Theoretical Methods Research Articles

Novel comparative analysis and equation development for body volume estimation using dual-energy x-ray absorptiometry in athletes.

Dual-energy x-ray absorptiometry (DXA) has been suggested as an alternative method for estimating body volume (BV), a component of the reference four-compartment body composition model. This study reports the development and validation of DXA-BVSilva, a novel DXA-derived BV equation. An additional aim was to develop an estimate of lean soft tissue density (DLST), a key variable in the theory-based approach, by estimating total body protein with a six-compartment model. A sample of 332 athletes (36.7% females) from several sports were randomly assigned to either the development (n = 232) or cross-validation group (n = 100). DXA-BVSilva was developed via linear regression of DXA-measured fat, lean soft tissue, and bone mineral mass against BV measured with air displacement plethysmography (ADP). A DLST estimate of 1.064 kg/L (SD = 0.006) was obtained from a subset of the development sample comprising 201 athletes (36.3% females) with available measurements of total-body water by deuterium dilution, bone mineral by DXA and BV by ADP, enabling total-body protein determination from a six-compartment model. DXA-BVSilva provided the closest BV estimation (mean difference = 0.05 L, SD = 0.46 L; ES [95% CI] = 0.11 [-0.08; 0.31]) and the 95% limits of agreement (-0.86 to 0.96 L) were narrower than existing empirical equations. We conducted the first comparative analysis of both empirical and theoretical BV estimation methods using DXA, demonstrating the validity of DXA-BVSilva for BV estimation in athletes, presenting a robust alternative to ADP, with potential applications in multicomponent body composition models.

Thermochemical Characterization of Sulfur-Containing Furan Derivatives: Experimental and Theoretical Study

The thermochemical properties of three sulfur-containing furan derivatives, 2-furanmethanethiol, furfuryl methyl sulfide, and methyl 2-methyl-3-furyl disulfide, were investigated using experimental and theoretical methods. Standard molar enthalpies of combustion were determined by combustion calorimetry, while enthalpies of vaporization were obtained through Calvet microcalorimetry. These experimental results allowed for the calculation of standard molar enthalpies of formation in the gas phase at 298.15 K. Theoretical calculations using high-level quantum chemical methods (G3) were performed to complement the experimental data. A comparison between experimental and theoretical values revealed good agreement, validating the computational approach. This study enhances the understanding of the energetic properties of sulfur furan derivatives, contributing reliable thermochemical data to existing databases and aiding in the development of predictive models for related molecular systems.

Optical Properties of the Semiconductor Nanoclusters

The paper presents the results of the study of the influence of external factors on the change in the morphology of nanoclusters in a matrix environment. Effective methods for calculating the optical characteristics of quantum-scale systems - semiconductor nanoclusters are highlighted. The prospect of combining theoretical methods of computer modeling (within the framework of molecular dynamics) with experimental studies of semiconductor nanoclusters in a matrix environment is illustrated.

Assisting Employers of Small and Medium-Sized Enterprises (SMEs) to Support Employees on Long-Term Sick-Leave: Development of a Web-Based SME Tool Using Intervention Mapping.

Employers of small and medium-sized enterprises (SMEs) face challenges in supporting employees on long-term sick-leave, due to limited resources and expertise available. This study aimed to develop an intervention assisting employers of SMEs in supporting long-term sick-listed employees during sick-leave and return to work (RTW). Intervention mapping (IM) steps 1-4 were employed to develop the intervention. For the needs assessment, 20 employers, 8 employees, 8 occupational physicians, and 9 other stakeholders were interviewed (step 1). A logic model of change was developed (step 2), followed by the identification of theoretical methods for achieving the changes required (step 3). The intervention was composed (step 4), incorporating the results of a pilot test with 4 employers, 4 employees, 4 occupational physicians, and 3 other stakeholders. Identified needs (step 1) span knowledge on legislation, communication skills, stakeholder engagement, practical support, actions regarding RTW, relapse prevention, and organizational policy. Using the self-determination theory as the theoretical basis for improving employer intention and ability to support sick-listed employees (steps 2 and 3), a web-based intervention was developed (step 4) (hereafter: SME tool). The SME tool includes succinct tips, communication videos, and practical checklists. Minor adjustments were made following the pilot test, such as adding supplementary information on privacy regulations and preventive strategies. By focusing on enhancing SME employers' intention and ability to support their long-term sick-listed employee(s), the developed SME tool has the potential to improve the satisfaction of employees with the sick-leave and RTW support of their employer during long-term sick-leave.

