An efficient method for oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics

In this paper, a novel numerical technique, the first-order Smooth Composite Chebyshev Finite Difference method, is presented. Imposing a first-order smoothness of the approximation polynomial at the ends of each subinterval is originality of the method. Both round-off and truncation error analyses of the method are performed beside the convergence analysis. Diffusion of oxygen in a spherical cell including nonlinear uptake kinetics is solved by using the method. The obtained results are compared with the existing methods in the literature and it is observed that the proposed method gives more reliable results.

When does the story matter? No evidence for the foregrounding hypothesis in math story problems

Math story problems are difficult for many solvers because comprehension of mathematical and linguistic content must occur simultaneously. Across two studies, we attempted to conceptually replicate and extend findings reported by Mattarella-Micke and Beilock (2010, https://doi.org/10.3758/PBR.17.1.106) and Jarosz and Jaeger (2019, https://doi.org/10.1002/acp.3471). Mattarella-Micke and Beilock found that multiplication word problems in which an irrelevant number was associated with the protagonist of the problem (i.e., foregrounded in the text) were solved less accurately than problems in other conditions. Jarosz and Jaeger used similar materials but tested the more general inconsistent-operations hypothesis that association with the protagonist would interfere with multiplication whereas dissociation would interfere with division. They found partial support: When division problems were primed with dissociative scenarios, solvers made more errors, but they failed to replicate the associative findings for multiplication. In the present research, we conducted two studies (Ns = 205 and 359), in which we similarly manipulated whether irrelevant content was associated with or dissociated from the story protagonist. In these studies, we did not find support for either the foregrounding or inconsistent-operations hypotheses. Exploratory error analyses suggested that solvers’ errors were most often the result of calculation difficulties or inappropriate operation choices and were unrelated to the presence of associative or dissociative story elements. Our careful implementation of this manipulation and much greater power to detect effects suggests that the association manipulation in irrelevant text does not influence adults’ performance on simple math story problems.

Towards Compilation of Balanced Protein Stability Datasets: Flattening the ΔΔG Curve through Systematic Under-sampling

Protein stability datasets contain neutral mutations that are highly concentrated in a much narrower ΔΔG range than destabilizing and stabilizing mutations. Notwith-standing their high density, often studies analyzing stability datasets and/or predictors ignore the neutral mutations and use a binary classification scheme labeling only destabilizing and stabilizing mutations. Recognizing that highly concentrated neutral mutations would affect the quality of stability datasets, we have explored three protein stability datasets; S2648, PON-tstab and the symmetric Ssym that differ in size and quality. A characteristic leptokurtic shape in the ΔΔG distributions of all three datasets including the curated and symmetric ones were reported due to concentrated neutral mutations. To further investigate the impact of neutral mutations on ΔΔG predictions, we have comprehensively assessed the performance of eleven predictors on the PON-tstab dataset. Correlation and error analyses showed that all of the predictors performed the best on the neutral mutations while their performance became gradually worse as the ΔΔG of the mutations departed further from the neutral zone regardless of the direction, implying a bias towards dense mutations. To this end, after unraveling the role of concentrated neutral mutations in biases of stability datasets, we described a systematic under-sampling approach to balance the ΔΔG distributions. Before under-sampling, mutations were clustered based on their biochemical and/or structural features and then three mutations were systematically selected from every 2 kcal/mol of each cluster. Upon implementation of this approach by distinct clustering schemes, we generated five subsets varying in size and ΔΔG distributions. All subsets notably showed amelioration of not only the shape of ΔΔG distributions but also other pre-existing imbalances in the frequency distributions. We also reported differences in the performance of the predictors between the parent and under-sampled subsets due to the enrichment of previously under-represented mutations in the subsets. Altogether, this study not only elaborated the pivotal role of concentrated mutations in the dataset biases but also contemplated and realized a rational strategy to tackle this and other forms of biases. Under-sampling code is available on GitHub (https://github.com/narodkebabci/gRoR).

