Identities on the k-ary Lyndon words related to a family of zeta functions

The main aim of this paper is to investigate and introduce relations between the numbers of k-ary Lyndon words and unified zeta-type functions which was defined by Ozden et al [15, p. 2785]. Finally, we give some identities on generating functions for the numbers of k-ary Lyndon words and some special numbers and polynomials such as the Apostol-Bernoulli numbers and polynomials, Frobenius-Euler numbers, Euler numbers and Bernoulli numbers.Comment: 9 page

Combinatorial identities associated with new families of the numbers and polynomials and their approximation values

Recently, the numbers $Y_{n}(\lambda )$ and the polynomials $Y_{n}(x,\lambda)$ have been introduced by the second author [22]. The purpose of this paper is to construct higher-order of these numbers and polynomials with their generating functions. By using these generating functions with their functional equations and derivative equations, we derive various identities and relations including two recurrence relations, Vandermonde type convolution formula, combinatorial sums, the Bernstein basis functions, and also some well known families of special numbers and their interpolation functions such as the Apostol--Bernoulli numbers, the Apostol--Euler numbers, the Stirling numbers of the first kind, and the zeta type function. Finally, by using Stirling's approximation for factorials, we investigate some approximation values of the special case of the numbers $Y_{n}\left( \lambda \right)$.Comment: 17 page

Dispositional Optimism and Well-being in Cancer Patients: The Role of CancerRelated Self-Efficacy

Optimistic attitudes of cancer patients are shown as an important personal resource for the psychological and physical adjustment to the illness. Coping styles and appraisals were suggested as indirect pathways through which optimism associates with better functioning in patients. The current study aimed to investigate the role of cancer-specific self-efficacy domains (i.e., coping with cancer-related side effects and stress, maintaining activity and independence, seeking and understanding medical information, and affect regulation and seeking social support) in the association between optimism and physical and psychological (i.e., depressive symptoms) well-being of cancer patients. A cross-sectional study was conducted with 120 patients in Ankara, Turkey. Majority of the participants were female, and about half of them were breast cancer patients. Participants filled a set of self-report questionnaires including Life Orientation Test-Revised, Cancer Behavior Inventory, Multidimensional Quality of Life Scale-Cancer, and Beck Depression Inventory. The data were analyzed separately for physical well-being and depressive symptoms through the bootstrapping method. Of the four self-efficacy domains, maintaining activity and independence accounted for a significant proportion of variance in the optimism-physical well-being and optimism-depressive symptoms relations. Findings highlight the importance of patients' beliefs in their ability to sustain their daily activities for having better physical and psychological well-being during cancer treatment as well as the role of optimism in promoting this particular self-efficacy domain. Interventions are suggested to focus on enhancing cancer patients' self-efficacy in maintaining activity and independence

Generating Functions for New Families of Combinatorial Numbers and Polynomials: Approach to Poisson–Charlier Polynomials and Probability Distribution Function

The aim of this paper is to construct generating functions for new families of combinatorial numbers and polynomials. By using these generating functions with their functional and differential equations, we not only investigate properties of these new families, but also derive many new identities, relations, derivative formulas, and combinatorial sums with the inclusion of binomials coefficients, falling factorial, the Stirling numbers, the Bell polynomials (i.e., exponential polynomials), the Poisson−Charlier polynomials, combinatorial numbers and polynomials, the Bersntein basis functions, and the probability distribution functions. Furthermore, by applying the p-adic integrals and Riemann integral, we obtain some combinatorial sums including the binomial coefficients, falling factorial, the Bernoulli numbers, the Euler numbers, the Stirling numbers, the Bell polynomials (i.e., exponential polynomials), and the Cauchy numbers (or the Bernoulli numbers of the second kind). Finally, we give some remarks and observations on our results related to some probability distributions such as the binomial distribution and the Poisson distribution

Does intravenous lidocaine added to nonsteroidal anti-inflammatory drugs reduce pain during colposcopy? A prospective randomized double-blind study

Objectives: In recent years, lidocaine infusion for pain management during long operations is becoming more widespread in anesthesiology practice. However, only a limited number of studies have reported the intravenous use of lidocaine for short-term interventions. The aim of this study was to investigate the effectiveness of intravenous lidocaine use in pain management during colposcopic cervical biopsy and endocervical curettage (ECC). Material and methods: Patients between the ages of 18 and 65 years with abnormal cytological findings or who were determined to be human papillomavirus (HPV)-positive were included in this randomized double-blind study. The lidocaine group (Group L, n = 30) was intravenously administered 50 mg dexketoprofen + 1.5 mg/kg lidocaine in 10 mL saline for 3 min 30 min before the procedure. The control group (Group C, n = 30) was intravenously administered 50 mg dexketoprofen in 10 mL saline for 3 min, 30 min before the procedure. During the procedure, pain scores were assessed using the visual analogue scale (VAS). In addition, patients, operator satisfaction and duration of procedure were assessed Results: There were no differences in the demographic data of the groups. Pain scores during biopsy and ECC were significantly lower in Group L than in Group C (p < 0.001). The duration of the procedure was significantly shorter in Group L than in Group C (5.00 ± 0.78 vs 6.12 ± 1.16, respectively; p < 0.001). Patient and operator satisfaction were significantly higher in Group L than in Group C (p < 0.001). Conclusions: Intravenous lidocaine administration can be used as an alternative approach to reduce pain and increase operator and patient satisfaction during colposcopy-directed biopsy and ECC procedures in office settings

Low Serum Triglyceride Levels as Predictors of Cardiac Death in Heart Failure Patients