Tecnologias de informação e comunicação em Angola e os seus problemas de acessibilidade: estudo realizado no magistério do Soyo

This article aims to analyze Information and Communication Technologies in Angola and their accessibility problems, specifically in the Soyo Teaching Department. Thus, a bibliographical review and documentary analysis were carried out, with qualitative research as the fundamental pillar, with the aim of delving into the epistemological foundations and contributions on the subject under study. Consequently, the presence of theoretical and empirical methods, in line with the duly outlined and established indicators. The collected data were presented and discussed with theoretical guidelines at the level of specialized literature. As a result, the research indicates that the use of technology in education considerably improves and expands the performance of the professional responsible for guiding the pedagogical process with their learners, taking them to a higher level. This makes it possible for them to easily perform and acquire the aspirations that are currently desired. However, there are digital inequalities, a lack of resources and deficient training of education professionals and, as if that were not enough, there are abysmal barriers to the acquisition of recommended equipment.

The living word: The key to dialogue and mutual understanding (to the 100th anniversary of the birth of Professor T. A. Ladyzhenskaya)

The article characterises the scientific legacy of Professor T.A. Ladyzhenskaya (5 April 1925– 22 November 2017), an outstanding Russian methodologist, doctor of pedagogical sciences, professor. She authored school and university textbooks, founded the Department of Rhetoric and Culture of Speech at Moscow State Pedagogical University (MGPI), headed the "Communication Rhetoric" school of thought. The study used such theoretical research methods as analysis and contrastive analysis of scientific literature on Russian language teaching methodology and speech development methodology. The article examines the major aspects of the methodology developed by T. A. Ladyzhenskaya to enhance students’ oral speech, as well as to teach essay writing. Additionally, we emphasize the systematicity and consistency principle as the conceptual foundation for the formation of the communicative and speech skills in students. The article reveals the fundamental principles of the school and university rhetoric course developed by T. A. Ladyzhenskaya. She understood rhetoric as linguistics of speech. In this study, we highlight the axiological aspect of rhetoric, its educational potential and characterise the moral and rhetorical ideas that form the basis of the rhetoric course. The article emphasises the relevance of T. A. Ladyzhenskaya’s methodological legacy for meeting the challenges Russian language teachers face nowadays.

Formação Inicial de Professores: Uma Abordagem sobre as Práticas Pedagógicas no curso de Biologia da escola superior Pedagógica do Cuanza-Norte

This study addresses the initial training of teachers. It analyses the Pedagogical Practices in the Biology course of the Cuanza-Norte Higher Pedagogical School, which aimed to analyse the strategies adopted by the Cuanza-Norte Higher Pedagogical School in the pedagogical practices of the Biology course. Regarding the nature, the research was applied; considering the objectives, it was worked on the basis of a descriptive research; considering the form of approach, it is considered mixed; and regarding the procedures, it was worked on the basis of a field research. To collect data and other information, theoretical methods were used, such as analysis-synthesis, induction-deduction and historical-logical. Regarding the empirical methods, the following stand out: observation, questionnaire survey, interview survey, pedagogical test and, lastly, statistical-mathematical. The population for this investigation was 360 students, with a sample of 108 students, corresponding to 30% of the population.The results show that there are no clear and defined strategies for pedagogical practices in the Biology course at the Cuanza-Norte Higher Pedagogical School, at least in documents, although there are some actions that do not significantly impact teacher professionalization, and there is an urgent need to work on the issue. In view of this, the participants in the process proposed some reflections that, due to the approach and justification, could serve to make a significant and qualitative leap in the training in Pedagogical Practices in the Biology course at the above school.

