Chromium (VI) a highly toxic metal, a major constituent of industrial waste. It is continuously release in soil and water, causes environmental and health related issues, which is increasing public concern in developing countries like Pakistan. The basic aim of this study was isolation and screening of chromium resistant bacteria from industrial waste collected from Korangi and Lyari, Karachi (24˚52ʹ46.0ʺN 66˚59ʹ25.7ʺE and 24˚48ʹ37.5ʺN 67˚06ʹ52.6ʺE). Among total of 53 isolated strains, seven bacterial strains were selected through selective enrichment and identified on the basis of morphological and biochemical characteristics. These strains were designated as S11, S13, S17, S18, S30, S35 and S48, resistance was determined against varying concentrations of chromium (100-1500 mg/l). Two bacterial strains S35 and S48 showed maximum resistance to chromium (1600 mg/l). Bacterial strains S35 and S48 were identified through 16S rRNA sequence and showed 99% similarity to Bacillus paranthracis and Bacillus paramycoides. Furthermore, growth condition including temperature and pH were optimized for both bacterial strains, showed maximum growth at temperature 30ºC and at optimum pH 7.5 and 6.5 respectively. It is concluded that indigenous bacterial strains isolated from metal contaminated industrial effluent use their innate ability to transform toxic heavy metals to less or nontoxic form and can offer an effective tool for monitoring heavy metal contamination in the environment.
In this manuscript, a class of generalized ψ , α , β -weak contraction is introduced and some fixed point theorems in the framework of b -metric space are proved. The result presented in this paper generalizes some of the earlier results in the existing literature. Further, some examples and an application are provided to illustrate our main result.
In this paper, we introduce a generalized multivalued ( α , L)-almost contraction in the b -metric space. Furthermore, we prove the existence and uniqueness of the fixed point for a specific mapping. The result presented in this paper extends some of the earlier results in the existing literature. Moreover, some examples are given to illuminate the usability of the obtained results.
Using the fixed point method, we prove the Hyers–Ulam stability of a cubic and quartic functional equation and of an additive and quartic functional equation in matrix Banach algebras.
In this article, a stabilized mixed finite element (FE) method for the Oseen viscoelastic fluid flow (OVFF) obeying an Oldroyd-B type constitutive law is proposed and investigated by using the Streamline Upwind Petrov-Galerkin (SUPG) method. To find the approximate solution of velocity, pressure and stress tensor, we choose lowest-equal order FE triples P1-P1-P1, respectively. However, it is well known that these elements do not fulfill the in f -sup condition. Due to the violation of the main stability condition for mixed FE method, the system becomes unstable. To overcome this difficulty, a standard stabilization term is added in finite element variational formulation. The technique is applied herein possesses attractive features, such as parameter-free, flexible in computation and does not require any higher-order derivatives. The stability analysis and optimal error estimates are obtained. Three benchmark numerical tests are carried out to assess the stability and accuracy of the stabilized lowest-equal order feature of the OVFF.case , and the time-dependent case of the same continuous interpolation was analysed by Baranger in .In Newtonian fluid flow, the Oseen equations are abridged to linearize the system. This is because the Oseen fluid flow model is the reduced linearized form of the Newtonian fluid which is described by the Navier-Stokes equation [10,11]. Moreover, the viscoelastic fluid flow model equations are non-linear equations in many terms. Hence, by taking the assumption of creeping fluid flow, the inertial part (u · ∇ u) of the momentum equation can be ignored. In this sense, the non-linearity arise only in the constitutive equation [12,13] which may be introduce in a linear form by fixing u(x) with a known velocity field b(x). The resulting system of equations can explicitly described the parameter space for α, λ and ∇b ∞ , which ensure the well-posedness of the continuous problem and its numerical approximation .In the FE framework, the main difficulty arises in the viscoelastic fluid flow due to its hyperbolic constitutive equation. It needs a stabilization (upwinding ) technique to approximate the FE solution. There are two main approaches that are mainly used to solve the Oldroyd-B model by using the OVFF technique; the discontinuous Galerkin (DG) approximation and the (SUPG) estimate to deal with the spurious oscillations of the hyperbolic constitutive equation; see . Herein, we consider SUPG method to solve the OVFF as an upwinding technique . To the best of our knowledge, V.J. Ervin et al. introduced the SUPG method in  to approximate the model equations with the standard FE or Hood-Taylor FE pair (P2 for velocity, P1 for pressure and P1 for continuous stress), where the existence and uniqueness of a solution to the problem was shown. Later, the same authors studied a defect correction method in , where they used the same standard FE (P2-P1) to approximate the velocity and pressure but for discontinuous stress. They have used the conforming ...
<abstract><p>In computational mathematics, the comparison of convergence rate in different iterative methods is an important concept from theoretical point of view. The importance of this comparison is relevant for researchers who want to discover which one of these iterations converges to the fixed point more rapidly. In this article, we study the different numerical methods to calculate fixed point in digital metric spaces, introduce a new k-step iterative process and conduct an analysis on the strong convergence, stability and data dependence of the mentioned scheme. Some illustrative examples are given to show that this iteration process converges faster.</p></abstract>
<abstract><p>This paper reports a modified F-iterative process for finding the fixed points of three generalized $ \alpha $-nonexpansive mappings. We assume certain assumptions to establish the weak and strong convergence of the scheme in the context of a Banach space. We suggest a numerical example of generalized $ \alpha $-nonexpansive mappings which exceeds, properly, the category of functions furnished with a condition (C). After that, we show that our modified F-iterative scheme of this example converges to a common fixed point of three generalized $ \alpha $-nonexpansive mappings. As an application of our main findings, we suggest a new projection-type iterative scheme to solve variational inequality problems in the setting of generalized $ \alpha $-nonexpansive mappings. The main finding of the paper is new and extends many known results of the literature.</p></abstract>
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