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Price promotions are a common tool used by retailers to increase sales. This study aims to investigate the effect of consumer's numerical skills and other demographic characteristics on their ability to determine the best deal when conducting a grocery shop (referred to as deal competency).

A consumer survey (n = 308) was conducted online, collecting information about respondent's demographics and grocery shopping behaviours, numerical literacy using the subjective numeracy scale (SNS), and deal competency (a novel measure). Multiple regression analysis and Pearson's correlations were conducted using SPSSv26.

Overall, the mean SNS score for the total sample was 31.47 (SD = 8.27), and the mean sample deal competency score was 13.5 (SD = 2.3). Spearman's correlation analysis identified a moderate significant positive relationship between numerical skills and deal competency, r_s(303) = 0.360, p < 0.001. Regression analysis found significant positive relationships between numerical skills and being male, and with mathematical achievement; and between deal competency and age, mathematical achievement and educational achievement. Regarding buying behaviour, correlation analyses identified only one significant relationship between numerical skills (SNS score) and deal competency and variables relating to buying behaviour, namely a negative relationship between deal competency and amount spent on promotional food items in top up grocery shops.

This study contributes to the gap in literature regarding consumer ability to work out the best deal on promotions, presents a novel scale for describing consumer deal competency, and considers the comparative usefulness of using objective and subjective scales in similar studies.

This study aims to develop an experimentally validated three-dimensional numerical model for predicting different flow patterns produced with a gas dynamic virtual nozzle (GDVN).

The physical model is posed in the mixture formulation and copes with the unsteady, incompressible, isothermal, Newtonian, low turbulent two-phase flow. The computational fluid dynamics numerical solution is based on the half-space finite volume discretisation. The geo-reconstruct volume-of-fluid scheme tracks the interphase boundary between the gas and the liquid. To ensure numerical stability in the transition regime and adequately account for turbulent behaviour, the k-ω shear stress transport turbulence model is used. The model is validated by comparison with the experimental measurements on a vertical, downward-positioned GDVN configuration. Three different combinations of air and water volumetric flow rates have been solved numerically in the range of Reynolds numbers for airflow 1,009–2,596 and water 61–133, respectively, at Weber numbers 1.2–6.2.

The half-space symmetry allows the numerical reconstruction of the dripping, jetting and indication of the whipping mode. The kinetic energy transfer from the gas to the liquid is analysed, and locations with locally increased gas kinetic energy are observed. The calculated jet shapes reasonably well match the experimentally obtained high-speed camera videos.

The model is used for the virtual studies of new GDVN nozzle designs and optimisation of their operation.

To the best of the authors’ knowledge, the developed model numerically reconstructs all three GDVN flow regimes for the first time.

Because of the anisotropy of the process and the variability in the quality of printed parts, finite element analysis is not directly applicable to recycled materials manufactured using fused filament fabrication. The purpose of this study is to investigate the numerical-experimental mechanical behavior modeling of the recycled polymer, that is, recyclable polyethylene terephthalate (rPET), manufactured by a deposition FFF process under compressive stresses for new sustainable designs.

In all, 42 test specimens were manufactured and analyzed according to the ASTM D695-15 standards. Eight numerical analyzes were performed on a real design manufactured with rPET using Young's compression modulus from the experimental tests. Finally, eight additional experimental tests under uniaxial compression loads were performed on the real sustainable design for validating its mechanical behavior versus computational numerical tests.

As a result of the experimental tests, rPET behaves linearly until it reaches the elastic limit, along each manufacturing axis. The results of this study confirmed the design's structural safety by the load scenario and operating boundary conditions. Experimental and numerical results show a difference of 0.001–0.024 mm, allowing for the rPET to be configured as isotropic in numerical simulation software without having to modify its material modeling equations.

The results obtained are of great help to industry, designers and researchers because they validate the use of recycled rPET for the ecological production of real-sustainable products using MEX technology under compressive stress and its configuration for numerical simulations. Major design companies are now using recycled plastic materials in their high-end designs.

