Rational Form Research Articles

Ternary Liquid-Liquid Equilibria in a Few Nonaqueous Two-Phase Systems

AbstractThe composition of coexisting phases for liquid-liquid and solid-liquid-liquid equilibria were measured at 298.2 and 313.2 K and under atmospheric pressure for the following systems: {sodium bromide + formamide + ethyl acetate}, {sodium thiocyanate + ethanol + (R)-limonene}, and {sodium thiocyanate + methanol + dibutyl ether}. These concentrations were determined mainly by chromatography and, for the first system, with the help of argentometric titration. The standard uncertainties in mole fractions varied between 0.001 and 0.008. The tie-line data were reproduced by the NRTL model with medium accuracy. Several empirical equations were used and tested to correlate binodal curves. The rational form of the equation, based on the liquid–liquid–solid tie-line, turned out to be the most adequate.

Militarized policing in the hinterlands: A Blackwater training ground and the cultural conceptions of security

AbstractResearch in recent decades shows that private military and security contractors have reshaped the tenor and reach of US military power abroad while also accelerating the militarization of domestic policing. Previous work on militarized policing has primarily centered on urban environments. This article examines Blackwater North, a facility in a rural Illinois community, which provided privatized, militarized police training from 2007 through 2010. Drawing from newspaper accounts, government records, and ethnographic fieldwork conducted in the community after the facility's closure, I analyze residents’ recollections of the local support of and opposition to Blackwater North. I argue that local supporters promoted a culture of perpetual preparedness that positioned militarized policing as a rational form of harm reduction, as well as one that could yield economic benefits to struggling host communities. I also examine the opposition and analyze the insider/outsider divides that emerged within the debate surrounding Blackwater North. At stake for both supporters and opponents were differing cultural conceptions of what increases, and what erodes, security. This case study focuses on rural spaces’ role in the landscape of militarized policing and illuminates the cultural processes by which privatized military power and militarized policing become accepted and resisted at the community level.

Bifurcation and multi-stability analysis of microwave engineering systems: Insights from the Burger–Fisher equation

The present article depicts the research being done on the microwave effect realized by the often-used Burger-Fisher equation. A particular view is on the emergence of multi-stability and the bifurcations associated with microwave engineering systems. A novel rational, trigonometric, and hyperbolic form of the traveling waves is furnished by the resolution of the non-linear issue with the aid of the advanced exp (−Ψ(η))-expansion function parameterization. Firstly, we will solve the exact form of the Burger-Fisher equation, which clarifies the behavior of the equation in different conditions. Subsequently, bifurcation analysis techniques will be employed to study the nuanced relationship between the system parameters and the emergence of multistability phenomena. Through our results, we exposed the complicated essential features of microwave physics and established crucial parameters that determine a system’s behavior. Next, we cover control principle issues and practical applications in microwave engineering problems. This model accommodates the essential features of multi-stable dynamic systems and provides an important framework for creating microwave devices and circuits.The main aim of this research work is to analyze the phenomenon of multi-stability and bifurcation in microwave engineering systems by applying Burger-Fisher equation. The study intends to obtain new solutions to the PDEs through the application of a new method, the exp (−Ψ(η))-expansion function method that uses rational, trigonometric, and hyperbolic traveling wave solutions. Existing research of the Burger-Fisher equation is not explicit and by solving the exact form the research aims at exploring the different conditions under which the equation behaves and studying the delicate interactions between the parameters of the multistable system.

A design strategy with the combination of neuro-regression and stochastic optimizations on the hyperelastic gasket

For numerous years, PVC and aluminum doors and windows have been integral components of buildings. The primary technical requisites for doors and windows encompass superior acoustic performance, thermal insulation, and effective sealing. Particularly, the sealing properties, crucially important, are ensured by the gaskets fitted onto the profiles. This paper aims to present a gasket design with a new methodology that includes a systematic modeling-optimization process based on multiple non-linear neuro-regression. Comprehensive research has been done by multiple non-linear neuro-regression analyses of gaskets due to deficient studies in the literature on hyperelastic materials. 17 candidate functional forms based on four basic mathematical structures (polynomial, trigonometric, logarithmic, and linear functions, and their hybrid or rational forms) have been proposed to model the FEM data of the gasket. Hybrid versions of three stochastic search algorithms, Differential Evolution, Random Search, and Simulated Annealing, are considered to solve highly non-linear, non-convex, multi-variables mixed continuous-discrete problems. The experimental results were compared with the numerical result using the finite-element analysis (FEA). Nonlinear static analyses were performed with Abaqus. Stress and logarithmic strain distributions are obtained. A good correlation was found between the experimental and the numerical results The optimum locations and numbers of the nodes have been found to obtain the minimum overflow distance and the maximum compression surface area for gaskets having the same topological structure.

