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Massimo Angrisani, Giovanni di Nella, Cinzia di Palo and Augusto Pianese

Abstract

This paper deals with the problem of the optimal rate of return to be paid by a defined contribution pension system to its participants’ savings, namely the rate that achieves the goal of the most favorable returns on their contributions jointly with the sustainability of the pension system.

We consider defined contribution pension systems provided with a funded component, and for their study we use the “theory of the logical sustainability of pension systems” already developed in several previous works. In this paper, we focus on pension systems in a demographically stable state, whereas the productivity of the active participants and the financial rate of return on the pension system’s fund, rates that constitute the “ingredients” of the optimal rate of return on contributions, are modeled by two stochastic processes.

We show that the decisional rule defining the optimal rate of return on contributions is optimal in the sense that it is effective in terms of sustainability, and also efficient in the sense that if the system pays to its participants’ contributions a rate of return that is either higher or lower than the one provided by the rule, then the pension system becomes unsustainable or overcapitalized, respectively.

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V. A. Rukavishnikov, E. V. Matveeva and E. I. Rukavishnikova

Abstract

We study the properties of the weighted space Hk (Ω) and weighted set Wk (Ω, δ)for boundary value problem with singularity.

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Susil Kumar Jena

Abstract

In p. 219 of R.K. Guy's Unsolved Problems in Number Theory, 3rd edn., Springer, New York, 2004, we are asked to prove that the Diophantine equation xn + yn = n!zn has no integer solutions with n ∈ N+ and n > 2. But, contrary to this expectation, we show that for n = 3, this equation has in finitely many primitive integer solutions, i.e. the solutions satisfying the condition gcd(x, y, z) = 1.

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Mustafa Saltan

Abstract

In this paper, we first give several properties with respect to subgroups of self-similar groups in the sense of iterate function system (IFS). We then prove that some subgroups of p-adic numbers ℚp are strong self-similar in the sense of IFS.

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Mohammad Ashraf, Shakir Ali and Bilal Ahmad Wani

Abstract

Let ℌ be an in finite-dimensional complex Hilbert space and A be a standard operator algebra on ℌ which is closed under the adjoint operation. It is shown that every nonlinear *-Lie higher derivation D = {δn}gn∈N of A is automatically an additive higher derivation on A. Moreover, D = {δn}gn∈N is an inner *-higher derivation.

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Romi Shamoyan and Seraphim Maksakov

Abstract

The survey collects many recent advances on area Nevanlinna type classes and related spaces of analytic functions in the unit disk concern- ing zero sets and factorization representations of these classes and discusses approaches, used in proofs of these results.

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Tuomo Kuusi, Giuseppe Mingione and Yannick Sire