Validation results have been presented on test specimens and real items, comparing experimental material configuration values with numerical results. Specifically, to the best of the authors’ knowledge, no industrial or scientific work has been conducted with rPET subjected to uniaxial compression loads for characterizing experimentally and numerically the material using these results for validating a real case of a sustainable industrial product.

This paper aims to analyze the propulsive performance of small-amplitude pitching foils at very high frequencies with double objectives: to find out scaling laws for the time-averaged thrust and propulsive efficiency at very high frequencies; and to characterize the Strouhal number above which the effect of turbulence on the mean values cannot be neglected.

The thrust force and propulsive efficiency of a pitching NACA0012 foil at high reduced frequencies (k) and a Reynolds number Re = 16 000 are analyzed using accurate numerical simulations, both assuming laminar flow and using a transition turbulence model. The time-averaged results are validated with available experimental data for k up to about 12 (Strouhal number, St, up to 0.6). This study also compares the present numerical results with the predictions of theoretical models and existing numerical results. For a foil pitching about its quarter chord with amplitude α₀ = 8^o, the reduced frequency is varied here up to k = 30 (St up to 2), much higher than in any previous numerical or experimental work.

For this pitch amplitude, turbulence effects are found negligible for St ≲ 0.8, and affecting less than 10% to the time-averaged thrust coefficient CT¯ for larger St Linear potential theory fails for very large k, even for the small pitch amplitude considered, particularly for the power coefficient, and therefore for the propulsive efficiency. It is found that CT¯ ∼ St² for large St, in agreement with recent models, and the propulsive efficiency decays as 1/k, in disagreement with the linear potential theory.

Pitching foils are increasingly studied as efficient propellers and energy harvesting devices. Their performance at very high reduced frequencies has not been sufficiently analyzed before. The authors provide accurate numerical simulations to discern when turbulence is relevant for the computation of the time-averaged thrust and efficiency and how their scaling with the reduced frequency is affected in relation to the laminar-flow predictions. This is relevant because some small-amplitude theoretical models predict high propulsive efficiency of pitching foils at very high frequencies over certain ranges of the structural parameters, and only very accurate numerical simulations may decide on these predictions.

The purpose of this paper is to describe the approach for the design of cowlings for a new fast helicopter from the perspective of airworthiness requirements regarding high-speed impact resistance.

Validated numerical simulation was applied to flat and simple curved test panels. High-speed camera measurement and non-destructive testing (NDT) results were used for verification of the numerical models. The final design was optimized and verified by validated numerical simulation.

The comparison between numerical simulation based on static material properties with experimental results of high-speed load shows no significant influence of strain rate effect in composite material.

Owing to the sensitivity of the composite material on technology production, the results are limited by the material used and the production technology.

The application of flat and simple curved test panels for the verification and calibration of numerical models allows the optimized final design of the cowling and reduces the risk of structural non-compliance during verification tests.

Numerical models were verified for simulation of the real composite structure based on high-speed camera results and NDT inspection after impact. The proposed numerical model was simplified for application in a complex design and reduced calculation time.

The purpose of this study is to develop stable, convergent and accurate numerical method for solving singularly perturbed differential equations having both small and large delay.

This study introduces a fitted nonpolynomial spline method for singularly perturbed differential equations having both small and large delay. The numerical scheme is developed on uniform mesh using fitted operator in the given differential equation.

The stability of the developed numerical method is established and its uniform convergence is proved. To validate the applicability of the method, one model problem is considered for numerical experimentation for different values of the perturbation parameter and mesh points.

In this paper, the authors consider a new governing problem having both small delay on convection term and large delay. As far as the researchers' knowledge is considered numerical solution of singularly perturbed boundary value problem containing both small delay and large delay is first being considered.

Buckling should be carefully considered in steel assemblies with members subjected to compressive stresses, such as bracing systems and truss structures, in which angles and built-up steel sections are widely employed. These type of steel members are affected by torsional and flexural-torsional buckling, but the European (EN 1993-1-2) and the American (AISC 360-16) design norms do not explicitly treat these phenomena in fire situation. In this work, improved buckling curves based on the EN 1993-1-2 were extended by exploiting a previous work of the authors. Moreover, new buckling curves of AISC 360-16 were proposed.