Dynamic of bifurcation, chaotic structure and multi soliton of fractional nonlinear Schrödinger equation arise in plasma physics

In this study, we examine the third-order fractional nonlinear Schrödinger equation (FNLSE) in \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(1+1)$$\\end{document}-dimensional, by employing the analytical methodology of the new extended direct algebraic method (NEDAM) alongside optical soliton solutions. In order to better understand high-order nonlinear wave behaviors in such systems, the researched model captures the physical and mathematical properties of nonlinear dispersive waves, with applications in plasma physics and optics. With the aid of above mentioned approach, we rigorously assess the novel optical soliton solutions in the form of dark, bright–dark, dark–bright, periodic, singular, rational, mixed trigonometric and hyperbolic forms. Additionally, stability assessments using conserved quantities, such as Hamiltonian property, and consistency checks were used to validate the solutions. The dynamic structure of the governing model is further examined using chaos, bifurcation, and sensitivity analysis. With the appropriate parameter values, 2D, 3D, and contour plots can all be utilized to graphically show the data. This work advances our knowledge of nonlinear wave propagation in Bose–Einstein condensates, ultrafast fibre optics, and plasma physics, among other areas with higher-order chromatic effects.

Examining the Causal and Heterogeneous Influence of Three-Dimensional Urban Forms on CO2 Emissions in 285 Chinese Cities

Despite the efforts to examine the influence of urban forms on CO2 emissions, most studies have mainly measured urban forms from a two-dimensional perspective, with relatively little attention given to three-dimensional urban forms and their causal relationships. Utilizing the built-up area dataset from the Global Human Settlement Layer (GHSL) project and the carbon emission dataset from the China City Greenhouse Gas Working Group (CCG), we examine a causal and heterogeneous effect of three-dimensional urban forms on CO2 emissions—specifically urban height, density, and intensity—in 285 Chinese cities. The empirical results reveal a robust and positive causal effect of 3D urban forms on carbon emissions. Even when incorporating the spatial spillover effect, the positive effect of 3D urban forms remains. Moreover, GDP per capita and total population have a greater impact on urban CO2 emissions. Additionally, we find that the influence of 3D urban forms on CO2 emissions is U-shaped, with total population serving as a moderating factor in this effect. Importantly, there is significant geographic and sectoral heterogeneity in the influence of 3D urban forms on CO2 emissions. Specifically, the influence of 3D urban forms is greater in eastern cities than in non-eastern cities. Furthermore, 3D urban forms primarily influence household carbon emissions rather than industrial and transportation carbon emissions. Therefore, in response to the growing challenges of global climate change and environmental issues, urban governments should adopt various strategies to develop more rational three-dimensional urban forms to reduce CO2 emissions.

Performance Assessment of a Novel Green Concrete Using Coffee Grounds Biochar Waste

An actual scientific problem in current concrete science is poor knowledge of the problem of modifying concrete with plant waste. At the same time, plant waste benefits from other types of waste because it is a recycled raw material. A promising technological approach to modifying concrete with plant waste is the introduction of components based on the processing of coffee production waste into concrete. This study aims to investigate the use of biochar additives from spent coffee grounds (biochar spent coffee grounds—BSCG) in the technology of cement composites and to identify rational formulations. A biochar-modifying additive was produced from waste coffee grounds by heat treatment of these wastes and additional mechanical grinding after pyrolysis. The phase composition of the manufactured BSCG additive was determined, which is characterized by the presence of phases such as quartz, cristobalite, and amorphous carbon. The results showed that the use of BSCG increases the water demand for cement pastes and reduces the cone slump of concrete mixtures. Rational dosages of BSCG have been determined to improve the properties of cement pastes and concrete. As a result of the tests, it was determined that the ideal situation is for the BSCG ratio to be at a maximum of 8% in the concrete and not to exceed this rate. For cement pastes, the most effective BSCG content was 3% for concrete (3%–4%). The compressive and flexural strengths of the cement pastes were 6.06% and 6.32%, respectively. Concrete’s compressive strength increased by 5.85%, and water absorption decreased by 6.58%. The obtained results prove the feasibility of using BSCG in cement composite technology to reduce cement consumption and solve the environmental problem of recycling plant waste.

