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Background: Modifications in Jaffe serum creatinine (sCr) assays question the suitability of the results for direct comparison. Methods: sCr in adult in-patients was routinely measured either by SRM 909-standardized/noncompensated (method A) or isotope dilution mass spectrometry traceable/compensated method (reference). We converted values by method A into values by the reference using a formula provided by the manufacturer [Beckman Coulter (BC)] and traditional equating methods. Results: The BC-based conversion and linear equating resulted in underestimated sCr values, whereas equipercentile equating (EE) provided sCr with not significantly different distribution from the reference values. Proportions of patients with renal impairment did not differ between the reference and EE-converted sCr, as opposed to BC-recalculated values. Three percent of patients were classified into better renal function category when applying BC versus EE conversion. Conclusions: Equipercentile equation was a more accurate method for recalculation of sCr obtained from different Jaffe reaction assays than the linear equating or the BC linear formula. This study emphasizes the importance of the derivation sample specificity when applying research results to other real-world populations. This study was supported by FEDER through the Operational Programme Competitiveness and Internationalization and national funding from the Foundation for Science and Technology (Portuguese Ministry of Science, Technology and Higher Education) under the Unidade de Investigação em Epidemiologia - Instituto de Saúde Pública da Universidade do Porto (EPIUnit) (POCI-01–0145-FEDER-006862; Ref. UID/DTP/04750/2013); the individual PhD Grant SFRH/BD/104037/2014 [“EMR (electronic medical record)-embedded predictive model for acute kidney injury in an acute care hospital”] was co-founded by the FCT and POCH/FSE Program.

Based on the existing analytic solution of two cylindrical bodies in contact, the method of reflected caustics is here employed to obtain the contact length, realized between disc/rings, made of a transparent optically isotropic elastic material, and the jaws of the International Society for Rock Mechanics (ISRM)’ standardized apparatus for the implementation of the Brazilian-disc test. In this context, assuming a negligible refraction index, because of a small thickness of the specimen, the equations of caustics are here rederived, giving emphasis to those due to light reflection from the rear face of the specimen. Revealing some further features relating reflected caustics from the front and rear face of the disc, the contact length is obtained in closed form by the aid of an existing simple linear formula, usually ignored because of unspecified data, defined here in the light of the new evidence.

Katerina Polivanova - Doctor of Sciences in Psychology, Professor, Director of the Center for Modern Childhood Research, Institute of Education, National Research University Higher School of Economics. E-mail: kpolivanova@mail.ruAleksandra Bochaver - Candidate of Sciences in Psychology, Research Fellow, Institute of Education, National Research University Higher School of Economics. E-mail: a-bochaver@yandex.ruAnastasiya Nisskaya - Candidate of Sciences in Psychology, Research Fellow, Institute of Education, National Research University Higher School of Economics. E-mail: anastasiyanisskaya@yandex.ruAddress: 20 Myasnitskaya St., 101000 Moscow, Russian FederationThe behavior of fifth-grade students from a Moscow school was observed during 12 weeks as an iteration of a similar project undertaken in the mid‑1960s [Elkonin, Dragunova 1967]. Since the original research results were represented not as a text but as individual descriptions of 13 school students, observation criteria had to be identified. The criteria were grouped into so-called spheres, describing how teenagers behave among peers, at home, and at school. The key behavioral characteristic was the indicators of the emerging feeling of adulthood in school children, i. e. of the drive for grown-up behavior, associated with freedom and responsibility. These criteria formed the basis of the 2016 observation program. The diversity of adolescent behavioral patterns has been found to be much greater than in the original study. In addition, the linear formula of the value of learning being replaced with that of communication with peers (close interpersonal relationships) has been brought into question. As it transpires, the value of learning remains high for most fifth-graders, regardless of whether they need communication or not. Such an attitude towards learning might be encouraged by family and school, which is typical for this category of children. Four types of school students have been identified based on the indicators of their interest in learning and communication. The article cites fragments of observation protocols and semi-structured interviews. Hypotheses on how the transition to adolescence is affected by family and school characteristics have been put forward, and further observations of school students with different background have been designed.

