Cross sections for geodesic flows and \alpha-continued fractions

We adjust Arnoux's coding, in terms of regular continued fractions, of the geodesic flow on the modular surface to give a cross section on which the return map is a double cover of the natural extension for the \alpha-continued fractions, for each $\alpha$ in (0,1]. The argument is sufficiently robust to apply to the Rosen continued fractions and their recently introduced \alpha-variants.Comment: 20 pages, 2 figure

Natural extensions and entropy of α\alpha-continued fractions

We construct a natural extension for each of Nakada's $\alpha$-continued fractions and show the continuity as a function of $\alpha$ of both the entropy and the measure of the natural extension domain with respect to the density function $(1+xy)^{-2}$. In particular, we show that, for all $0 < \alpha \le 1$, the product of the entropy with the measure of the domain equals $\pi^2/6$. As a key step, we give the explicit relationship between the $\alpha$-expansion of $\alpha-1$ and of $\alpha$

Lieb-Thirring inequalities for Schr\"odinger operators with complex-valued potentials

Inequalities are derived for power sums of the real part and the modulus of the eigenvalues of a Schr\"odinger operator with a complex-valued potential.Comment: 9 pages; typos correcte

The effective bandwidth problem revisited

The paper studies a single-server queueing system with autonomous service and $\ell$ priority classes. Arrival and departure processes are governed by marked point processes. There are $\ell$ buffers corresponding to priority classes, and upon arrival a unit of the $k$th priority class occupies a place in the $k$th buffer. Let $N^{(k)}$, $k=1,2,...,\ell$ denote the quota for the total $k$th buffer content. The values $N^{(k)}$ are assumed to be large, and queueing systems both with finite and infinite buffers are studied. In the case of a system with finite buffers, the values $N^{(k)}$ characterize buffer capacities. The paper discusses a circle of problems related to optimization of performance measures associated with overflowing the quota of buffer contents in particular buffers models. Our approach to this problem is new, and the presentation of our results is simple and clear for real applications.Comment: 29 pages, 11pt, Final version, that will be published as is in Stochastic Model

The Lyapunov exponent in the Sinai billiard in the small scatterer limit

We show that Lyapunov exponent for the Sinai billiard is $\lambda = -2\log(R)+C+O(R\log^2 R)$ with $C=1-4\log 2+27/(2\pi^2)\cdot \zeta(3)$ where $R$ is the radius of the circular scatterer. We consider the disk-to-disk-map of the standard configuration where the disks is centered inside a unit square.Comment: 15 pages LaTeX, 3 (useful) figures available from the autho

Age-related changes in the energy of human mesenchymal stem cells

Aging is a physiological process that leads to a higher risk for the most devastating diseases. There are a number of theories of human aging proposed, and many of them are directly or indirectly linked to mitochondria. Here, we used mesenchymal stem cells (MSCs) from young and older donors to study age-related changes in mitochondrial metabolism. We have found that aging in MSCs is associated with a decrease in mitochondrial membrane potential and lower NADH levels in mitochondria. Mitochondrial DNA content is higher in aged MSCs, but the overall mitochondrial mass is decreased due to increased rates of mitophagy. Despite the higher level of ATP in aged cells, a higher rate of ATP consumption renders them more vulnerable to energy deprivation compared to younger cells. Changes in mitochondrial metabolism in aged MSCs activate the overproduction of reactive oxygen species in mitochondria which is compensated by a higher level of the endogenous antioxidant glutathione. Thus, energy metabolism and redox state are the drivers for the aging of MSCs/mesenchymal stromal cells

Design of Supply Chain Strategy as a Tool for the Development of the Country's Economy

Abstract- Modern society has entered the stage of its development when the objective world around us, created by supply chai nstrategies, is experiencing a period of rapid growth. More and more complex are filling market niches. The requirements for consumer properties of products are becoming ever higher. Today it is already obvious that only collective creativity can ensure high competitiveness of products. Today, design is a strategic tool, the correct use of which leads to success in business. The relevance of the study is caused by a very low level of research on the development aspect of the country's economy – supply chain design

Multi-level Dynamical Systems: Connecting the Ruelle Response Theory and the Mori-Zwanzig Approach

In this paper we consider the problem of deriving approximate autonomous dynamics for a number of variables of a dynamical system, which are weakly coupled to the remaining variables. In a previous paper we have used the Ruelle response theory on such a weakly coupled system to construct a surrogate dynamics, such that the expectation value of any observable agrees, up to second order in the coupling strength, to its expectation evaluated on the full dynamics. We show here that such surrogate dynamics agree up to second order to an expansion of the Mori-Zwanzig projected dynamics. This implies that the parametrizations of unresolved processes suited for prediction and for the representation of long term statistical properties are closely related, if one takes into account, in addition to the widely adopted stochastic forcing, the often neglected memory effects.Comment: 14 pages, 1 figur

On the construction of generalized Grassmann representatives of state vectors

Generalized $Z_k$-graded Grassmann variables are used to label coherent states related to the nilpotent representation of the q-oscillator of Biedenharn and Macfarlane when the deformation parameter is a root of unity. These states are then used to construct generalized Grassmann representatives of state vectors.Comment: 8 page