In quantum-plank calculus, \(q\)-derivatives and \(h\)-derivatives are fundamental factors. Recently, a composite form of both derivatives is introduced and called \(q-h\)-derivative. This paper aims to present a further generalized notion of derivatives will be called \((q,p-h)\)-derivatives. This will produce \(q\)-derivative, \(h\)-derivative, \(q-h\)-derivative and \((p,q)\)-derivative. Theory based on all aforementioned derivatives can be generalized via this new notion. It is expected, this paper will be useful and beneficial for researchers working in diverse fields of sciences and engineering.

Bacterial bloodstream infections are important causes of morbidity and mortality, globally. The aim of the present study was to determine the bacterial profile of bloodstream infections and their antibiotic susceptibility pattern among the patients admitted to ICU at a tertiary care hospital.This prospective study was conducted over a period of eighteen months. Inclusion criteria comprised of patients admitted to ICU who belonged to either gender and were in the age group of 15-60 years. Over the course of study, 30 out of total 140 blood culture samples were identified to be culture positive (18 GNB and 11GPB). The most common Gram-positive isolate was Staphylococcus spp (26%) while Escherichia coli was the most common gram negative isolate (36%).Escherichia coli expressed highest resistance to all the drugs but sensitivity to Meropenemand Polymyxin B was 72% and 90%, respectively. High degree of resistance was noted to cephalosporins and piperacillin -tazobactam, among all the groups. The study indicated high level of antimicrobial resistance among Gram negative bacilli, esp E.Coli and justifies the need for antimicrobial stewardship to prevent development of further resistance.

We find the maximum and minimum connected unicyclic and connected well-covered unicyclic graphs of a given order with respect to \(\preceq\). This extends 2013 work by Csikv’ari where the maximum and minimum trees of a given order were determined and also answers an open question posed in the same work. Corollaries of our results give the graphs that minimize and maximize \(\xi(G)\) among all connected (well-covered) unicyclic graphs. We also answer more related open questions posed by Oboudi in 2018 and disprove a conjecture due to Levit and Mandrescu from 2008. The independence polynomial of a graph \(G\), denoted \(I(G,x)\), is the generating polynomial for the number of independent sets of each size. The roots of \(I(G,x)\) are called the independence roots of \(G\). It is known that for every graph \(G\), the independence root of smallest modulus, denoted \(\xi(G)\), is real. The relation \(\preceq\) on the set of all graphs is defined as follows, \(H\preceq G\) if and only if \(I(H,x)\ge I(G,x)\text{ for all }x\in [\xi(G),0].\)

In this paper, the fuzzy nonlinear partial differential equations of fractional order are considered. The generalization differential transform method (DTM) and fuzzy variational iteration method (VIM) were applied to solve fuzzy nonlinear partial differential equations of fractional order. The above methods are investigated based on Taylor’s formula, and fuzzy Caputo’s fractional derivative. The proposed methods are also illustrated by some examples. The results reveal the methods are a highly effective scheme for obtaining the fuzzy fractional partial differential equations.

Leibniz’s rule for the \(n\)-th derivative of a product is a very well-known and extremely useful formula. This article introduces an analogous explicit formula for the \(n\)-th derivative of a quotient of two functions. Later, we use this formula to derive new partition identities and to develop expressions for some particular \(n\)-th derivatives.

This paper deals with nonnegative solutions of the Neumann initial-boundary value problem for an attraction-repulsion chemotaxis model with logistic source term of Eq. (1) in bounded convex domains \(\Omega\subset\mathbb{R}^{n},~ n\geq1\), with smooth boundary. It is shown that if the ratio \(\frac{\mu}{\chi \alpha-\xi \gamma}\) is sufficiently large, then the unique nontrivial spatially homogeneous equilibrium given by \((u_{1},u_{2},u_{3})=(1,~\frac{\alpha}{\beta},~\frac{\gamma}{\eta})\) is globally asymptotically stable in the sense that for any choice of suitably regular nonnegative initial data \((u_{10},u_{20},u_{30})\) such that \(u_{10}\not\equiv0\), the above problem possesses uniquely determined global classical solution \((u_{1},u_{2},u_{3})\) with \((u_{1},u_{2},u_{3})|_{t=0}=(u_{10},u_{20},u_{30})\) which satisfies \(\left\|u_{1}(\cdot,t)-1\right\|_{L^{\infty}(\Omega)}\rightarrow{0},~~
\left\|u_{2}(\cdot,t)-\frac{\alpha}{\beta}\right\|_{L^{\infty}(\Omega)}\rightarrow{0},\left\|u_{3}(\cdot,t)-\frac{\gamma}{\eta}\right\|_{L^{\infty}(\Omega)}\rightarrow{0}\,,\) \(\mathrm{as}~t\rightarrow{\infty}\).

The purpose of this paper is to emphasize the role of the Bayesian Vector Autoregressive models (VAR) in macroeconomic analysis and forecasting. To help the policy-makers to do better, the Bayesian VAR models are considered more robust and valuable because they put in the model the mathematician’s beliefs or priors and the data. By using BVAR(1), we get the main results: (i)the best out sample point forecasts; (ii) the exchange rate shock contributes more to inflation; (iii) the inflation shock has high effects on exchange rate innovation. These results are due to the dollarization of this small open economy.

This article considers the limit cycles of a class of Kukles polynomial differential systems of the form Eq. (5). We obtain the maximum number of limit cycles that bifurcate from the periodic orbits of a linear center \(\dot{x}=y, \dot{y}=-x,\) by using the averaging theory of first and second order.

This research presents the solution of the generalized version of Abel’s integral equation, which was computed considering the first and second kinds. First, Abel’s integral equation and its generalization were described using fractional calculus, and the properties of Orthogonal polynomials were also described. We then developed a technique of solution for the generalized Abel’s integral equation using infinite series of orthogonal polynomials and utilized the numerical method to approximate the generalized Abel’s integral equation of the first and second kind, respectively. The Riemann-Liouville fractional operator was used in these examples. Our technique was implemented in MAPLE 17 through some illustrative examples. Absolute errors were estimated. In addition, the occurred errors between using orthogonal polynomials for solving Abel’s integral equations of order \(0\ <\ \alpha \ <\ 1\) and the exact solutions show that the orthogonal polynomials used were highly effective, reliable and can be used independently in situations where the exact solution is unknown which the numerical experiments confirmed.

Stochastic differential equations (SDEs) are a powerful tool for modeling certain random trajectories of diffusion phenomena in the physical, ecological, economic, and management sciences. However, except in some cases, it is generally impossible to find an explicit solution to these equations. In this case, the numerical approach is the only favorable possibility to find an approximative solution. In this paper, we present the mean and mean-square stability of the Non-standard Euler-Maruyama numerical scheme using the Vasicek and geometric Brownian motion models.