CAPA: An important concept of Quality Assurance in Pharmaceutical Industry

CAPA is used in the improvements to be made in product, process or quality system to eliminate non-conformities and other undesirable situation. CAPA could be regulatory concept that focuses on systematic investigations to search out the root cause, understanding and correcting discrepancies while attempting to avoid their reoccurrence. Instructions for a way they must be handled within the organization just in case of potential product problems, customer complaints or action to eliminate the cause of a detected nonconformities or incident. Regulatory inspections give more importance for CAPA, for the explanation, it will high light the systems followed within the company additionally because the technical capability of the people concerned. Changes proposed are to be verified and validated to confirm the effectiveness and quality attribution. CAPA is also an integrated part of ISO: 13485 and Good Manufacturing Practice (GMP) for medical products. The FDA defines the purpose of a CAPA procedure as: collecting and analyzing information, identifying and investigating product and quality problems, and taking appropriate and effective corrective and/or preventive action to prevent their recurrence. There is not a regulatory defined framework for the CAPA process only different requirements. The CAPA system investigation document will provide a clear picture of how the standard system works and hence, Regulatory Inspectors give lot of importance to audit this method. Real root cause is to be identified with scientific proof and which further may not be generated. This review provides comprehensive views on steps involved in corrective action and preventive action (CAPA), mechanism of taking CAPA enabling to boost the system of quality management. CAPA is a component of the overall quality management system. As per the FDA documents CAPA accounts for 30-50% of FDA-483 forms issued for noncompliance.

On Tribonacci Functions and Gaussian Tribonacci Functions

In this work, Gaussian Tribonacci functions are defined and investigated on the set of real numbers $\mathbb{R},$ \textit{i.e}., functions $f_{G}$ $:$ $\mathbb{R}\rightarrow \mathbb{C}$ such that for all $% x\in \mathbb{R},$ $n\in \mathbb{Z},$ $f_{G}(x+n)=f(x+n)+if(x+n-1)$ where $f$ $:$ $\mathbb{R}\rightarrow \mathbb{R}$ is a Tribonacci function which is given as $f(x+3)=f(x+2)+f(x+1)+f(x)$ for all $x\in \mathbb{R}$. Then the concept of Gaussian Tribonacci functions by using the concept of $f$-even and $f$-odd functions is developed. Also, we present linear sum formulas of Gaussian Tribonacci functions. Moreover, it is showed that if $f_{G}$ is a Gaussian Tribonacci function with Tribonacci function $f$, then $% \lim\limits_{x\rightarrow \infty }\frac{f_{G}(x+1)}{f_{G}(x)}=\alpha \ $and\ $\lim\limits_{x\rightarrow \infty }\frac{f_{G}(x)}{f(x)}=\alpha +i,$ where $% \alpha $ is the positive real root of equation $x^{3}-x^{2}-x-1=0$ for which $\alpha >1$. Finally, matrix formulations of Tribonacci functions and Gaussian Tribonacci functions are given. In the literature, there are several studies on the functions of linear recurrent sequences such as Fibonacci functions and Tribonacci functions. However, there are no study on Gaussian functions of linear recurrent sequences such as Gaussian Tribonacci and Gaussian Tetranacci functions and they are waiting for the investigating. We also present linear sum formulas and matrix formulations of Tribonacci functions which have not been studied in the literature.

Topological Properties of the Immediate Basins of Attraction for the Secant Method

We study the discrete dynamical system defined on a subset of $$R^2$$ R 2 given by the iterates of the secant method applied to a real polynomial p. Each simple real root $$\alpha $$ α of p has associated its basin of attraction $${\mathcal {A}}(\alpha )$$ A ( α ) formed by the set of points converging towards the fixed point $$(\alpha ,\alpha )$$ ( α , α ) of S. We denote by $${\mathcal {A}}^*(\alpha )$$ A ∗ ( α ) its immediate basin of attraction, that is, the connected component of $${\mathcal {A}}(\alpha )$$ A ( α ) which contains $$(\alpha ,\alpha )$$ ( α , α ) . We focus on some topological properties of $${\mathcal {A}}^*(\alpha )$$ A ∗ ( α ) , when $$\alpha $$ α is an internal real root of p. More precisely, we show the existence of a 4-cycle in $$\partial {\mathcal {A}}^*(\alpha )$$ ∂ A ∗ ( α ) and we give conditions on p to guarantee the simple connectivity of $${\mathcal {A}}^*(\alpha )$$ A ∗ ( α ) .