Influence of effective decay constant uncertainty on radon exhalation rate measurement from medium surfaces using CR-39.

Influence of effective decay constant uncertainty on radon exhalation rate measurement from medium surfaces using CR-39.

The Effects of Casing Profile on the Aerodynamics of Integrated Intermediate Turbine Ducts

Abstract To reduce the engine’s length and weight, the concept of the integrated intermediate turbine duct (IITD) is proposed, in which the first row of the low-pressure turbine vanes is replaced by the turning struts in the intermediate turbine duct. The effects of the casing profile on the flow features and loss mechanism in the IITD are investigated by experimental, numerical, and theoretical methods. In the baseline case, the casing passage vortex at the exit of the IITD is featured with two branches, which is caused by the entrainment effect of the suction side leg of horseshoe vortex near casing. By making the casing profile upstream of the leading edge more downward convex, the thickness of the casing boundary layer can be reduced, and the horseshoe vortex is weakened. The structure of the exit casing secondary flow is thus more integral. In the IITD with higher mean rise angle, the entrainment effect has the ability to reduce the low-momentum fluid and suppress the separation on the suction surface. A method of controlling the casing secondary flow is proposed accordingly. To analyze the loss mechanism, the loss is broken down into the parts generated by mean vortex and turbulence theoretically. The casing boundary layer acceleration can lead to a larger velocity gradient and loss caused by mean vortex. While the turbulent dissipation will be reduced on the other hand. Large turbulent dissipation can also be generated when the mixing between the casing secondary flow and wake is enhanced.

Research on rock fracture evolution prediction model based on Adam-ConvLSTM and transfer learning

The propagation of rock fractures is essential for maintaining engineering safety, yet traditional theoretical methods are burdened by challenges such as complex sample collection and lengthy prediction processes. To address these challenges, this study develops a deep learning model based on an adaptive moment estimation optimized convolutional long short-term memory neural network (Adam-ConvLSTM) to predict the evolution of rock fractures. We generated a rock fracture dataset through numerical simulation and then incorporated it into a machine-learning imagework to produce a predictive model. Initially, PFC2D numerical simulations were conducted on rocks with various pore defects under uniaxial compression, resulting in five sets of fracture propagation images. These images were processed using sliding window techniques to construct a foundational dataset. Considering the spatiotemporal correlations among different rock fractures, one dataset was used to train the Adam-ConvLSTM model, yielding an initial model that accurately predicts fracture propagation for a single rock dataset. Utilizing transfer learning, this initial model was adapted and independently fine-tuned for four additional datasets with varying pore defect sizes, resulting in four distinct predictive models. These models were integrated to form a more comprehensive predictive system. In practical applications, the comprehensive model uses structure similarity index measure to align test samples with the most similar images from the model, selecting the predictive model with the most similar images for forecasting fracture evolution. Comparative validation indicates that this comprehensive model outperforms traditional methods and basic deep learning algorithms in both prediction efficiency and accuracy. This model not only enhances the efficiency and precision of rock fracture evolution forecasting but also offers a practical approach for monitoring rock mass fractures, substantially enhancing engineering safety.

JOYCE3.0: A General Protocol for the Specific Parametrization of Accurate Intramolecular Quantum Mechanically Derived Force Fields.