The mechanical properties of frozen soils are closely related to the unfrozen water content. It has been generally recognized that the unfrozen water content varies with plasticity of soils, while the quantitative relationship between the plastic index and the unfrozen water content is yet to be further examined. This paper takes soil samples with different plasticity as study objects, which are prepared from two typical soil materials, i.e., the Chinese ISO standard sand and bentonite. Nuclear magnetic resonance (NMR) is used to measure the unfrozen water content of soil samples under different temperatures. Test results show that there are three stages in the soil-freezing characteristic curve (SFCC), i.e., the super-cooling stage, the rapid-drop stage and the stable stage. With the increase of the plasticity index, the super-cooling stage is less significant, while the curve in the rapid-drop stage becomes gentler. In the stable stage, the unfrozen water content is barely affected by plasticity. A piecewise function consisting of a linear formula and a power formula is then proposed to describe the SFCC, where the formula parameters are functions of the plastic index. It is found that the unfrozen water content calculated by the proposed formula agrees with the measured results.

For three-dimensional bio-printed cell-laden hydrogel tissue constructs, the well-designed internal porous geometry is tailored to obtain the desired structural and cellular properties. However, significant differences often exist between the designed and as-printed scaffolds because of the inherent characteristics of hydrogels and cells. In this study, an iterative feedback bio-printing (IFBP) approach based on optical coherence tomography (OCT) for the fabrication of cell-laden hydrogel scaffolds with optimal geometrical fidelity and cellular controllability was proposed. A custom-made swept-source OCT (SS-OCT) system was applied to characterize the printed scaffolds quantitatively. Based on the obtained empirical linear formula from the first experimental feedback loop, we defined the most appropriate design constraints and optimized the printing process to improve the geometrical fidelity. The effectiveness of IFBP was verified from the second run using gelatin/alginate hydrogel scaffolds laden with C3A cells. The mismatch of the morphological parameters greatly decreased from 40% to within 7%, which significantly optimized the cell viability, proliferation, and morphology, as well as the representative expression of hepatocyte markers, including CYP3A4 and albumin, of the printed cell-laden hydrogel scaffolds. The demonstrated protocol paves the way for the mass fabrication of cell-laden hydrogel scaffolds, engineered tissues, and scaled-up applications of the 3D bio-printing technique.

A method for determining the proportionality coefficient K in the Rusanov linear formula σ = KR for the surface tension σ of a small object using the size dependence e(R) of the specific total surface energy (R is the particle radius) is proposed. Unlike the function σ(R), the dependence e(R) is easily found as a result of the computer simulation of nanoparticles.

Infrared spectroscopy was used for tea polyphenols detection of 14 cultivars tea.Characteristic wavenumbers were selected using PLS, iPLS, biPLS, and random frog.Quantitative determination of tea polyphenols was achieved based on the characteristic wavenumbers.Infrared spectroscopy in tea polyphenols determination is promising. The potential of infrared spectroscopy for fast determination of tea polyphenols (TP) of 14 cultivars of tea trees was investigated based on data mining technique. And the TP determination models were respectively developed for large leaf cultivars, middle leaf cultivars and all the cultivars. Interval partial least squares (iPLS) was proposed to extract and optimize feature from full-spectrum data. Regression models were respectively established based on PLS, iPLS and biPLS. Modeling results showed that the model based on the biPLS with the optimal subinterval selection (2452-dimensional wavenumbers) outperformed the other models, and the optimal regression model was obtained with high validation correlation of 0.9059, and low RMSE of 1.0277. On the basis of the optimal subinterval selection from biPLS, a further excavation of characteristic wavenumber was done by random frog. Thus, 18 optimal wavenumbers were selected for the TP determination, and the corresponding linear formula of the TP measurement was established. The results proved the feasibility of infrared spectra for measurement of the TP content of tea.

Aims. We investigated whether self-monitoring of blood glucose could be used to assess dawn phenomenon in Chinese people with type 2 diabetes mellitus (T2DM).Methods. A total of 306 people with T2DM underwent continuous glucose monitoring and self-monitoring of blood glucose for 72 h. A linear model was used to fit the optimal linear formula of the magnitude of dawn phenomenon (ΔDawn) and self-monitoring of blood glucose values.Results. The prevalence of dawn phenomenon was similar within different oral antidiabetic drug groups (42.5%, 31.5%, and 40.9%,P=0.216). Multiple variable linear regression showed that prebreakfast, prelunch, and predinner glucose measurements were independently and significantly correlated with ΔDawn. The linear formula between ΔDawn and blood glucose was as follows:ΔDawn mg/dL=0.557×prebreakfast−0.065×prelunch−0.164×predinner−20.894 mg/dL(adjustedR2=0.302,P=0.000).Conclusions. Dawn phenomenon could be partly assessed by blood glucose self-monitoring in Chinese people with T2DM using the abovementioned formula. The incidence of dawn phenomenon was similar among patients in different oral antidiabetic drug groups.

