Linearization of Hyperbolic Finite-Time Processes

We adapt the notion of processes to introduce an abstract framework for dynamics in finite time, i.e.\ on compact time sets. For linear finite-time processes a notion of hyperbolicity namely exponential monotonicity dichotomy (EMD) is introduced, thereby generalizing and unifying several existing approaches. We present a spectral theory for linear processes in a coherent way, based only on a logarithmic difference quotient, prove robustness of EMD with respect to a suitable (semi-)metric and provide exact perturbation bounds. Furthermore, we give a complete description of the local geometry around hyperbolic trajectories, including a direct and intrinsic proof of finite-time analogues of the local (un)stable manifold theorem and theorem of linearized asymptotic stability. As an application, we discuss our results for ordinary differential equations on a compact time-interval.Comment: 32 page

A note on the implicit function theorem for quasi-linear eigenvalue problems

We consider the quasi-linear eigenvalue problem $-\Delta_p u = \lambda g(u)$ subject to Dirichlet boundary conditions on a bounded open set $\Omega$, where $g$ is a locally Lipschitz continuous functions. Imposing no further conditions on $\Omega$ or $g$ we show that for small $\lambda$ the problem has a bounded solution which is unique in the class of all small solutions. Moreover, this curve of solutions depends continuously on $\lambda$.Comment: 7 page

Stability of Chiral States, Role of Intermolecular Interactions and Molecular Parity Violation

We study the problem of stability of chiral states, also known as problem of chirality, within the framework of a two-dimensional approximation of a symmetric double-well potential. We show how the symmetry breaking of the potential due to the molecular parity violation can stop the tunneling in a coherent way, accordingly stabilize the chiral states. Then, we use the quantum Brownian motion within a linear Lindblad-type equation to model how the intermolecular interactions make the tunneling incoherent, thus inducing a racemization by dephasing. Finally, we investigate the normal physical conditions where the dephasing racemization does not suppress the effects of the molecular parity violation, accordingly the molecular parity violation may be observed experimentally.Comment: 5 pages, 2 Figure

On the structure of the set of bifurcation points of periodic solutions for multiparameter Hamiltonian systems

This paper deals with periodic solutions of the Hamilton equation with many parameters. Theorems on global bifurcation of solutions with periods $2\pi/j,$ $j\in\mathbb{N},$ from a stationary point are proved. The Hessian matrix of the Hamiltonian at the stationary point can be singular. However, it is assumed that the local topological degree of the gradient of the Hamiltonian at the stationary point is nonzero. It is shown that (global) bifurcation points of solutions with given periods can be identified with zeros of appropriate continuous functions on the space of parameters. Explicit formulae for such functions are given in the case when the Hessian matrix of the Hamiltonian at the stationary point is block-diagonal. Symmetry breaking results concerning bifurcation of solutions with different minimal periods are obtained. A geometric description of the set of bifurcation points is given. Examples of constructive application of the theorems proved to analytical and numerical investigation and visualization of the set of all bifurcation points in given domain are provided. This paper is based on a part of the author's thesis [W. Radzki, ``Branching points of periodic solutions of autonomous Hamiltonian systems'' (Polish), PhD thesis, Nicolaus Copernicus University, Faculty of Mathematics and Computer Science, Toru\'{n}, 2005].Comment: 35 pages, 4 figures, PDFLaTe

An optimized, robust and reproducible protocol to generate well-differentiated primary nasal epithelial models from extremely premature infants

Extremely premature infants are prone to severe respiratory infections, and the mechanisms underlying this exceptional susceptibility are largely unknown. Nasal epithelial cells (NEC) represent the first-line of defense and adult-derived ALI cell culture models show promising results in mimicking in vivo physiology. Therefore, the aim of this study was to develop a robust and reliable protocol for generating well-differentiated cell culture models from NECs of extremely premature infants. Nasal brushing was performed in 13 extremely premature infants at term corrected age and in 11 healthy adult controls to obtain NECs for differentiation at air-liquid interface (ALI). Differentiation was verified using imaging and functional analysis. Successful isolation and differentiation was achieved for 5 (38.5%) preterm and 5 (45.5%) adult samples. Preterm and adult ALI-cultures both showed well-differentiated morphology and ciliary function, however, preterm cultures required significantly longer cultivation times for acquiring full differentiation (44 +/- 3.92 vs. 23 +/- 1.83 days; p <0.0001). Moreover, we observed that recent respiratory support may impair successful NECs isolation. Herewithin, we describe a safe, reliable and reproducible method to generate well-differentiated ALI-models from NECs of extremely premature infants. These models provide a valuable foundation for further studies regarding immunological and inflammatory responses and respiratory disorders in extremely premature infants.Peer reviewe

Can Vitex Agnus Castus be Used for the Treatment of Mastalgia? What is the Current Evidence?

