Decomposable polynomials in second order linear recurrence sequences

We study elements of second order linear recurrence sequences $(G_n)_{n= 0}^{\infty}$ of polynomials in $\mathbb{C}[x]$ which are decomposable, i.e. representable as $G_n=g\circ h$ for some $g, h\in \mathbb{C}[x]$ satisfying $\operatorname{deg}g,\operatorname{deg}h>1$. Under certain assumptions, and provided that $h$ is not of particular type, we show that $\operatorname{deg}g$ may be bounded by a constant independent of $n$, depending only on the sequence.Comment: 26 page

Explicit bounds for composite lacunary polynomials

Let f, g, h ℂ [x] be non-constant complex polynomials satisfying f(x)=g(h(x)) and let f be lacunary in the sense that it has at most l non-constant terms. Zannier proved in [9] that there exists a function B1(l) on ℕ, depending only on l and with the property that h(x) can be written as the ratio of two polynomials having each at most B1(l) terms. Here, we give explicit estimates for this function or, more precisely, we prove that one may take for instance B1(l)=(4l)(2l)(3l)l+1. Moreover, in the case l=2, a better bound is obtained using the same strategy

Nurse’s Experience As Educator in Hemodialysis Care to End Stage Renal Disease Patient in Hospital X: a Phenomenology Study

End Stage Renal Disease (ESRD) is progressive and irreversible damage to kidney function,which can reduce the quality of life of patients and death due to accumulation of uremia toxins in the blood. Hemodialysis is a temporary therapy used to prolong the life of the patient. The uncertainty of the treatment provides a unique response which became an interesting phenomenon for researchers to conduct research Sethe qualitative strategy for explore the nurses’ experience and to describe it especially in the nurses’ role as educator in hemodialysis care to ESRD patient in Hospital X.Aim of this study to provide an overview of nurse’s experience as educator in ESRD patients during hemodialysis therapy in the Hemodialysis Unit Hospital X. this research used a qualitative method with a phenomenological approach has been conducted. The data collection technique used was using in-depth interviews. A purposive sampling was used to recruited the participant and, namely ten nurses were involded in this study with inclusion critearia as follows: (1) work as an executive nurse in HD unit, (2) have minimum Diploma III as basic education level. Data analysis using Colaizzi’s method and then using thematic analysis. Four themes were found in this study: lifestyle changes, uncooperative patients, responsive patients, and patients do not want to stop dialysis. Future research can be conduct in fourth theme concerning withdrawal dialysis in ESRD patients in various perspectives including: ethical perspective and decision making for futile treatment, health coverage policies, and palliative care

Hyperelliptic Continued Fractions and Generalized Jacobians:

These are notes from the minicourse given by Umberto Zannier (Scuola Normale Superiore di Pisa). The notes were worked out by Laura Capuano, Peter Jossen,1 Christina Karolus, and Francesco Veneziano. Most of the material of these lectures, except for the numerical examples which were added by us, is already available in [42]. The authors wish to thank Umberto Zannier for the lively discussions in Alpbach, and Olaf Merkert for providing computations of the examples 3.17, 3.28, 3.29, 3.33, and 3.2

Nurse's Experience as Educator in Hemodialysis Care to End Stage Renal Disease Patient in Hospital X: A Phenomenology Study

End Stage Renal Disease (ESRD) is progressive and irreversible damage to kidney function,which can reduce the quality of life of patients and death due to accumulation of uremia toxins in the blood. Hemodialysis is a temporary therapy used to prolong the life of the patient. The uncertainty of the treatment provides a unique response which became an interesting phenomenon for researchers to conduct research Sethe qualitative strategy for explore the nurses' experience and to describe it especially in the nurses' role as educator in hemodialysis care to ESRD patient in Hospital X.Aim of this study to provide an overview of nurse's experience as educator in ESRD patients during hemodialysis therapy in the Hemodialysis Unit Hospital X. this research used a qualitative method with a phenomenological approach has been conducted. The data collection technique used was using in-depth interviews. A purposive sampling was used to recruited the participant and, namely ten nurses were involded in this study with inclusion critearia as follows: (1) work as an executive nurse in HD unit, (2) have minimum Diploma III as basic education level. Data analysis using Colaizzi's method and then using thematic analysis. Four themes were found in this study: lifestyle changes, uncooperative patients, responsive patients, and patients do not want to stop dialysis. Future research can be conduct in fourth theme concerning withdrawal dialysis in ESRD patients in various perspectives including: ethical perspective and decision making for futile treatment, health coverage policies, and palliative care