The buckling curves provided in the norms and the proposed ones were compared with the results of numerical investigation. Compressed angles, tee and cruciform steel members at elevated temperature were studied. More than 41,000 GMNIA analyses were performed on profiles with different lengths with sections of class 1 to 3, and they were subjected to five uniform temperature distributions (400–800 C) and with three steel grades (S235, S275, S355).

It was observed that the actual buckling curves provide unconservative or overconservative predictions for various range of slenderness of practical interest. The proposed curves allow for safer and more accurate predictions, as confirmed by statistical investigation.

This paper provides new design buckling curves for torsional and flexural-torsional buckling at elevated temperature since there is a lack of studies in the field and the design standards do not appropriately consider these phenomena.

We study an efficient numerical method for pricing European options when the dynamics of the underlying asset are described by Levy processes. In this case. we can write a characteristic function solution for a specific Levy option model and then take its inversion numerically. Specifically we use Variance Gamma process as an example of Levy option model and consider various characteristic function representation forms of European option price such as Carr and Madan (1999), Bakshi and Madan (2000). and Lewis (2001). Fast Fourier Transform method is applied to solve the numerical inversion problem with parameters for the KOSPI 200 options data. After analysing the problems in the FFT method, we propose alternative numerical inversion method, Gaussian Quadrature. This paper reports that Gaussian Quadrature numerical inversion method with the representation form of Bakshi & Madan (2000) is more efficient and accurate than other alternatives considered in this paper.

Emissions produced by oceangoing vessels not only negatively affect the environment but also may deteriorate health of living organisms. Several regulations were released by the International Maritime Organization (IMO) to alleviate negative externalities from maritime transportation. Certain polluted areas were designated as “Emission Control Areas” (ECAs). However, IMO did not enforce any restrictions on the actual quantity of emissions that could be produced within ECAs. This paper aims to perform a comprehensive assessment of advantages and disadvantages from introducing restrictions on the emissions produced within ECAs. Two mixed-integer non-linear mathematical programs are presented to model the existing IMO regulations and an alternative policy, which along with the established IMO requirements also enforces restrictions on the quantity of emissions produced within ECAs. A set of linearization techniques are applied to linearize both models, which are further solved using the dynamic secant approximation procedure. Numerical experiments demonstrate that introduction of emission restrictions within ECAs can significantly reduce pollution levels but may incur increasing route service cost for the liner shipping company.

Two mixed-integer non-linear mathematical programs are presented to model the existing IMO regulations and an alternative policy, which along with the established IMO requirements also enforces restrictions on the quantity of emissions produced within ECAs. A set of linearization techniques are applied to linearize both models, which are further solved using the dynamic secant approximation procedure.

Numerical experiments were conducted for the French Asia Line 3 route, served by CMA CGM liner shipping company and passing through ECAs with sulfur oxide control. It was found that introduction of emission restrictions reduced the quantity of sulfur dioxide emissions produced by 40.4 per cent. In the meantime, emission restrictions required the liner shipping company to decrease the vessel sailing speed not only at voyage legs within ECAs but also at the adjacent voyage legs, which increased the total vessel turnaround time and in turn increased the total route service cost by 7.8 per cent.

This study does not capture uncertainty in liner shipping operations.

The developed mathematical model can serve as an efficient practical tool for liner shipping companies in developing green vessel schedules, enhancing energy efficiency and improving environmental sustainability.

Researchers and practitioners seek for new mathematical models and environmental policies that may alleviate pollution from oceangoing vessels and improve energy efficiency. This study proposes two novel mathematical models for the green vessel scheduling problem in a liner shipping route with ECAs. The first model is based on the existing IMO regulations, whereas the second one along with the established IMO requirements enforces emission restrictions within ECAs. Extensive numerical experiments are performed to assess advantages and disadvantages from introducing emission restrictions within ECAs.