There have been many treatments suggested for the management of mastalgia; one of these is the fruit extract of Vitex Agnus castus L. commonly known as Agnus castus, an extract of a deciduous shrub native to Mediterranean Europe and Central Asia. It is postulated that A. castus suppresses the stress-induced latent hyperprolactinemia which is a release of supra-physiological levels of prolactin in some patients in response to stressful stimuli. It is postulated that A. castus could be effective in the treatment of cyclical mastalgia by inhibiting the release of excess prolactin by blocking Dopamine-2 receptor type on pituitary. The adverse events following A. castus treatment are mild and reversible. The aim of this review is assess the efficacy of A. castus in the treatment of mastalgia. Data from randomized and non-randomized studies regarding the efficacy and safety of A. castus is reviewed in a systematic fashion. It is concluded that A. castus can be considered as an efficient alternative phytotherapeutic agent in the treatment of mastalgia

The Effects of Social Presence on Adherence-Focused Guidance in Problematic Cannabis Users: Protocol for the CANreduce 2.0 Randomized Controlled Trial

Background: In European countries, including Switzerland, cannabis is the most commonly used illicit drug. Offering a Web-based self-help tool could potentially reach users who otherwise would not seek traditional help. However, such Web-based self-help tools often suffer from low adherence. Objective: Through adherence-focused guidance enhancements, the aim of this study was to increase adherence in cannabis users entering a Web-based self-help tool to reduce their cannabis use and, in this way, augment its effectiveness. Methods: This paper presents the protocol for a three-arm randomized controlled trial (RCT) to compare the effectiveness of (1) an adherence-focused, guidance-enhanced, Web-based self-help intervention with social presence; (2) an adherence-focused, guidance-enhanced, Web-based self-help intervention without social presence; and (3) a treatment-as-usual at reducing cannabis use in problematic users. The two active interventions, each spanning 6 weeks, consist of modules designed to reduce cannabis use and attenuate common mental disorder (CMD) symptoms, including depression, anxiety, and stress-related disorder symptoms based on the approaches of motivational interviewing and cognitive behavioral therapy. With a target sample size of 528, data will be collected at baseline, 6 weeks, and 3 months after baseline. The primary outcome measurement will be the number of days of cannabis use on the preceding 7 days. Secondary outcomes will include the quantity of cannabis used in standardized cannabis joints, the severity of cannabis dependence, changes in CMD symptoms, and adherence to the program. Data analysis will follow the intention-to-treat principle and employ (generalized) linear mixed models. Results: The project commenced in August 2016; recruitment is anticipated to end by December 2018. First results are expected to be submitted for publication in summer 2019. Conclusions: This study will provide detailed insights on if and how the effectiveness of a Web-based self-help intervention aiming to reduce cannabis use in frequent cannabis users can be improved by theory-driven, adherence-focused guidance enhancement

The Effects of Social Presence on Adherence-Focused Guidance in Problematic Cannabis Users: Protocol for the CANreduce 2.0 Randomized Controlled Trial

Background: In European countries, including Switzerland, cannabis is the most commonly used illicit drug. Offering a Web-based self-help tool could potentially reach users who otherwise would not seek traditional help. However, such Web-based self-help tools often suffer from low adherence. Objective: Through adherence-focused guidance enhancements, the aim of this study was to increase adherence in cannabis users entering a Web-based self-help tool to reduce their cannabis use and, in this way, augment its effectiveness. Methods: This paper presents the protocol for a three-arm randomized controlled trial (RCT) to compare the effectiveness of (1) an adherence-focused, guidance-enhanced, Web-based self-help intervention with social presence; (2) an adherence-focused, guidance-enhanced, Web-based self-help intervention without social presence; and (3) a treatment-as-usual at reducing cannabis use in problematic users. The two active interventions, each spanning 6 weeks, consist of modules designed to reduce cannabis use and attenuate common mental disorder (CMD) symptoms, including depression, anxiety, and stress-related disorder symptoms based on the approaches of motivational interviewing and cognitive behavioral therapy. With a target sample size of 528, data will be collected at baseline, 6 weeks, and 3 months after baseline. The primary outcome measurement will be the number of days of cannabis use on the preceding 7 days. Secondary outcomes will include the quantity of cannabis used in standardized cannabis joints, the severity of cannabis dependence, changes in CMD symptoms, and adherence to the program. Data analysis will follow the intention-to-treat principle and employ (generalized) linear mixed models. Results: The project commenced in August 2016; recruitment is anticipated to end by December 2018. First results are expected to be submitted for publication in summer 2019. Conclusions: This study will provide detailed insights on if and how the effectiveness of a Web-based self-help intervention aiming to reduce cannabis use in frequent cannabis users can be improved by theory-driven, adherence-focused guidance enhancement

Existence, uniqueness, and nondegeneracy of positive solutions of semilinear elliptic equations

We study positive solutions of the Dirichlet problem: Δ u ( x )+ f ( u ( x ))=0, x ∈ D n , u ( x )=0, x ∈∂ D n , where D n is an n -ball. We find necessary and sufficient conditions for solutions to be nondegenerate. We also give some new existence and uniqueness theorems.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46528/1/220_2005_Article_BF01468138.pd