Multistep Methods Research Articles

A Class of Efficient Multistep Methods for Forward Backward Stochastic Differential Equations

A Class of Efficient Multistep Methods for Forward Backward Stochastic Differential Equations

Addressing the Challenge of a Simultaneous Destructive Assay of Plutonium and Uranium: Highly Precise, Robust, Universal, and Reagent-Free Differential Pulse Voltametric Method Development in Biodegradable Methanesulfonic Acid Medium.

The destructive assay of bulk uranium and plutonium, a cornerstone for chemical quality control and nuclear material accounting of fuel matrices, mandates robust and precise methodologies. Despite ongoing research, simultaneous, matrix independent determination of U and Pu has eluded solution owing to inherent limitations in aqueous acid medium, viz., coexistence of multiple oxidation states, coupled electrochemical reactions, smaller potential window, and requirement for multistep sample preconditioning and tedious electrode modification. The present study addresses this challenge wherein non-aqueous methanesulfonic acid (MSA) served the dual role of solvent and analyte media with a bare glassy carbon (GC) electrode. Fuel matrices, viz., (U, Pu)C, (U, Pu)O2, PuO2, UO3, UO2, and U3O8, were quantitatively dissolved in biodegradable MSA, without using any additives. Redox speciation of the analytes, U and Pu, in MSA was probed by ultraviolet-visible spectrophotometry and electrometry, revealing the absence of electrocatalytic regeneration and stabilization of single oxidation state, viz., U(VI) and Pu(IV), along with relevant redox-energetic (electron transfer and reversibility) and kinetic data. Bidentate coordination of MSA with the U analyte was indicated by X-ray absorption spectroscopy studies and was corroborated by density functional theory-based investigations, providing the optimized structure, viz., [UO2(MSA)2] and [Pu(MSA)4], binding modes and energy, partial charges, and molecular orbital diagrams. Based on these insights, the feasibility of differential pulse voltammetry (DPV)-based assay method development for U and Pu separately and in different U/Pu ratios, representing assorted fuel matrices, was probed. Analytical figures of merit for both U and Pu (detection limit of ∼10-5 M, precision of ∼0.2%, accuracy of ∼0.2%, high sensitivity, repeatability, and non-influence of relevant interferences) were determined, method validated employing actual fuel samples, and compared with the established, multi-step biamperometry method. Hence, a universal, simultaneous U and Pu destructive assay method in non-aqueous MSA media based on DPV with a commercial GC electrode was demonstrated.

Prime number-based multistep measurement for separation of roundness errors

Roundness measurement is critical in manufacturing, as it ensures that products conform to precise design specifications. However, traditional multistep measurements for roundness error separation are time-consuming and limited in their ability to separate specific Fourier components. In this study, we propose a novel combined multistep measurement method with prime numbers that overcomes these limitations. We demonstrate this method through three experimental cases, achieving high levels of Fourier components in error separation with a limited number of measurements. Our method combines two ( p and q) or three ( p, q, and r) steps of prime numbers to achieve high levels of Fourier components for error separation, compared to traditional multistep measurements that require more steps. In the first experimental case, we use a 2-step and 5-step measurement to achieve traditional multistep measurement in ten steps. In the second case, we use 3-step and 5-step measurements, and in the third, we combine the 2-step, 3-step, and 5-step measurements. We achieve roundness deviations (RONt) of 12.7, 7.8, and 9.9 nm, respectively, and maximum En-values of 0.8, 0.8, and 0.7, respectively. Our proposed combined multistep measurement method using prime numbers has practical applications in manufacturing, as it reduces the time and resources required for roundness error separation while achieving a higher level of Fourier components. Our results demonstrate the effectiveness of our method and its potential to revolutionize roundness measurement in industry.

A nonlinear fractional fishery resource system model with Crowley–Martin functional response under Mittag-Leffler kernel

This article studies the action of predators and the predator-dependent functional response in the fishery resource model. We employ the Atangana–Baleanu–Caputo fractional derivative to study the proposed fractional fishery resource model in the presence of predators with Crowley–Martin functional response. We present a theoretical and numerical analysis of the governing nonlinear differential equations of the model consisting of the biomass density of the fish population inside the unrestricted fishing zone, the biomass density of the fish population inside the reserve or restricted fishing zone, and the predator population. Using the fixed point theory and nonlinear analysis, we establish the existence and uniqueness results of the proposed ABC fractional fishery resource model. We establish stability analysis of the fishery model using the Ulam–Hyers stability approach. The numerical scheme of the fractional Adams–Bashforth method is provided and the approximate solutions for the model under consideration are given and discussed. We observe that an increase in the fish capturing rates increases the size of the predator population and reduces the fish subpopulations. To maintain a high number of fish species, we recommend a control measure to reduce the fish capturing rate by the predators.

