Applications of degenerate q-Euler and q-Changhee polynomials with weight α

In this paper, we give new identities involving degenerate q-Euler polynomials with weight α and q-Changhee polynomials of the second kind with weight α, using the Faà di Bruno formula and some identities of the Bell polynomials of the second kind

ON BINOMIAL SUMS WITH THE TERMS OF SEQUENCES {g_kn} AND {h_kn}

In this paper, we derive sums and alternating sums of products of terms ofthe sequences $\left\{ g_{kn}\right\}$ and $\left\{ h_{kn}\right\}$ withbinomial coefficients. For example,\begin{eqnarray*} &\sum\limits_{i=0}^{n}\binom{n}{i}\left( -1\right) ^{i} \left(c^{2k}\left(-q\right) ^{k}+c^{k}v_{k}+1\right)^{-ai}h_{k\left( ai+b\right) }h_{k\left(ai+e\right) } \\ &=\left\{ \begin{array}{clc} -\Delta ^{\left( n+1\right) /2}g_{k\left( an+b+e\right) }g_{ka}^{n}\left( c^{2k}\left( -q\right) ^{k}+c^{k}v_{k}+1\right) ^{-an} & \text{if }n\text{ is odd,} & \\ \Delta ^{n/2}h_{k\left( an+b+e\right) }g_{ka}^{n}\left( c^{2k}\left( -q\right) ^{k}+c^{k}v_{k}+1\right) ^{-an} & \text{if }n\text{ is even,} & \end{array}% \right.\end{eqnarray*}%and\begin{eqnarray*} &&\sum\limits_{i=0}^{n}\binom{n}{i}i^{\underline{m}}g_{k\left( n-ti\right) }h_{kti} \\ &&=2^{n-m}n^{\underline{m}}g_{kn}-n^{\underline{m}}\left( c^{2k}\left( -q\right) ^{k}+c^{k}v_{k}+1\right) ^{n\left( 1-t\right) }h_{kt}^{n-m}g_{k\left( tm+tn-n\right) },\end{eqnarray*}%where $a, b, e$ is any integer numbers, $c$ is nonzero real number and $m$is nonnegative integer

On triangles with coordinates of vertices from the terms of the sequences {U_kn} and {V_kn}

In this paper, we determine some results of the triangles with coordinates of vertices involving the terms of the sequences {Ukn} and {Vkn} where Ukn are terms of a second order recurrent sequence and Vkn are terms in the companion sequence for odd positive integer k, generalizing works of Čerin. For example, the cotangent of the Brocard angle of the triangle Δkn is cot(ΩΔkn = (Uk(2n+3)V2k − Vk(2n+3)Uk) / ((−1)nU2k)

On Certain Hessenberg Matrices Related with Linear Recurrences

In this paper, we present the permanents and determinants of some Hessenbergmatrices. Also, some special cases for permanents are given

Inappropriate antimicrobial use in Turkish pediatric hospitals: A multicenter point prevalence survey

Objectives: Although well-defined principles of rational antimicrobial use are available, inappropriate prescribing patterns are reported worldwide. Accurate information on the usage of antimicrobials, including factors associated with and influencing their use, is valuable for improving the quality of prescription practices. Methods: In this cross-sectional point prevalence survey, data on patients hospitalized in 12 different children's hospitals were collected on a single day. Appropriateness of prescription was compared between the types of antimicrobials prescribed, indications, wards, and presence of/consultation with an infectious disease physician (IDP). Results: A total 711 of 1302 (54.6%) patients evaluated were receiving one or more antimicrobial drugs. The antimicrobial prescription rate was highest in pediatric intensive care (75.7%) and lowest in the surgery wards (37.0%). Of the 711 patients receiving antimicrobials, 332 patients (46.7%) were found to be receiving at least one inappropriately prescribed drug. Inappropriate use was most frequent in surgery wards (80.2%), while it was less common in oncology wards (31.8%; p < 0.001). Respiratory tract infection was the most common indication for antimicrobial use (29.4%). Inappropriate use was more common in deep-seated infections (54.7%) and respiratory infections (56.5%). Fluoroquinolones were used inappropriately more than any other drugs (81.8%, p = 0.021). Consultation with an IDP appears to increase appropriate antimicrobial use (p = 0.008). Conclusions: Inappropriate antimicrobial use remains a common problem in Turkish pediatric hospitals. Consultation with an IDP and prescribing antimicrobial drugs according to microbiological test results could decrease the inappropriate use of antimicrobials

On Reciprocal Series of Generalized Fibonacci Numbers with Subscripts in Arithmetic Progression

We investigate formulas for closely related series of the forms: ∑∞=01/(++), ∑∞=0(−1)+/(++)2, ∑∞=02(+)/(2++)2 for certain values of , , and

Some weighted sums of products of Lucas sequences

In this paper, we consider the weighted sums of products of Lucas sequences of the form (Formula Presented) where rn and sn are the terms of Lucas sequences {Un} and {Vn} for some positive integers t and m. By using generating function methods, we compute the weighted sums of products of Lucas sequences and show that these sums could be expressed via terms of the Lucas sequences

Formulae for two weighted binomial identities with the falling factorials

In this paper, we will give closed formulae for weighted and alternating weighted binomial sums with the generalized Fibonacci and Lucas numbers including both falling factorials and powers of indices. Furthermore we will derive closed formulae for weighted binomial sums including odd powers of the generalized Fibonacci and Lucas numbers. © 2018 Charles Babbage Research Centre. All rights reserved

Nonlinear variants of the generalized Filbert and Lilbert matrices

In this paper, we present variants of the generalized Filbert and Lilbert matrices by products of the general Fibonacci and Lucas numbers whose indices are in certain nonlinear forms of the indices with certain integer parameters. We derive explicit formulæ for inverse matrix, LU -decomposition and inverse matrices L-1 and U-1 for all matrices. Generally, we present q -versions of these matrices and their related results