Investigation of exact solutions to the (2+1)-dimensional Sakovich equation with time dependent coefficients using analytical methods

In this paper, the exact solutions of the (2 + 1)-dimensional variable coefficient Sakovich equation are investigated. Four distinct analytical methods, containing the unified method, the modified Kudryashov method, the modified G′G2 -expansion method and the improved Riccati sub-equation method, are implemented to find new exact solutions of this equation. Soliton and periodic soliton solutions, elliptic solutions, kink solutions and traveling wave solutions, which are expressed in polynomial, rational, trigonometric and hyperbolic forms, have been obtained and are graphically represented with the aim of exhibiting the structures and dynamic behaviors of the equation. Furthermore, we have discussed the influence of variable coefficients on soliton behaviors in detail.

Mechanisms of dissolution and crystallization of amorphous glibenclamide

Amorphous solid dispersions enhance the dissolution and oral bioavailability of poorly water-soluble drugs. However, the link between polymer properties and formulation performance has not been fully clarified yet. We studied the effect of hydroxypropyl cellulose (HPC) polymers molecular weight (Mw) on the storage stability, dissolution kinetics and supersaturation stability of spray-dried amorphous glibenclamide (GLB) formulations. The solid-state stability of amorphous GLB during storage was significantly enhanced by both the 40 kDa (HPC-SSL) and 84 kDa (HPC-L) polymers, regardless of Mw differences. In contrast, HPC-SSL maintained significantly higher aqueous drug concentrations during dissolution, compared to HPC-L (its higher Mw analogue). Dedicated dissolution experiments, in situ optical microscopy and solid-state characterization revealed that aqueous drug concentrations were determined by the interplay between crystallization inhibition, drug ionization, wetting and solubilization effects: (1) HPC prevents surface nucleation, hence inhibiting crystallization, (2) intestinal colloids (bile salts and phospholipids) increase supersaturated drug concentrations via wetting and solubilization effects and (3) pH and drug ionization severely impact the degree of supersaturation. The better performance of the lower Mw HPC-SSL was due to its superior inhibition of surface crystallization. These insights into the molecular mechanisms of dissolution and crystallization of amorphous solids provide foundation for rational formulation development.

A quantum-corrected Peng‒Robinson equation of state for helium-4 from 3 K to 50 K considering quantum swelling effects through the Feynman‒Hibbs correction of the EXP-6 potential

Accurate and efficient prediction of the properties of helium-4 (He-4) via an equation of state (EOS) is a prerequisite for evaluating liquid helium-4 (LHe-4) storage technology. However, the performance of the Peng–Robinson (PR) EOS in predicting the density of LHe-4 and vapour helium-4 (VHe-4) deteriorates within the thermodynamic ranges of the LHe-4 tank: 3–50 K and 60–600 kPa. To modify the PR EOS, we establish first-order and second-order Feynman–Hibbs (FH)-corrected EXP-6 potentials and propose a reduced effective particle diameter (REPD) correlation with four parameters to consider the quantum swelling effects of LHe-4. On the basis of the rational function form of the REPD correlation, we introduce a quantum-corrected covolume term to develop a regression model for the FH-corrected Peng–Robinson (FH-PR) EOS. Moreover, to improve the effectiveness of regression near the saturation curve, we propose a hypothetical boundary consisting of the saturation curve from 3 K to the critical temperature and a virtual saturation curve from the critical pressure to 600 kPa. The results indicate that the FH − PR EOS shows satisfactory engineering application performance in predicting the density of He-4 within the studied range. Under verification conditions, the average absolute relative deviation (AARD) of the density determined via the FH − PR EOS ranges from 0.72 % to 1.77 %, and the maximum relative deviation (MRD) ranges from 2.17 % to 5.62 %. Under test conditions, the AARD of the density ranged from 1.06 % to 1.71 %, and the MRD ranged from 3.77 % to 7.38 %.

The Particle Drifting Effect: A Combined Function of Colloidal and Drug Properties.