Formation of high areal density core using an efficient and robust implosion method for fast ignition

Abstract A new fuel compression method for a fast ignition scheme is discussed. To form a high areal density fuel plasma for the ignition condition, homogenous isentropic compression (HIC) with solid spherical target is effective. We improve a multi-step pulse shape method that uses progressive shockwaves and reflected shockwaves for the compression, where a precisely controlled step-pulse laser drives the shockwaves to compress the fuel and suppress entropy increase. Another advantage of this approach is the relatively smooth high dense fuel is distributed at maximum compression time, compared to our previous design based on Kidder’s HIC method. In addition, we insert a power dip as a preconditioning before the last pulse step to reduce the electron and ion temperature near critical density. As a result, an optimum implosion is designed using 245 kJ of implosion laser energy to meet the ignition condition.

Bacterial Purine Nucleoside Phosphorylases from Mesophilic and Thermophilic Sources: Characterization of Their Interaction with Natural Nucleosides and Modified Arabinofuranoside Analogues.

The enzymatic synthesis of nucleoside derivatives is an important alternative to multi-step chemical methods traditionally used for this purpose. Despite several undeniable advantages of the enzymatic approach, there are a number of factors limiting its application, such as the limited substrate specificity of enzymes, the need to work at fairly low concentrations, and the physicochemical properties of substrates-for example, low solubility. This research conducted by our group is dedicated to the advantages and limitations of using purine nucleoside phosphorylases (PNPs), the main enzymes for the metabolic reutilization of purines, in the synthesis of modified nucleoside analogues. In our work, the substrate specificity of PNP from various bacterial sources (mesophilic and thermophilic) was studied, and the effect of substrate, increased temperature, and the presence of organic solvents on the conversion rate was investigated.

Global Analysis of a Fractional‐Order Hepatitis B Virus Model Under Immune Response in the Presence of Cytokines

AbstractThis research proposes and investigates an epidemiological model to study the dynamic behaviors of the Hepatitis B virus (HBV) under immune response and cytokine influence. The model's stability, positivity, boundedness, and equilibria are analyzed using Lyapunov functional methods and the Routh–Hurwitz criterion under Caputo fractional derivative. The study evaluates nucleoside analogues and interferon treatments, determining critical drug efficiencies. Equilibria, including infection‐free and endemic states, are analyzed using the fundamental reproduction number, , to predict disease elimination. Numerical simulations utilize the fractional Adams method and the L1 scheme, capturing memory traces as the fractional order changes. Results show the L1 scheme effectively captures memory traces, providing empirical support for the theoretical findings. Furthermore, Ulam–Hyers stability is treated according to the equilibrium point, which describes relationships between functions. Notably, the findings of the study yielded profound insights. They revealed that the HBV system remains locally asymptotic stable at disease‐free and the endemic point when . At the same time, the simulations illustrated a correlation between the rate of infection and the rise in infected individuals, indicating the feasibility of eradicating and effectively managing HBV infections through a multifaceted approach and various measures such as vaccination and effective drug administration protocols. The proposed framework can guide medical professionals and decision‐makers in developing effective strategies to limit and eliminate the spread of HBV in the population.

The impact of the carbohydrate-binding module on how a lytic polysaccharide monooxygenase modifies cellulose fibers