Parafoveal processing of orthographic, morphological, and semantic information during reading Arabic: A boundary paradigm investigation

Evidence shows that skilled readers extract information about upcoming words in the parafovea. Using the boundary paradigm, we investigated native Arabic readers’ processing of orthographic, morphological, and semantic information available parafoveally. Target words were embedded in frame sentences, and prior to readers fixating them, one of the following previews were made available: (a) Identity preview; (b) Preview that shared the pattern morpheme with the target; (c) Preview that shared the root morpheme with the target; (d) Preview that was a synonym with the target word; (e) Preview with two of the root letters were transposed thus creating a new root, while preserving all letter identities of the target; (f) Preview with two of the root letters were transposed thus creating a pronounceable pseudo root, while also preserving all letter identities of the target; and (g) Previews that was unrelated to the target word and shared no information with it. The results showed that identity, root-preserving, and synonymous preview conditions yielded preview benefit. On the other hand, no benefit was obtained from the pattern-preserving previews, and significant disruption to processing was obtained from the previews that contained transposed root letters, particularly when this letter transposition created a new real root. The results thus reflect Arabic readers’ dependance on morphological and semantic information, and suggest that these levels of representation are accessed as early as orthographic information. Implications for theory- and model-building, and the need to accommodate early morphological and semantic processing activities in more comprehensive models are further discussed.

NUMERICAL HYBRID ITERATIVE TECHNIQUE FOR SOLVING NONLINEAR EQUATIONS IN ONE VARIABLE

In recent years, some improvements have been suggested in the literature that has been a better performance or nearly equal to existing numerical iterative techniques (NIT). The efforts of this study are to constitute a Numerical Hybrid Iterative Technique (NHIT) for estimating the real root of nonlinear equations in one variable (NLEOV) that accelerates convergence. The goal of the development of the NHIT for the solution of an NLEOV assumed various efforts to combine the different methods. The proposed NHIT is developed by combining the Taylor Series method (TSM) and Newton Raphson’s iterative method (NRIM). MATLAB and Excel software has been used for the computational purpose. The developed algorithm has been tested on variant NLEOV problems and found the convergence is better than bracketing iterative method (BIM), which does not observe any pitfall and is almost equivalent to NRIM.

Application of a Generalized Secant Method to Nonlinear Equations with Complex Roots

The secant method is a very effective numerical procedure used for solving nonlinear equations of the form f(x)=0. In a recent work (A. Sidi, Generalization of the secant method for nonlinear equations. Appl. Math. E-Notes, 8:115–123, 2008), we presented a generalization of the secant method that uses only one evaluation of f(x) per iteration, and we provided a local convergence theory for it that concerns real roots. For each integer k, this method generates a sequence {xn} of approximations to a real root of f(x), where, for n≥k, xn+1=xn−f(xn)/pn,k′(xn), pn,k(x) being the polynomial of degree k that interpolates f(x) at xn,xn−1,…,xn−k, the order sk of this method satisfying 1<sk<2. Clearly, when k=1, this method reduces to the secant method with s1=(1+5)/2. In addition, s1<s2<s3<⋯, such that limk→∞sk=2. In this note, we study the application of this method to simple complex roots of a function f(z). We show that the local convergence theory developed for real roots can be extended almost as is to complex roots, provided suitable assumptions and justifications are made. We illustrate the theory with two numerical examples.

Real Root Polynomials and Real Root Preserving Transformations

Polynomials can be used to represent real-world situations, and their roots have real-world meanings when they are real numbers. The fundamental theorem of algebra tells us that every nonconstant polynomial p with complex coefficients has a complex root. However, no analogous result holds for guaranteeing that a real root exists to p if we restrict the coefficients to be real. Let n ≥ 1 and P n be the vector space of all polynomials of degree n or less with real coefficients. In this article, we give explicit forms of polynomials in P n such that all of their roots are real. Furthermore, we present explicit forms of linear transformations on P n which preserve real roots of polynomials in a certain subset of P n .

Stability Regions of Fractional First Order Controllers Applied to Fractional Order Delay Systems

This paper focuses on the problem of stabilizing fractional order time delay systems by fractional first order controllers. A solution is proposed to find the set of all stability regions in the controller’s parameter space. The D-decomposition method is employed to find the real root boundary and complex root boundaries which are used to identify the stability regions. Illustrative examples are given to show the effectiveness of the proposed approach, and it is remarked that the stability region obtained for the fractional order controller is larger than the non-fractional controller.

Lyapunov exponent, ISCO and Kolmogorov–Senai entropy for Kerr–Kiselev black hole

Geodesic motion has significant characteristics of space-time. We calculate the principle Lyapunov exponent (LE), which is the inverse of the instability timescale associated with this geodesics and Kolmogorov–Senai (KS) entropy for our rotating Kerr–Kiselev (KK) black hole. We have investigate the existence of stable/unstable equatorial circular orbits via LE and KS entropy for time-like and null circular geodesics. We have shown that both LE and KS entropy can be written in terms of the radial equation of innermost stable circular orbit (ISCO) for time-like circular orbit. Also, we computed the equation marginally bound circular orbit, which gives the radius (smallest real root) of marginally bound circular orbit (MBCO). We found that the null circular geodesics has larger angular frequency than time-like circular geodesics ($$Q_o > Q_{\sigma }$$ Q o > Q σ ). Thus, null-circular geodesics provides the fastest way to circulate KK black holes. Further, it is also to be noted that null circular geodesics has shortest orbital period $$(T_{photon}< T_{ISCO})$$ ( T photon < T ISCO ) among the all possible circular geodesics. Even null circular geodesics traverses fastest than any stable time-like circular geodesics other than the ISCO.