The particle drifting effect, where nanosized colloidal drug particles overcome the diffusional resistance of the aqueous boundary layer adjacent to the intestinal wall and increase drug absorption rates, is drawing increasing attention in pharmaceutical research. However, mechanistic understanding and accurate prediction of the particle drifting effect remain lacking. In this study, we systematically evaluated the extent of the particle drifting effect affected by drug and colloidal properties, including the size, number, and type of the moving species using biphasic diffusion experiments combined with computational fluid dynamics simulations and mass transport analyses. The results showed that the particle drifting effect is a sequential reaction of particle dissolution/dissociation in the diffusional boundary layer, followed by absorption of the free drug. Therefore, factors affecting the rate-limiting step, which can be either process or both under different circumstances, alter the particle drifting effect. Experimental results also agree with the theory that the particle dissolution rate is dependent on particle size, concentration, and drug solubility. In addition, rapid bile micelle dissociation and bile salt absorption facilitated drug absorption by the particle drifting effect. Our findings explain the highly dynamic nature of the particle drifting effect and will contribute to rational formulation development and better bioavailability prediction for formulations containing colloidal particles.

Estimating net energy requirements of male Djallonke sheep

Context Energy requirements in sheep can vary significantly due to various factors, including age, breed, sex and environmental conditions. Genetic selection and crossbreeding further contribute to this variability. Although guidelines from the US and UK national research councils are commonly used for formulating sheep diets, they may not adequately account for the unique characteristics of sheep in Africa. Aims The study aimed to estimate the net maintenance energy requirement of male Djallonke sheep. This estimation will provide a basis for comparing the energy requirements of Djallonke sheep with national recommendations and recent estimates for other sheep breeds. Methods Sixteen entire male Djallonke sheep were selected and grouped by weight. They were then randomly allocated to four treatment groups in a 4 × 4 Latin square design. The sheep were fed to achieve intake levels ranging from 1 to 1.75 multiples of their maintenance energy requirement. Gas exchange data were collected using the GreenFeed system over a 3-day period at the conclusion of each treatment period. Heat production was calculated using the established Brouwer’s equation. A linear regression equation was developed to relate heat production to metabolisable energy intake scaled by metabolic bodyweight to calculate the net energy for maintenance. Key results The estimated net energy for maintenance for male Djallonke sheep was determined to be 0.354 MJ/kg BW0.75. This estimation indicated that the energy requirements of male Djallonke sheep exceeded the recommendations provided by the US National Research Council and the UK Agricultural and Food Research Council. However, it closely aligned with an updated estimate of 0.358 MJ/kg BW0.75. Conclusions Based on the study’s findings, male Djallonke sheep have higher energy requirements for maintenance than what is commonly recommended by existing guidelines. Therefore, it is advisable to update ration formulation software for male Djallonke sheep to better reflect their actual energy requirements for maintenance. Implications These results have practical implications for the formulation of diets and feeding management practices for male Djallonke sheep. Adhering to updated energy requirement estimates can help improve the efficiency and productivity of sheep production in the context of Djallonke sheep farming.

New algorithm for deriving rational form solutions in the generalized Date-Jimbo-Kashiwara-Miwa model

This paper introduces, for the first time, the application of rational form solutions involving sine-cosine and sinh-cosh functions to address a nonlinear model emerging in the realm of plasma physics. The model under consideration is derived from the KP hierarchy and is denoted as the Date-Jimbo-Kashiwara-Miwa equation. In this study, the proposed model is extended to incorporate arbitrary coefficients, encompassing both nonlinearity and dispersion factors. The solutions obtained are presented through 2D and 3D plots, revealing three distinct types of solitary wave propagation: moving singular-periodic, kink, and singular solutions. These solutions, as reported in this work, have the potential for broader applications, including optics and quantum physics.