Understanding the influence of sex differences on predictors of cardiac mortality rates in chronic heart failure might enable us to lengthen lifetimes and to improve lives. This study describes the influence of sex on cardiovascular mortality rates among chronic heart failure patients. From January 2003 through December 2009, we evaluated 637 consecutive patients (409 men and 228 women) with chronic heart failure, who ranged in age from 18 through 94 years (mean age, 64 ± 13 yr) and ranged in New York Heart Association (NYHA) functional class from II through IV. The mean follow-up period was 38 ± 15 months, the mean age was 64 ± 13 years, and the mean left ventricular ejection fraction was 0.27 ±0.11. By the end of the study, both sexes had similar cardiovascular mortality rates (36% men vs 37% women, P=0.559). In Cox regression analysis, NYHA functional class, triglyceride level, and history of coronary artery disease were independent predictors of cardiovascular death for women with chronic heart failure. For men with chronic heart failure, the patient\u27s age, ejection fraction, and sodium level were independent predictors of cardiovascular death. In a modern tertiary referral heart failure clinic, decreased triglyceride levels were, upon univariate analysis, predictors of poor outcomes for both men and women. However, upon Cox regression analysis, reduced triglyceride levels were independent predictors of cardiac death only in women

Ingénierie de la surface des bulles pour la récolte des microalgues par flottation à l'aide d'une approche biophysique

Assisted flotation represents a promising harvesting technique that consists in air dispersed into microbubbles rising through a microalgae suspension. As a result, microalgae cells get attached to bubbles and are carried out and accumulated on the surface, without being damaged. Flotation is thus a relatively rapid operation that needs low space, has moderate operational costs, and that could thus overcome the bottleneck of feasible microalgal biofuel production. To make this technique more efficient for harvesting microalgae, the original proposed strategy relies on functionalizing the bubbles produced during the process with adhesive compounds, allowing bubbles to effectively capture the cells during their ascent. This requires (i) developing methods where microsize is produced bubble and their interaction with individual cells are modulated. Then (ii) determining which molecules are present on the surface of microalgae to identify a molecule that adheres to them. In order to identify which molecule could adhere to microalgae cells, we first analyzed the composition of their wall using a combination of techniques such as liquid chromatography and X-ray photoelectron spectroscopy (XPS). The information obtained from these analyses revealed the presence of chitin-like molecule such as chitosan on the cell surface. Then in a second step we (iii) determine whether the identified molecule effectively allows adherence to cells, for that at the molecular level the interactions between chitosan and the cell wall were measured using atomic force microscopy (AFM). After understanding the molecular basis of these interactions we then (iv) chemically modify this molecule to make it amphiphilic to functionalize the bubble surface. Basically, we added an hydrophobic group to hydrophilic chitosan through N-alkylation by reductive amination. Finally, we evaluate the possibility to functionalize the bubble and modulate its interaction with cells we have in a fourth step v) we evaluate the interaction between the functionalized bubbles and cells, and optimize an efficient functionalized bubble flotation process at microalgae population scale. The results of this project, by proposing a new efficient harvesting technique, will allow to exploit the full potential of microalgae biomass for the production of third generation biofuels and thus to limit the environmental impact of human activity.La flottation assistée représente une technique de récolte prometteuse qui consiste à faire monter de l'air dispersé en microbulles à travers une suspension de microalgues. En conséquence, les cellules de microalgues se fixent aux bulles et sont transportées et accumulées à la surface, sans être endommagées. La flottation est donc une opération relativement rapide qui nécessite peu d'espace, a des coûts opérationnels modérés, et qui pourrait ainsi surmonter le goulot d'étranglement de la production réalisable de biocarburants à base de microalgues. Afin de rendre cette technique plus efficace pour la récolte des microalgues, la stratégie originale proposée repose sur la fonctionnalisation des bulles produites au cours du processus avec des composés adhésifs, permettant aux bulles de capturer efficacement les cellules au cours de leur ascension. Pour cela, il faut (i) développer des méthodes permettant de moduler la taille des bulles produites et leur interaction avec les cellules individuelles. Puis (ii) de déterminer quelles molécules sont présentes à la surface des microalgues afin d'identifier une molécule qui adhère à celles-ci. Pour le faire, nous avons d'abord analysé la composition de leur paroi en utilisant une combinaison de techniques telles que la chromatographie liquide et la spectroscopie photoélectronique à rayons X (XPS). Les informations obtenues à partir de ces analyses ont révélé la présence de molécules de type chitine telles que le chitosan à la surface des cellules. Puis, dans un deuxième temps, nous (iii) déterminons si la molécule identifiée permet effectivement l'adhésion aux cellules, pour cela au niveau moléculaire les interactions entre le chitosan et la paroi cellulaire ont été mesurées à l'aide AFM. Après avoir compris la base moléculaire de ces interactions, nous avons ensuite (iv) modifié chimiquement cette molécule pour la rendre amphiphile afin de fonctionnaliser la surface de la bulle. Nous avons ajouté un groupe hydrophobe au chitosane hydrophile par N-alkylation par amination réductrice. Enfin, nous évaluons la possibilité de fonctionnaliser la bulle et de moduler son interaction avec les cellules que nous avons dans une quatrième étape v) nous évaluons l'interaction entre les bulles fonctionnalisées et les cellules, et optimisons un processus efficace de flottation de bulles fonctionnalisées à l'échelle de la population de microalgues. Les résultats de ce projet, en proposant une nouvelle technique de récolte efficace, permettront d'exploiter tout le potentiel de la biomasse des microalgues pour la production de biocarburants de troisième génération et ainsi de limiter l'impact environnemental de l'activité humaine