While the intrinsically multiscale nature of most advanced materials necessitates the use of cost-effective computational models based on classical physics, a reliable description of the structure and dynamics of their components often requires a quantum-mechanical treatment. In this work, we present JOYCE3.0, a software package for the parametrization of accurate, quantum-mechanically derived force fields (QMD-FFs). Since its original release, the code has been extensively automated and expanded, with all novel implementations thoroughly discussed. To illustrate its general applicability, QMD-FFs are parametrized for seven benchmark cases, encompassing molecules with diverse structures and properties. These range from exotic stiff scaffolds, flexible polymeric chains, and polyenes of biological interest to transition-metal complexes. On the one hand, JOYCE3.0 FFs consistently outperform available general-purpose descriptions, achieving excellent agreement with higher-level theoretical methods or available experimental validation data. On the other hand, the remarkable accuracy found in the description of the molecular structures extends to electronic excited states, enabling the integration of the JOYCE3.0 QMD-FFs into multilevel protocols aimed at reliably predicting selected properties and spectral line shapes in advanced optoelectronic materials. The high quality of the results─spanning molecular structures, condensed-phase properties, and spectroscopic features─in combination with the enhanced interface with popular quantum-mechanical codes and molecular dynamics engines, as well as its applicability to chemically diverse species, strongly suggests that JOYCE3.0 could play a pivotal role in the rational design of functionalized materials and heterogeneous systems.

Utilizing Some Indole Derivatives to Control Mild Steel Corrosion in Acidic Environments: Electrochemical and Theoretical Methods

Ethyl 3-formyl-1H-indol-2-carboxylate (FIC) and 2-(4-methoxyphenyl)-2,4-dihydropyrrolo [3,4-b]indol-3-ol (MPI) were synthesized as indole derivatives. The chemical structures of FIC and MPI were established through analytical and spectroscopic techniques. The inhibitory impacts of FIC and MPI on mild steel (MS) in an acidic environment (0.5 M H2SO4) were investigated by employing methodologies including open circuit potential (OCP), electrochemical impedance spectroscopy (EIS), and potentiodynamic polarization (PDP). As the studied indole derivatives adsorbed on the surface of MS, they created a barrier to mass and charge movement, shielding the MS from dangerous ions. It was observed that the inhibitory efficiency (%EF) values increased with the molar concentration of indole derivatives (FIC and MPI). At all concentrations, the two indole derivatives being studied, FIC and MPI, had high efficiency values. The highest efficiencies at 90 ppm were 81.2% with MPI and 76.2% with FIC. The polarization curves also clearly showed that MPI and FIC function as mixed-type inhibitors. Additionally, this study used density functional theory (DFT) and molecular dynamics (MD) simulations to investigate how well the two indole derivatives prevented mild steel corrosion.

Theoretical Evaluation of Urea Derivatives on Fe (110) and Sn (111) Surfaces: DFT and Monte Carlo Simulation Approaches

Present-day theoretical computation methods are quite effective at anticipating how corrosion inhibitors would behave on metal surfaces, conserving time and resources on laboratory testing. The present study aims to predict the inhibitory effectiveness of certain furan derivatives on surfaces of Fe (110) and Sn (111) in acidic media. To compare their fundamental attributes against corrosion as well as their behavior on iron (Fe) and tin (Sn) surfaces in an acid medium, six urea derivatives have been chosen for this purpose: Imidazolidin-2-one (Cpd A), 4-methylimidazolidine-2-one (Cpd B), Tetrahyropyrimidin-2(1H)-one (Cpd C), 1,3-dimethylimidazolidin-2-one (Cpd D), 1,1-diethylurea (Cpd E), 1,3-dimethylurea (Cpd F). The anti-corrosive characteristics of Cpds A - F were generally explored using Density Functional Theory and Monte Carlo simulations. The results indicate that the compounds had low energy gaps, the highest occupied molecular orbital energy, global hardness, as well as ionization energy and high Electron affinity, ELUMO, global softness, and number of transferred electrons, which explained their corrosion inhibition potentials. Electrostatic potential (ESP) and Fukui indices identified the reactive sites with the ability to accept and donate electrons via back-donation to the metal's d-orbital. The Monte Carlo simulation demonstrated a favorable contact between the Fe (110) and Sn (111) surfaces and inhibitory molecules in the acidic medium. In the industrial sectors, these compounds may be secured as corrosion protectors.