49 Crossing-talk between micronutrient and macronutrient metabolism: Implication in health and disease

Abstract Recent goals of swine ration formulation have evolved from preventing nutritional deficiency diseases and maximizing growth performance to optimizing immune function and disease resistance with least climate impact. Thus, certain micronutrients such as selenium (Se) are widely considered to be health beneficial at dietary concentrations above nutrient requirements. During the past decade, we have conducted a number of experiments to determine impacts and mechanisms of dietary Se concentrations (0.03 to 1 or 3 mg/kg) on metabolism of carbohydrate, lipid, and protein in pigs from growing to finishing. Strikingly, pigs fed high-Se diets developed hyperinsulinemia and insulin resistance. Those pigs also had increased lipid, protein, saturated fatty acids (myristic, palmitic, stearic, and behenic acids), and aspartic acid, glutamine, and alanine and decreased polyunsaturated fatty acids (dihomo-γ-linolenic, oleic, α-linolenic, and eicosatrienoic acids) in the liver and(or) adipose tissues. The high-Se diets increased and decreased amounts of 5 and 2 selenoproteins, respectively, in tissues of pigs. These effects were associated with down-regulated insulin signaling (INSR and AKT), glycolysis (glucokinase) and gluconeogenesis (PEPCK) and up-regulated lipogenesis (FOXO1, SREBP1, ACC and FAS), and protein synthesis (mTOR and RPS6/S6). In contrast, high dietary fat intakes up- or down-regulated expressions of all selenoproteins except for TXNRD2 and TXNRD3 and showed a strong effect on expressions of DIO2, GPX6, and SELENOK. These induced selenogenome expression changes were associated with increased serum malondialdehyde and plasma concentrations of tumor necrosis factor alpha and interleukin-6, along with risk of obesity and chronic inflammation. Altogether, metabolisms of micronutrients and macronutrients in pigs are coordinated through interdependent and mutually regulated crossing talks at tissue, cellular, biochemical, and signal levels.

Oil unsaturation degree dictates emulsion stability through tuning interfacial behaviour of proteins

The unsaturated vegetable oil is commonly incorporated as protein-stabilized emulsion into fat-substituted emulsified meat products (FSEMP), whose quality is closely related with the emulsion stability. Here, we systematically investigated the effects of oil unsaturation degree (UD) on the interfacial properties (structural changes, adsorption dynamics, interfacial rheology, adsorption layer thickness) of proteins and thus the emulsion stability. The oleic acid and linolenic acid were mixed with dodecane as model oils. Three types of proteins were selected as model emulsifiers (fibrous myofibrillar protein, MP; globular whey protein, WP; random-coiled sodium caseinate, SC). The proteins diffused slower to the higher UD interface, resulting in a lower interfacial pressure. This led to a larger droplet size of the higher UD oil emulsion upon emulsification. However, the proteins penetrated and rearranged faster at the higher UD interface ascribed to a more extensive structural unfolding, enabling the formation of stiffer and thicker adsorption layers. This contributed to a stronger short-term stability of MP- and WP-stabilized higher UD oil emulsion; while for the random-coiled SC, the higher UD oil emulsion was less short-term stable, which was primarily determined by the initial (larger) droplet size but not the interfacial layer properties. The stiffer layer at the higher UD interface was on the other hand less stretchable, which tended to yield when subjected to higher strain. This probably accounted for the weaker long-term stability of the higher UD oil emulsion, regardless of protein types. These results highlighted that the oil UD should be elaborately considered for the rational formulation of FSEMP.

The prospects for the use of alternative gel formers for hydraulic fracturing

The article discusses the relevance of using alternative gel-forming agents in the preparation of fracturing fluids for hydraulic fracturing (HF). Besides the obvious tasks, such as increasing the residual conductivity of the fractures created during stimulation, it also addresses the impact of alternative gelforming agents on the treatment process. The author, supported by field data, concludes that under otherwise equal conditions, replacing traditional fracturing fluids with alternative ones significantly reduces frictional pressure losses in the pipes, which is particularly important when treating deep and extensive horizontal wells with limited internal pipe diameters. Moreover, the aforementioned impact of gel-forming agents on frictional pressure losses allows for a reserve of power in the hydraulic fracturing fleet equipment. Consequently, the treatment can be performed with higher flow rates under otherwise equal conditions, without the need for additional high-pressure pumps or the deployment of more expensive, stronger, larger-diameter tubing. Another important conclusion reached by the author is that due to the specific properties of alternative fracturing fluids, their ability to transport and retain proppant is significantly increased. This property of fracturing fluids is especially important when treating low-permeability, fractured formations and during the stimulation of long horizontal wells. On the other hand, the use of alternative gel-forming agents raises the requirements for the controlled breakdown of fracturing fluids, complicating the task of selecting a rational formulation and necessitating additional research.