Recommender systems provide useful recommendations to a set of users for items or products that may be of interest to them. Several techniques have been proposed for recommendation such as collaborative, content-based, knowledge-based, and demographic techniques. Each of these techniques suffers from scalability, data sparsity, and cold-start problems when applied individually resulting in poor quality recommendations. This paper proposes an adaptive hybrid recommender system that combines multiple techniques together to enhance the overall recommendation process. Collaborative filtering and demographic techniques are combined in a weighted linear formula. Experiment results using movieLen dataset show that this adaptable hybrid framework is able to outperform the weaknesses shown by traditional recommendation techniques.

The creep-fatigue life of a cast Ti-45Al-8.0Nb-0.2W-0.2B-0.1Y (at.%) alloy was investigated at 750 °C by the consideration of effective dwell time. The life to failure decreases linearly with the increase of effective dwell time, and decreases exponentially with the increase of minimum creep rate. A linear formula and a power-law formula for the life prediction of creep-fatigue were proposed. Both creep-fatigue life prediction formulae have a good agreement with the experimental data.

Although the fly ash concrete with machine-made sand (MSFAC) was widely used in recent years in China, it was lack of studies on relations of compressive strength at different ages. According to the specification of Chinese standard, there are three ways of admixing fly ash (FA) into concrete, i.e. the additional admixing, the equal-mass replacing cement and the over-mass replacing cement. In this paper, 56 groups test data with additional admixing FA, 98 groups test data with equal-mass replacing cement and 86 groups test data with over-mass replacing cement for MSFAC are summarized from published references. Three linear formulas and Slatter formulas are fitted and compared for MSFAC by the different methods of admixing FA, all of them have good fitness with test data. The compressive strength at 28d can be predicted by the compressive strength at 7d with linear formula and Slatter formula for MSFAC.

Using non-equilibrium molecular dynamics simulations, we have studied the effect of disorder on the thermal conductivity of two-dimensional (2D) C1−xNx alloys. We find that the thermal conductivity not only depends on the substitution concentration of nitrogen, but also strongly depends on the disorder distribution. A general linear relationship is revealed between the thermal conductivity and the participation ratio of phonons in 2D alloys. Localization mode analysis further indicates that the thermal conductivity variation in the ordered alloys can be attributed to the number of inequivalent atoms. As for the disordered alloys, we find that the thermal conductivity variation can be described by a simple linear formula with the disorder degree and the substitution concentration. The present study suggests some general guidance for phonon manipulation and thermal engineering in low dimensional alloys.

The special wind compensation system recently adopted by Federation Internationale de Ski (FIS; International Ski Federation) to consider the effects of changing wind conditions has caused some controversy. Here, the effect of wind on jumping distance in ski jumping was studied by means of computer simulation and compared with the wind compensation factors used by FIS during the World Cup season 2009/2010. The results showed clearly that the effect of increasing head/tail wind on jumping distance is not linear: +17.4 m/ − 29.1 m, respectively, for a wind speed of 3 m/s. The linear formula used in the trial period of the wind compensation system was found to be appropriate only for a limited range of jumping distances as the gradient of the landing slope slows down the rate of distance change in long jumps.

Objective To develop an age-based weight estimation rule in a Chinese population and to compare its performance with existing formulae. Design Population-based observational study. Setting Schools and kindergartens in Hong Kong. Subjects Healthy Chinese children aged 1–10 years old on their last birthday. Interventions Weight was measured to the nearest 0.2 kg. Main outcome measures Linear regression was used to derive a simple formula relating weight to the child's age on his or her last birthday. The accuracy and precision of different age-based weight formulae was compared using coefficient of variation, Bland Altman plots, and by determining the proportion of children with estimates >30% outside the actual weight. Results The Chinese Age Weight Rule is a simple linear formula that is more accurate than and at least as precise as any other age-based weight estimation rule: weight in kg=(3×age last birthday)+5. It is accurate and precise in children

The paper compares various methods for computing the equivalent stress amplitude for stress cycles of non-zero mean value in stress-life fatigue prediction. A set of 11 calculation methods is evaluated. In addition to formulations based on common static or fatigue properties, the Walker formula and the generalized Linear formula are included in the investigation. These two methods use an optimization routine to find the material parameters. The final response of the methods is compared and discussed. The Walker method provides a better solution. The generalized Linear method produces inferior results, i.e. the linear fit of the segment of the Haigh diagram is not an optimal solution.

