## Abstract

In this paper we study *ϕ*-recurrence *τ* -curvature tensor in (*k, µ*)-contact metric manifolds.

In this paper we study *ϕ*-recurrence *τ* -curvature tensor in (*k, µ*)-contact metric manifolds.

In this paper we derive a sequence from a movement of center of mass of arbitrary two planets in some solar system, where the planets circle on concentric circles in a same plane. A trajectory of center of mass of the planets is discussed. A sequence of points on the trajectory is chosen. Distances of the points to the origin are calculated and a distribution function of a sequence of the distances is found.

We consider and solve extremal problems in various bounded weakly pseudoconvex domains in ℂ* ^{n}* based on recent results on boundedness of Bergman projection with positive Bergman kernel in Bergman spaces

We prove that a closed convex hypersurface of the Euclidean space with almost constant anisotropic first and second mean curvatures in the *L ^{p}*-sense is

In this paper, the standard almost complex structure on the tangent bunle of a Riemannian manifold will be generalized. We will generalize the standard one to the new ones such that the induced (0, 2)-tensor on the tangent bundle using these structures and Liouville 1-form will be a Riemannian metric. Moreover, under the integrability condition, the curvature operator of the base manifold will be classified.

In this paper, we introduce the Mus-Sasaki metric on the tangent bundle *T M* as a new natural metric non-rigid on *T M*. First we investigate the geometry of the Mus-Sasakian metrics and we characterize the sectional curvature and the scalar curvature.

The *q*-derivative operator approach is illustrated by reviewing several typical summation formulae of terminating basic hypergeometric series.

We provide a two good model of oligopolistic production and trade with one good being commodity money. There is the usual demand function of the consumers for the produced good that producer-sellers face. Each seller is a budget constrained preference maximizer and derives utility (or satisfaction) from consuming bundles comprising commodity money and the produced good. We define a competitive equilibrium strategy profile and a Cournotian equilibrium and show that under our assumptions both exist. We further show that at a competitive equilibrium strategy profile, each seller maximizes profits given his own consumption of the produced good and the price of the produced good, the latter being determined by the inverse demand function. Similarly we show that at a Cournotian the sellers are at a Cournot equilibrium given their own consumption of the produced good. Assuming sufficient differentiability of the cost functions we show that at a competitive equilibrium each seller either sets price equal to marginal cost or exhausts his capacity of production; at a Cournotian equilibrium each seller either sets marginal revenue equal to marginal cost or exhausts his capacity of production. We also study the evolution of Cournotian strategies as the sellers and buyers are replicated. As the number of buyers and sellers go to infinity any sequence of interior symmetric Cournotian equilibrium strategies admits a convergent subsequence, which converges to an interior symmetric competitive equilibrium strategy. In a final section we discuss the Bertrand Edgeworth price setting game and show that a Bertrand Edgeworth equilibrium must be a derived from a competitive equilibrium price. Here we show that if at a symmetric competitive equilibrium, the sellers consume positive quantities of the produced good then the competitive equilibrium cannot be a Bertrand Edgeworth equilibrium. Thus, if at all symmetric competitive equilibria the sellers consume positive amounts of the produced good, then a Bertrand Edgeworth equilibrium simply does not exist.

There are numerous attempts to estimate hiking time since the age of the ancient Roman Empire, the new digital era calls for more precise and exact solutions to be implemented in mobile applications. The importance of the topic lies in the fact that route planning algorithms and shortest path problems apply time estimations as cost functions. Our intention is to design a hiking time estimation method that accounts for terrain circumstances as well as personal factors, while the level of accuracy and the simplicity of the algorithm should enable the solution to be utilised in the practice. We refine Tobler’s earlier results to estimate a relation between terrain steepness and hiker’s velocity. Later we use fitted curve to design our novel, personalised hiking time estimation method.

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.