Twistor theory of the Chen–Teo gravitational instanton**Dedicated to Nick Woodhouse on the occasion of his 75th birthday.

Abstract Toric Ricci--flat metrics in dimension four correspond to certain holomorphic vector bundles over a
twistor space. We construct these bundles explicitly, by exhibiting and characterising their patching matrices, 
for the five--parameter family of Riemannian ALF metrics constructed by Chen and Teo. The Chen--Teo family contains
a two--parameter family of asymptotically flat gravitational instantons. The patching matrices for these 
instantons take a simple rational form.

Assessing the effects of different types of environmental supervision policies on green economy efficiency of China

Well-designed environmental regulatory tools are essential for environmental, economic, and social sustainability. This paper explores the effects of different types of environmental supervision policies on green economic efficiency in China from 2003 to 2021. In the first stage, the environmental supervision policies are divided into four types based on the governmental behavioral patterns and the composite index of environmental supervision policies is constructed based on multiple criteria, and the super-efficiency DEA-SBM model is used to measure green economic efficiency. In the second stage, the Tobit model is used to explore the effects of four different types of environmental supervision policies on green economic efficiency. The results show that: (1) Command policies inhibit green economic efficiency in the short term, while the long-term effect increases green economic efficiency. (2) Collaboration policies increase green economy efficiency from the second to the fifth year of implementation, but the subsequent long-term effects show a dampening effect. (3) Planning policies inhibit green economy efficiency in the short term, while they increase green economy efficiency after two years of implementation. (4) Guidance policies inhibit green economic efficiency in the short term but can enhance green economic efficiency after three years of implementation. The result provides theoretical guidance for the rational formulation and implementation of environmental supervision policies by environmental administrations in the future.

Rational formulation of saponin and dexamethasone for the synergistic treatment of rheumatoid arthritis in vivo

Rheumatoid arthritis (RA) is a common autoimmune disease, and the abnormal proliferation of fibroblast-like synoviocytes (FLSs) in inflamed joints plays a key role in the pathogenesis of RA, which has become an important therapeutic target for RA treatment. This work reported a facilely formulated nanoparticle from saponin (Sap) and dexamethasone (Dex) in precise ratio, affording the resultant Dex@Sap nanoparticles. Benefiting from the enlargement of vascular endothelial cell gap at the inflammation site and intra-articular injection, Dex@Sap could accumulate at the inflamed joints to inhibit excessive proliferation of FLSs and mediate cell apoptosis, achieving symptomatic relief and efficient RA treatment, while reducing the amount of drug needed as well as the occurrence of adverse reactions. Typical AKT (also known as protein kinase B, PKB)/mTOR (mammalian target of rapamycin) pathway was observed to be inhibited, and the mitochondria-mediated intracellular reactive oxygen species (ROS) level was also upregulated by Dex@Sap. Further in vivo evaluations demonstrated that Dex@Sap could significantly alleviate RA-induced inflammatory response and the expression of pro-inflammatory cytokines to cure joint damage in collagen-induced arthritis mice and rats. This work provides a clinically promising nanomedicine to synergistically treat RA.

Ariadne's Thread Metacognition for emancipatory rationality in education

Emancipatory rationality in education empowers individuals and promotes social justice.Metacognition and critical thinking play vital roles in supporting this approach by encouraging learners and professionals to reflect on their thinking processes, question assumptions, and develop the ability to engage critically with information. The research presented in this paper falls within the action research framework, which provides for theinvestigation to be conducted in the field based on close collaboration between researchers and practitioners. Action research aims to generate improvement and change in the context in which it is implemented. The roots of this approach can be found in Dewey’s criticism of the traditional separation of knowledge and action and in Freire’s idea of conscientization, the process of developing critical awareness through reflection and action. In their view, learning depends upon uncovering real problems and actual needs. Starting from four criticalincidents, the paper demonstrates how reflective practices based on metacognition can be used to train education professionals. Metacognitive work is essential for analyzing problems and responsibilities and identifying any distortions preventing educational action from responding effectively to people's needs. When faced with an educational problem, the professional needs to be able to use two forms of rationality: heuristic-reflective andemancipatory. The first type of rationality guides through the investigation of the experience to build the necessary knowledge to interpret and manage it. The second makes the educator an agent of transformation and change.