In the present paper, the effects of side slopes, bed slopes and bed roughness on the flow over free overfalls in triangular channels have been studied experimentally. For this purpose, three models of triangular channels with free overfalls have been constructed and fixed in a 6m length laboratory flume. These three models had length of 244cm with different values of side slopes (Z) (0.8(H):1(V), 1:1 and 1.33:1). Each one of these models had four different bed slopes (S) (0, 0.0041, 0.0082 and 0.0123). For each bed slope, the bed was roughened with three particle sizes of sand (ds) (1.18mm, 2.36mm, and 4.75mm). The experimental testing program included sixteen series of experiments for each model. Four of them were for smooth beds and twelve for rough beds. A total of forty eight experiments were tested for different rates of discharge (Q). Experimental results of all models showed that Froude number (Frb) of flow decreases with the increasing of end depth ratio values (yb/yc) for different bed roughness, different bed slopes. The relations between the brink depth (yb) and the critical depth (yc) were found to be a simple linear formula for various bottom slope and different bottom roughness. An empirical expression was obtained for the flow over the free overfall in triangular channels for different bed slopes and roughness. The results of the present study have been compared with studies were obtained by other investigators, the comparison shows a very good agreement between them.

It has been suggested that the static lateral response procedure for a base-isolated structure presented in the International Building Code (IBC) somewhat overestimates the seismic storey force. In this paper an IBC-equivalent static method for base-shear distribution of seismic isolated structures is evaluated. The results of the equivalent static procedure in the vertical distribution of base shear are compared with results obtained from dynamic linear and nonlinear analysis and the efficiency of its application is studied. In general, the results of the equivalent lateral response procedure in the proposed triangular distribution of base shear are somewhat conservative. Based on linear and nonlinear analysis results of isolated structures, therefore, two new formulae are proposed for the vertical distribution of the base shear. The proposed linear formula is based on the first mode shape of the isolated structure and the nonlinear formula follows three first mode shapes, which imply contribution of higher modes in a more realistic nonlinear analysis. The accuracy of the new formulae is examined by comparing the results obtained from this study with those calculated from linear and nonlinear time history analysis.

When nucleotide (G, C, T and A) contents were plotted against each nucleotide, their relationships were clearly expressed by a linear formula, y = alphax + beta in the coding and non-coding regions. This linear relationship was obtained from the complete single-stranded DNA. Similarly, nucleotide contents at all three codon positions were expressed by linear regression lines based on the content of each nucleotide. In addition, 64 codon usages were also expressed by linear formulas against nucleotide content. Thus, the nucleotide content not only in coding sequence but also in non-coding sequence can be expressed by a linear formula, y = alphax + beta, in 145 organisms (112 bacteria, 15 archaea and 18 eukaryotes). Based on these results, the ratio of C/T, G/T, C/A or G/A one can essentially estimate all four nucleotide contents in the complete single-stranded DNA, and the determination of any ratio of two kinds of nucleotides can essentially estimate four nucleotide contents, nucleotide contents at the three different codon positions and codon distributions at 64 codons in the coding region. The maximum and minimum values of G content were approximately 0.35 and approximately 0.15, respectively, among various organisms examined. Codon evolution occurs according to linear formulas between these two values.

The decoupling statuses of the consumption of 22 kinds of metal with economic growth were analyzed. Metals were Fe, Al, Cu, Cr, Zn, Mn, Pb, Ni, Co, Sn, Sb, Si, Mo, W, Li, In, Ga, Ag, Au, Pt, Pd and rare earths. The relations of the annual consumption per capita of each metal to GDP per capita were approximated into two steps of liner formulas; yM=aM, 1 X (X cM), where yM is the annual consumption of the metal M per capita, X is GDP per capita. The metal which has only single relation of yM=aM, 1 X was judged to stay in the state of coupling. When aM, 1>aM ,2, the state was judged to be decoupling. Furthermore, it was judged to be the status of an absolute decoupling when aM, 2

Suppression of type I migration is essential for the retention of protoplanetary cores which are sufficiently massive to accrete gas in their nascent disks and evolve into gas giant planets. We explore here the possibility that special disk properties at the snow line may be the dominant process which stalled the type I migration. We simply use a 1-D model to calculate the torque with linear formula and find that, if the surface density jump near snowline is great enough, the migration can be efficiently slowed down or even halted. This mechanism offers an explanation to the observed peak, at 2–3 AU, in the extra solar planets' semi major axis distribution.