BackgroundIn recent years, lytic polysaccharide monooxygenases (LPMOs) that oxidatively cleave cellulose have gained increasing attention in cellulose fiber modification. LPMOs are relatively small copper-dependent redox enzymes that occur as single domain proteins but may also contain an appended carbohydrate-binding module (CBM). Previous studies have indicated that the CBM “immobilizes” the LPMO on the substrate and thus leads to more localized oxidation of the fiber surface. Still, our understanding of how LPMOs and their CBMs modify cellulose fibers remains limited.ResultsHere, we studied the impact of the CBM on the fiber-modifying properties of NcAA9C, a two-domain family AA9 LPMO from Neurospora crassa, using both biochemical methods as well as newly developed multistep fiber dissolution methods that allow mapping LPMO action across the fiber, from the fiber surface to the fiber core. The presence of the CBM in NcAA9C improved binding towards amorphous (PASC), natural (Cell I), and alkali-treated (Cell II) cellulose, and the CBM was essential for significant binding of the non-reduced LPMO to Cell I and Cell II. Substrate binding of the catalytic domain was promoted by reduction, allowing the truncated CBM-free NcAA9C to degrade Cell I and Cell II, albeit less efficiently and with more autocatalytic enzyme degradation compared to the full-length enzyme. The sequential dissolution analyses showed that cuts by the CBM-free enzyme are more evenly spread through the fiber compared to the CBM-containing full-length enzyme and showed that the truncated enzyme can penetrate deeper into the fiber, thus giving relatively more oxidation and cleavage in the fiber core.ConclusionsThese results demonstrate the capability of LPMOs to modify cellulose fibers from surface to core and reveal how variation in enzyme modularity can be used to generate varying cellulose-based materials. While the implications of these findings for LPMO-based cellulose fiber engineering remain to be explored, it is clear that the presence of a CBM is an important determinant of the three-dimensional distribution of oxidation sites in the fiber.

Resource utilization of coal-derived sludge and low-rank coal by multi-step thermochemical co-treatment method

Both coal-derived sludge and low-rank coal possess significant potential for resource utilization and have garnered considerable attention in recent years. The TG−DTG analysis method showed that the thermal conversion components of coal-derived sludge tended to migrate to coal and interacted with low-rank coal. The dewatering effect of low-rank coal on coal-derived sludge was investigated using the sludge-specific resistance to filtration (SRF) method. The results showed that the addition of coal promoted the transformation of interstitial water and surface water of sludge, especially the interstitial water to free water. Dewatering and deoxidation of low-rank coal and coal-derived sludge were realized by decarboxylation and C−O bond cleavage on benzene during hydrothermal co-treatment at 140−220 ℃. The average water content of hydrochar was 3.96 % after hydrothermal co-treatment, and its calorific value increased from 19.77 MJ/kg to 21.74 MJ/kg after hydrothermal co-treatment. Hydrothermal oil was produced during hydrothermal co-treatment. GC−MS analysis showed that the contents of N and S increased in the hydrothermal oil with the increase of hydrothermal temperature, indicating that the hydrothermal co-treatment can remove the impurity elements (such as N and S) contained in coal-derived sludge and low-rank coal. The pyrolysis experiments of the hydrochar at 600–900 ℃ showed that the hydrochar produced less pyrolysis gas and emitted less CO2 than the result without hydrothermal co-treatment. This study provided an effective strategy for the treatment and resource utilization of sludge and coal.

High-Quality Single-Step Growth of GaAs on C-Plane Sapphire by Molecular Beam

We report on the growth of high-quality GaAs semiconductor materials on an AlAs/sapphire substrate by molecular beam epitaxy. The growth of GaAs on sapphire centers on a new single-step growth technique that produces higher-quality material than a previously reported multi-step growth method. Omega-2theta scans confirmed the GaAs (111) orientation. Samples grown at 700 °C displayed the highest crystal quality with minimal defects and strain, evidenced by narrow FWHM values of the rocking curve. By varying the As/Ga flux ratio and the growth temperature, we significantly improved the quality of the GaAs layer on sapphire, as compared to that obtained in multi-step studies. Photoluminescence measurements at room temperature and 77 K further support these findings. This study underscores the critical role of the As/Ga flux ratio and growth temperature in optimizing GaAs epitaxial growth on sapphire.