Error analyses of a Multi-Input-Multi-Output cantilever beam test

Multi-Input-Multi-Output vibration testing typically requires the determination of inputs to achieve desired response at multiple locations. First, the responses due to each input are quantified in terms of complex transfer functions in the frequency domain. In this study, two Inputs and five Responses were used leading to a 5 × 2 transfer function matrix. Inputs corresponding to the desired Responses are then computed by inversion of the rectangular matrix using Pseudo-Inverse techniques that involve least-squared solutions. It is important to understand and quantify the various sources of errors in this process toward improved implementation of Multi-Input-Multi-Output testing. In this article, tests on a cantilever beam with two actuators (input controlled smart shakers) were used as Inputs while acceleration Responses were measured at five locations including the two input locations. Variation among tests was quantified including its impact on transfer functions across the relevant frequency domain. Accuracy of linear superposition of the influence of two actuators was quantified to investigate the influence of relative phase information. Finally, the accuracy of the Multi-Input-Multi-Output inversion process was investigated while varying the number of Responses from 2 (square transfer function matrix) to 5 (full-rectangular transfer function matrix). Results were examined in the context of the resonances and anti-resonances of the system as well as the ability of the actuators to provide actuation energy across the domain. Improved understanding of the sources of uncertainty from this study can be used for more complex Multi-Input-Multi-Output experiments.

Numerical solution of two-dimensional nonlinear fractional order reaction-advection-diffusion equation by using collocation method

In this article, two-dimensional nonlinear and multi-term time fractional diffusion equations are solved numerically by collocation method, which is used with the help of Lucas operational matrix. In the proposed method solutions of the problems are expressed in terms of Lucas polynomial as basis function. To determine the unknowns, the residual, initial and boundary conditions are collocated at the chosen points, which produce a system of nonlinear algebraic equations those have been solved numerically. The concerned method provides the highly accurate numerical solution. The accuracy of the approximate solution of the problem can be increased by expanding the terms of the polynomial. The accuracy and efficiency of the concerned method have been authenticated through the error analyses with some existing problems whose solutions are already known.

An Efficient Weighted Residual Time Integration Family

A new family of time integration methods is formulated. The recommended technique is useful and robust for the loads with large variations and the systems with nonlinear damping behavior. It is also applicable for the structures with lots of degrees of freedom, and can handle general nonlinear dynamic systems. By comparing the presented scheme with the fourth-order Runge–Kutta and the Newmark algorithms, it is concluded that the new strategy is more stable. The authors’ formulations have good results on amplitude decay and dispersion error analyses. Moreover, the family orders of accuracy are [Formula: see text] and [Formula: see text] for even and odd values of [Formula: see text], respectively. Findings demonstrate the superiority of the new family compared to explicit and implicit methods and dissipative and non-dissipative algorithms.

Heat Transfer in Nanomaterial Suspension (CuO and Al2O3) Using KKL Model

Novel nonlinear power-law flux models were utilized to model the heat transport phe-nomenon in nano-micropolar fluid over a flexible surface. The nonlinear conservation laws (mass, momentum, energy, mass transport and angular momentum) and KKL cor-relations for nanomaterial under novel flux model were solved numerically. Computed results were used to study the shear-thinning and shear-thickening nature of nano pol-ymer suspension by considering n-diffusion theory. Normalized velocity, temperature and micro-rotation profiles were investigated under the variation of physical parame-ters. Shear stresses at the wall for nanoparticles (CuO and Al2O3) were recorded and dis-played in the table. Error analyses for different physical parameters were prepared for various parameters to validate the obtained results.

FACTORS AFFECTING STUDENTS IN TRANSLATING TEXTS IDIOMATICALLY

The discussion of translation used by students has been investigated long time ago in which the setup of the Second Language Development was firstly established, i.e around 1900s. Many Error Analyses on translation have been analyzed by linguists which become the valuable contributions towards the study of translation. This study deals with error analysis of students’ project on translations of English Department of UNIMED so that there could be drawn some factors that make students are in difficulty in translating texts idiomatically. Qualitative method is used in analyzing this study and all the data are taken from students’ projects and worksheets on translation. Among factors that cause students are in difficulty in translating texts idiomatically are less understanding the meanings of the texts, do not fully master the lexicogrammar, do not understand the language concepts, social context, language use, etc.