to reduce the problem to hyperbolic polygons bounded by at most two hyperbolic geodesics; secon...

In this note we show that there are algebraic families of hyperbolic, FermatWaring type hypersurfaces in P of degree 4(n − 1), for all dimensions n ≥ 2. Moreover, there are hyperbolic Fermat-Waring hypersurfaces in P of degree 4n − 2n + 1 possessing complete hyperbolic, hyperbolically embedded complements. Many examples have been given of hyperbolic hypersurfaces in P (e.g., see [ShZa] and the ...