Aim Currently, the widely adopted renal dynamic imaging in clinical practice uses Gates' method to calculate the glomerular filtration rate (GFR), but many researchers have proven that Gates' method may result in bias. Thus, this article explores alternative improved formulae to calculate GFR by renal dynamic imaging. Methods Three hundred and sixty-seven patients were selected and their GFR values were measured using renal dynamic imaging and the two-plasma method with 99mTc-diethylenetriaminepentaacetic acid (99mTc-DTPA) as the imaging agent. With the two-plasma GFR as reference value, two equations were obtained from linear and non-linear regression analyses between the renal uptake percentage and two-plasma GFR. The 367 patients were divided into two random groups, with the first group used to derive the regression formulae and the second to verify the formulae. Finally, all patients were studied to derive the formulae to calculate GFR. The comparison of our formulae with the commonly used Gates' formula was conducted by the Bland-Altman method. Results The linear and non-linear GFR formulae were as follows: GFR (ml/min/1.73 m2)=(631.633 x renal uptake percentage - 2.040) x 1.73/BSA (BSA, body surface area) and GFR (ml/min/1.73 m2)=(-1996.585 x renal uptake percentage2 + 1013.526 x renal uptake percentage - 12.739) x 1.73/BSA, respectively. The biases of the GFR values calculated using the linear and non-linear formulae and Gates' formula relative to the two-plasma GFR were -2.5 +/- 19.1 ml/min/1.73 m2, -2.0 +/- 19.3 ml/min/1.73 m2 and 3.4 +/- 19.4 ml/min/1.73 m2, respectively. Conclusions The GFR values calculated using our new formulae correlate better with the reference GFR value than does GFR calculated by Gates' formula, and the GFR values measured using the non-linear formula are more accurate than those obtained using the linear formula.

The aim of the study was to evaluate the effect that coronary artery bypass grafting (CABG) and aneurysmectomy in the same session have on QT dispersion (QTd) in moderate or severe left ventricular dysfunction.Forty-four patients underwent QT interval analyses before and 1 month after aneurysmectomy and CABG. QT interval and QTd were corrected for heart rate using the square root formula of Bazett (QTCB), the cubic root formula of Fridericia (QTCF), and the linear formula of Sagie et al (QT CS ).The mean pre- and postsurgery QTd results were 65.29 +/- 29.25 and 51.76 +/- 18.49 milliseconds, respectively; the corresponding findings for QT CF were 68.06 +/- 31.26 and 55.16 +/- 24.56 milliseconds; and the corresponding findings for QT CS were 66.53 +/- 32.22 and 51.10 +/- 18.29 milliseconds. With these 3 methods, the postoperative findings were significantly lower than the preoperative findings ( P.05 for all). In contrast, the opposite was true with the QT CB method (preoperative 71.1 +/- 65.80 vs postoperative 76.43 +/- 7.96 milliseconds, P.05).The study showed that based on the methods of Fridericia (QT CF ) and Sagie et al (QT CS ), QT intervals are significantly decreased after CABG and aneurysmectomy.

There is no simple and general relationship between the thermal conductivity of a soil, λ, and its volumetric water content, θ, because the porosity, n, and the thermal conductivity of the solid fraction, λ s , play a major part. Experimental data including measurements of all the variables are scarce. Using a numerical modelling approach, we have shown that the microscopic arrangement of water influences the relation between A and 0. Simulated values for n ranging from 0.4 to 0.6, λ s ranging from 2 to 5 W m -1 K -1 and θ from 0.1 to 0.4 can be fitted by a simple linear formula that takes into account n, λ s and θ. The results given by this formula and by the quadratic parallel (QP) model widely used in physical property studies are in satisfactory agreement with published data both for saturated rocks and for unsaturated soils. Consequently, the linear formula and the QP model can be used as practical and efficient tools to investigate the effects of water content and porosity on the thermal conductivity of the soil and hence to optimize the design of thermal in situ techniques for monitoring water content.

