Minimization of the number of periodic points for smooth self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers

Let f be a smooth self-map of m-dimensional, m ≥ 4, smooth closed connected and simply-connected manifold, r a fixed natural number. For the class of maps with periodic sequence of Lefschetz numbers of iterations the authors introduced in [Graff G., Kaczkowska A., Reducing the number of periodic points in smooth homotopy class of self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers, Ann. Polon. Math. (in press)] the topological invariant J[f] which is equal to the minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of f. In this paper the invariant J[f] is computed for self-maps of 4-manifold M with dimH ₂(M; ?) ≤ 4 and estimated for other types of manifolds. We also use J[f] to compare minimization of the number of periodic points in smooth and in continuous categories.     

Modeling of timing belt construction

The frictional and profiling character of timing belt coupling with pulleys and the importance of surface state and workmanship accuracy of pulleys for the coupling quality have not been taken into account. In case of toothed cylindrical gears, operation tests have shown a huge significance of not only workmanship accuracy of pulleys, but also the technology of their working [1, 5]. Series of parameters essential for belt coupling with pulleys may be distinguished here, such as: profile of belt and pulley, surface state, barrel profile, whip and parallelism of shafts. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Variable square pulse vs conventional PFN pumping of Er:YAG laser

The influence of the flashlamp pump current pulse shape on Er:YAG laser efficiency and laser rod thermal focusing was studied theoretically and experimentally. Two pulse shapes, PFN (Pulse Forming Network) and VSP (Variable Square Pulse), were considered. Theoretical modeling and experimental measurements show that the pump pulse shape itself does not have a significant influence on the Er:YAG laser efficiency or thermal focusing. Instead, the major parameter influencing Er:YAG laser efficiency and thermal focusing was found to be the overall pulse duration. For PFN pulses, rise and fall times directly define the overall pulse duration, and therefore do have influence on thermal focusing. By contrast, VSP pulse duration is defined by the externally controlled on-time of the switching transistor. For square shaped pulses, short rise and fall times do not have a direct beneficial influence on thermal lensing.     

Normality of orbit closures for Dynkin quivers¶of type ?n

It is known that the orbit closures for the representations of the equioriented Dynkin quivers ? _n are normal and Cohen–Macaulay varieties with rational singularities. In the paper we prove the same for the Dynkin quivers ? _n with arbitrary orientation. Received: 25 October 2000 / Revised version: 28 February 2001     

Global regular and singular solutions for a model of gravitating particles

The existence of solutions of a nonlinear parabolic equation describing the gravitational interaction of particles is studied for the initial data in spaces of (generalized) pseudomeasures. This approach permits us to relax regularity assumptions on the initial conditions and to prove asymptotic stability results for the above problem.Mathematics Subject Classification (2000):35B40, 35K15, 82C21     

On an Extremal Problem for Poset Dimension

Let f(n) be the largest integer such that every poset on n elements has a 2-dimensional subposet on f(n) elements. What is the asymptotics of f(n)? It is easy to see that f(n) = n ^1/2. We improve the best known upper bound and show f(n) = O (n ^2/3). For higher dimensions, we show \(f_{d}(n)=\O \left (n^{\frac {d}{d + 1}}\right )\), where f _d (n) is the largest integer such that every poset on n elements has a d-dimensional subposet on f _d (n) elements.     

Analyzing total-factor energy efficiency in Croatian counties: evidence from a non-parametric approach

Central European Journal of Operations Research - Using energy efficiently has become top priority concern which requires an adequate policy reaction bearing in mind both energy conservation and...     

On the stationary flows of viscous,incompressible and heat-conducting fluids

We consider a boundary-value problem describing the motion of viscous, incompressible and heat-conducting fluids in a bounded domain in ?³. We admit non-homogeneous boundary conditions, the appearance of exterior forces and heat sources. Our aim is to prove the existence of a solution of the problem in Sobolev spaces.