Innovative reinforcement method for metal foam cell wall using CNTs

Carbon nanotubes (CNTs) and their composites are gaining popularity due to their exceptional strength qualities. It is well known that adding CNTs to metal foam composites boosts compressive strength. On the other hand CNT addition is still a costly process due to high cost of the CNTs. This study presents a novel and cost-effective solution by selectively adding CNTs to the structurally weakest regions of aluminum foam materials produced via powder metallurgy, employing a newly developed focused multi-step additive method. The cell borders of aluminum foam are strengthened with multiple spherical layers of CNTs, using a transfer method by initially coating the space holders used at the foaming process. The strength increase effect of this CNT addition method was compared with the widely known aluminum foam production parameters via a 4-parameter design of experiment (DOE) study. Compressive strength values of the samples were evaluated using a constant speed compression test acc. to ISO13314. The compacting pressure, CNT concentration, sintering temperature, and sintering period were chosen as DOE parameters, and 78% of the interactions effecting on final compressive strength could be explained with the model. As a result, it was established that, compared to the other parameters, sintering duration had the highest influence on compressive strength. But besides It has also been shown that adding 0.53% CNT by weight only to the cell border regions increases overall strength by 9%. This weight-strength increase ratio is compared with similar studies in the literature and found to be providing a production cost advantage due to the lower amount of CNT addition requirement for the comparable weight relative strength increase. Focused strength increase method has potential to enable controlled failure of foam materials by selectively strengthening strength critical areas of a component.

A shape memory cationized chitosan sponge loaded with thrombin for high-effective hemostasis and antibacterial activity

This study presents a thrombin-loaded cationized chitosan (TCCS) sponge with highly effective hemostatic and antibacterial activity. The TCCS sponge, prepared using a multistep method, features a porous structure, favorable mechanical properties, excellent water absorption ability, and shape recovery triggered by water or blood. The TCCS sponge exhibited strong antibacterial activity against Methicillin-resistant Staphylococcus aureus and Escherichia coli. Additionally, it demonstrated enhanced procoagulant and hemostatic efficacy in rat tail amputation and rat liver perforation wound models compared to commercial hemostats. Furthermore, the sponge exhibited favorable biocompatibility and biosafety. These findings suggest that the TCCS sponge has substantial potential for practical applications in managing severe hemorrhages and bacterial infections.

Evaluation of Nickel-Iron (Oxy)Hydroxide Catalysts in Varied Electrode Geometries Under Industrially Realistic Conditions for Enhanced Alkaline Water Electrolysis

In pursuit of realizing a hydrogen-based economy, the challenge lies in enhancing the efficiency of crucial water electrolysis technologies. Alkaline water electrolysis (AWE) holds promise as an ecologically friendly method for H2 production, primarily due to its capacity for employing non-precious metals as electrocatalysts, in contrast to more costly options which can only switch to noble metals such as ruthenium or iridium. However, this technology faces a significant challenge arising from the sluggish kinetics of the oxygen evolution reaction (OER), which constrains the overall efficiency. [1] Furthermore, the limited stability of many OER catalysts alternatives developed at lab scale and less harsh conditions poses a substantial obstacle to the commercialization of this technology.[2] To overcome this issue, the development of highly active OER catalysts that maintain their activity under industrial conditions is of major importance explaining the growing attention that this topic is gaining in literature. Nevertheless, most of the reported systems are tested at low current densities under easily manageable conditions in the laboratory (≤ 100 mA cm-2, 1 M KOH, RT). Without disagreeing that this approach is necessary to identify promising options among the numerous catalyst systems, it is not sufficient when competing with existing technologies that already achieve high current densities. In this context, we investigate a low-cost, abundantly available non-precious metal based OER-catalyst under industrially relevant conditions (≤ 1.2 A cm-2, 30 wt.-% KOH, 80 °C). The synthesis is based on a multistep galvanic deposition method introduced by Wu et al [3], receiving a highly porous NiFeOOH catalyst. Addressing the complexity of the multiphase process of AWE that involves gas-liquid-solid interfaces, the catalyst system is transferred to numerous nickel electrodes with different 3D geometries (plain woven mesh, knitted mesh, expanded metal mesh) for the investigation of their impact on bubble formation and detachment. To further optimize the catalyst system a variation of the iron content with respect to its’ molar fraction relatively to nickel has been carried out from x(Fe)=0 to x(Fe)=0.75, which after synthesis were first examined using SEM and EDS. The structure can be considered as pompom-shaped particles, forming a porous framework, as can be seen exemplarily in Figure 1a) on a knitted nickel-wire mesh coated with NiFeOOH. Observing variations in iron content, it becomes evident that a higher iron content results in larger particle sizes, thereby altering pore sizes. However, the surface morphologies of each catalyst until a molar fraction x(Fe)=0.5 is reached, can be considered as very similar. When comparing the SEM images of the mesh with a molar fraction x(Fe)=0.75 to the other molar fractions, a secondary phase becomes apparent on the surface. Notably, the porous structure persists within the crystalline phase. It could be shown by EDS that the target values for the molar fractions set in the galvanic bath and the actual molar fractions nearly show no deviations. Further, a uniform dispersion of Ni, Fe and O is observed.The electrochemical investigation of the prepared catalysts was done in a 3-electrode PTFE beaker cell setup in 30 wt % KOH and at 80 °C. The measurement protocol we introduce consists of galvanostatic steps between 0-1.2 A cm-2. The stability is tested chronopotentiometrically as well by maintaining a current density of 500 mA cm-2 for 100 h. It becomes apparent that no optimum is reached in the tested range of iron content and that the potential continues to drop as the molar fraction of Fe increases, achieving the lowest potential with 1.38 V vs. RHE at 50 mA cm-2 and 1.42 V vs. RHE at 750 mA cm-2 with x(Fe)=0.75. It could be further proved that the NiFeOOH catalyst with x(Fe)=0.75 is a highly stable catalyst, resulting in a potential increase of 27 mV over 100 h of testing at 500 mA cm-2, making it to an appropriate OER catalyst for the application in the AWE. The highly porous structure is maintained after testing, proved by SEM imaging. The iron contents after testing are also very similar, which means that there is almost no iron loss in the coating. For the different tested electrode geometries coated with NiFeOOH (x(Fe)=0.5), similar activity is observed, shown in Figure 1b) with a ranging potential between 1.38 V to 1.41 V vs. RHE at 50 mA cm-2 and 1.42 V to 1.45 V vs. RHE at 750 mA cm-2.[1] a) Cao et al., Energy Environ. Sci. 2012 b) Zhao et al., ACS Chemical Reviews 2023.[2] Zeng et al., Journal of Energy Chemistry 2022.[3] Wu et al., Applied Surface Science 2021. Figure 1