The amount of the consumption of ready-mixed concrete was defined as the index for the amount of the structures constructed. The regional difference in the amount of the investment for construction in Japan was characterized in terms of the amount of the structures constructed, that is, the amount of consumption of ready-mixed concrete. The relationship between the population density and the amount of the consumption of ready-mixed concrete per unit area in each prefecture in Japan was revolved by linear formula and the correlation was higher than the relationship between the population and the consumption of ready-mixed concrete in each prefecture. The intercept and the inclination of the linear relationship were proposed as the indices for the characteristics of the investment for construction.

Statistical results of all the 1621 failure analyses, which cover a four-year effort, are presented. The failure analyses were part of an elaborate test and ESS process of a high-reliability system. Of the failure analyses, 97.5% identified the root cause. The classification of the failures by 11 root cause classes, including the test and ESS process itself is provided. The distribution of failure root causes detected during the various phases of the process is shown. Each test phase was analyzed according to the share of failures found and the fraction of failures that occurred during that phase. Applying a linear formula that summarizes the relative efficacy of each test phase compares the performances of the various phases. The term efficacy is used to describe the ability of a test phase to reveal failures without generating new problems. Copyright © 2002 John Wiley & Sons, Ltd.

This paper gets the Q through the AVF inversion which uses the new frequency dependent absorptive reflectivity linearization and the least-squares method. The new linear formula expands the suggest that elastic overburden overlays a high attenuation target to those that any (elastic or attenuate) overburden overlays a high attenuation target. So the new linear formula makes the expression more reasonable and more universal. Besides that, AVF inversion is unstable because of wavelet and noise. So we develop a method here of casting the AVF inverse problem as a leastsquares minimization problem. The results show that leastsquares AVF inversion can get exact and stable Q.

Knowledge of rock alteration can be used to give a reliable zonation of a dam foundation for grouting purposes. Rock alteration does affect both water-loss and the uptake of grout by the rock, and the existence of a close connection between water-loss and grout consumption has been accepted for years. However, the strength of this relationship is still debated and at the same time rock alteration is not considered to be possible indicator of grout consumption. In this study, the effect of rock alteration upon permeability and grout consumption has been investigated using the results of grouting at the Yenihayat Dam in Turkey. Using a geological field study, the alteration categories at the investigation area are identified, and zonation of the dam site according to these categories is made. The need for grouting was determined with the help of these alteration categories and these conjectures are tested using the results of injection work. Furthermore, the relationship between water-loss and grout take is investigated and a linear formula with a moderate explanatory power is established by statistical analysis. The formula also has a physical interpretation. This study shows that zonation according to the alteration degree can be a useful approach for grouting decisions. Similar studies at different sites and on different rock types are needed to verify the validity of this approach. (C) 2000 Elsevier Science B.V. All rights reserved.

A simple linear formula is developed for estimation of the mass exchange rate between an adsorbent particle and its surroundings undergoing a cyclic change in concentration. The formula is shown to be valid for any cycle period, and the coefficients in the formula are simple functions of the cycle period and fully predicted. Sample calculations demonstrated that the formula provides an excellent representation of the mass exchange rate in cyclic adsorption systems.

We present a new analysis of the dependence of electrical conductivity on liquid fraction for a foam. Ignoring the contribution of the films to both the liquid content and the conductivity, we consider only the network of liquid-filled Plateau borders and the junctions at which they meet. The effect of the junctions is calculated in the form of a vertex correction to both the conductivity and liquid fraction of the network. The correction is sufficient to account for the deviation from the linear formula of Lemlich for liquid fractions up to about 10%.

It is argued here that there is not necessarily a contradiction between the general linear and equal ratio approaches to equity, and the two may be integrated to make more precise predictions. It was hypothesized that, (a) equity is best represented by a limited equal ratio rule ; (b) the more a linear distribution systematically deviates from equal input/outcome ratios, the more unfair it will be judged, but (c) subjects will prefer a distribution that accords with a general linear formula in certain cases where an equal ratio distribution of available outcomes would actually infringe a preeminent or established equal ratio distribution. Four studies are presented, the results of which seem broadly to support these ideas. However, the results also suggest that equity judgments can be strongly influenced by framing effects.

International audience; The aim of the paper is to provide a linearization approach to the $\mathbb{L}^{\infty}$-control problems. We begin by proving a semigroup-type behaviour of the set of constraints appearing in the linearized formulation of (standard) control problems. As a byproduct we obtain a linear formulation of the dynamic programming principle. Then, we use the $\mathbb{L}^{p}$ approach and the associated linear formulations. This seems to be the most appropriate tool for treating $\mathbb{L}^{\infty}$ problems in continuous and lower semicontinuous setting.