Green extraction of chitin from hard spider crab shells

A green protocol to extract chitin from crab shells using water soluble ionic liquids (ILs) is here reported. Compared to conventional multistep acid-base extraction methods, this one-pot procedure achieves pulping of recalcitrant crustacean waste shells by employing ammonium acetate, ammonium formate and hydroxylammonium acetate as water-soluble, low-cost and easy to prepare ILs. An extensive parametric analysis of the pulping process has been carried out with different ILs, different ratios, temperature and time. The optimized protocol provides a high-quality chitin comparable, if not better, to commercial chitin. The best results were obtained at 150 °C with ammonium formate prepared in-situ from aqueous ammonia and formic acid: chitin was isolated in a 17 wt% yield (based on dried crab shells as starting biowaste), a degree of acetylation (DA) > 94 %, a crystallinity index of 39–46 %, a molecular weight up to 6.6 × 105 g/mol and a polydispersity of ca 2.0.

Derivation and Performance Analysis of Composite Trapezoidal Iterative Methods

The pursuit of more efficient and reliable numerical methods to solve nonlinear systems of equations has long intrigued many researchers. Among these, the Broyden method has stood out since its introduction, serving as a foundational technique from which various derivative methods have evolved. These derivative methods, commonly referred to as Broyden-like iterative methods, often surpass the traditional Broyden method in terms of both the number of iterations required and the computational time needed. This study aimed to develop new Broyden-like methods by incorporating weighted combinations of different quadrature rules. Specifically, the research focused on leveraging the Composite Trapezoidal rule with n=3n=3, and comparing it against the Midpoint, Trapezoidal, and Simpson quadrature rules. By integrating these approaches, three novel methods were formulated. The findings revealed that several of these new methods demonstrated enhanced efficiency and robustness compared to their established counterparts. In a detailed comparative analysis with the classical Broyden method and other improved versions, the Midpoint–Composite Trapezoidal (M<i>T_3</i>) method emerged as the top performer. This method consistently provided superior numerical outcomes across all benchmark problems examined in the study. The results highlight the potential of these new methods to significantly advance the field of numerical analysis, offering more powerful tools for researchers and practitioners dealing with complex nonlinear systems of equations. Through this innovative approach, the study not only broadens the understanding of Broyden-like methods but also sets the stage for further advancements in the development of efficient numerical solutions.

Pharmacokinetic Simulation and Area under the Curve Estimation of Drugs Subject to Enterohepatic Circulation.

Enterohepatic circulation (EHC) is a complex process where drugs undergo secretion and reabsorption from the intestinal lumen multiple times, resulting in pharmacokinetic profiles with multiple peaks. The impact of EHC on area under the curve (AUC) has been a topic of extensive debate, questioning the suitability of conventional AUC estimation methods. Moreover, a universal model for accurately estimating AUC in EHC scenarios is lacking. To address this gap, we conducted a simulation study evaluating five empirical models under various sampling strategies to assess their performance in AUC estimation. Our results identify the most suitable model for EHC scenarios and underscore the critical role of meal-based sampling strategies in accurate AUC estimation. Additionally, we demonstrate that while the trapezoidal method performs comparably to other models with a large number of samples, alternative models are essential when sample numbers are limited. These findings not only illuminate how EHC influences AUC but also pave the way for the application of empirical models in real-world drug studies.

An adaptive numerical method for multi-cellular simulations of tissue development and maintenance

In recent years, multi-cellular models, where cells are represented as individual interacting entities, are becoming ever popular. This has led to a proliferation of novel methods and simulation tools. The first aim of this paper is to review the numerical methods utilised by multi-cellular modelling tools and to demonstrate which numerical methods are appropriate for simulations of tissue and organ development, maintenance, and disease. The second aim is to introduce an adaptive time-stepping algorithm and to demonstrate it’s efficiency and accuracy. We focus on off-lattice, mechanics based, models where cell movement is defined by a series of first order ordinary differential equations, derived by assuming over-damped motion and balancing forces. We see that many numerical methods have been used, ranging from simple Forward Euler approaches through to higher order single-step methods like Runge–Kutta 4 and multi-step methods like Adams–Bashforth 2. Through a series of exemplar multi-cellular simulations, we see that if: care is taken to have events (births deaths and re-meshing/re-arrangements) occur on common time-steps; and boundaries are imposed on all sub-steps of numerical methods or implemented using forces, then all numerical methods can converge with the correct order. We introduce an adaptive time-stepping method and demonstrate that the best compromise between L∞ error and run-time is to use Runge–Kutta 4 with an increased time-step and moderate adaptivity. We see that a judicious choice of numerical method can speed the simulation up by a factor of 10–60 from the Forward Euler methods seen in Osborne et al. (2017), and a further speed up by a factor of 4 can be achieved by using an adaptive time-step.

Stability of implicit deferred correction methods based on BDF methods

The Dahlquist barrier states that the highest attainable order for an A-stable linear multistep method is limited to 2. In this paper, we adopt the deferred correction approach with the BDF methods to develop A-stable third and fourth-order multistep methods with low stages. The stability of the methods is investigated to show how A-stability can be achieved. Numerical experiments are conducted to validate the accuracy and stability of the proposed methods when applied to stiff problems.

Study of a Numerical Integral Interpolation Method for Electromagnetic Transient Simulations

In the fixed time-step electromagnetic transient (EMT)-type program, an interpolation process is applied to deal with switching events. The interpolation method frequently reduces the algorithm’s accuracy when dealing with power electronics. In this study, we use the Butcher tableau to analyze the defects of linear interpolation. Then, based on the theories of Runge–Kutta integration, we propose two three-stage diagonally implicit Runge–Kutta (3S-DIRK) algorithms combined with the trapezoidal rule (TR) and backward Euler (BE), respectively, with TR-3S-DIRK and BE2-3S-DIRK for the interpolation and synchronization processes. The proposed numerical integral interpolation scheme has second-order accuracy and does not produce spurious oscillations due to the size change in the time step. The proposed method is compared with the critical damping adjustment method (CDA) and the trapezoidal method, showing that it does not produce spurious numerical oscillations or first-order errors.

A Possible Approach to the Translation Critique of the Chinese New Living Translation: Towards a Combined Holistic Method for Evaluating a “Daughter Translation”

The Chinese New Living Translation (CNLT, 2012) is a daughter translation of the American NLT (1996), a very popular Bible translation in the English-speaking world. By its own account, it follows the style and the character of the American “mother version” with its lively, easy-to-understand and easy-to-read contemporary language, coupled with exegetical accuracy. The interesting question that arises in this paper is how to methodically study the purposes and specifics of a daughter translation such as CNLT. A multi-step method is proposed with the aim of evaluating CNLT with a view to its self-imposed goals. As a short example, the method is applied to a passage in Ps 23 to illustrate the approach. The specific problems of CNLT as a daughter translation such as error propagation and the acceptability problem are addressed in a final hermeneutical and missiological reflection.