Multi-scale study on stress concentration and strength characteristics of 3D braided composites containing two symmetrical holes

3D braided composites are widely used in stress-concentrated structures. This study employs a multi-scale approach to investigate stress concentration in a 3D 4-directional braided composite plate containing two symmetrical holes. Two theoretical methods are developed to predict inter-hole transverse stress based on different correction assumptions. The stress distribution between the holes is investigated through theoretical analysis and finite element simulations. Results show that increasing the hole radius intensifies stress concentration, while sufficient hole spacing minimizes inter-hole interaction. The tensile strength of the composite plate is further evaluated based on the point stress criterion (PSC) and numerical simulations, revealing that the strength characteristics are significantly influenced by hole radius and braided angle, while a smaller hole spacing leads to a noticeable reduction in tensile strength. These findings provide insights into the mechanical behavior of 3D braided composites and contribute to the structural design of components with defects.

The philosophical dimensions of cultural dynamics in society's evolution

Introduction: Philosophical and cultural research is positioned to study culture's structure, function, and role. At the same time, the philosophy of the cultural phenomenon focuses on identifying the main evolutionary cultural trends and understanding the causes of crisis phenomena.Objective: This research implements a scientific inquiry into the cultural aspects of societal development in the context of philosophical knowledge. A systematic analysis of the societal and cultural development stages was carried out to comprehend these processes according to the established periodisation in philosophical teachings.Methods: A number of theoretical research methods were used, including historical, philosophical and philosophical-cultural methods, holistic and systemic analysis, synthesis, methods of comparison, generalization, and others.Results: It is substantiated that the synergy of philosophy and culture forms a unique reflective-conceptual framework for the cultural development of society, endowing it with integrity and orderliness and enabling the rationalisation of individual elements within the social system. It has been proven that the model of philosophical knowledge within the traditional cognitive and cultural paradigm, which correlates with order, balance, stability, and determinism, does not correspond to the realities and challenges of the modern world with its chaos, imbalance, instability, and volatility. The study found that the ideas of synergism have not lost their paradigmatic significance to this day.Conclusions: Thus, it is demonstrated that the essence of the philosophical nature of cultural aspects is positioned as the development of the human position in the philosophical-cultural dimension in a historical-temporal context.

An Innovative Algorithm for Damage Mapping in Multiaxial Fatigue Using the Stress Scale Factor (SSF) Concept

Predicting damage to materials under multiaxial fatigue is a complex challenge, especially when normal and shear stresses interact in dynamic and non-linear ways. Traditional methods often oversimplify these interactions, leading to less reliable fatigue predictions and limiting their usefulness in real-world applications. To address this, we present a novel algorithm based on the principles of the Stress Scale Factor (SSF), designed to dynamically evaluate the relative contributions of normal and shear stresses to fatigue damage. By providing a more accurate mapping of multiaxial fatigue damage, this approach enables improved predictions of fatigue life. The methodology combines experimental insights with mathematical modeling to create a flexible and adaptive framework. By making it possible to map multiaxial fatigue damage with greater precision, this SSF-based approach not only enhances the understanding of fatigue behavior but also enables better design decisions. The result is safer, more reliable, and efficient structures across a range of applications. This study bridges the gap between theoretical methods and practical needs, offering engineers and researchers a powerful tool to improve fatigue analysis and optimize structural performance.

Integration of mind mapping and In-Situ Simulation training to enhance the implementation of sepsis Hour-1 Bundle treatment

BackgroundSepsis is one of the most challenging and complex clinical states, with persistently high mortality rates. Guidelines recommend the early identification of sepsis patients and immediate initiation of the Hour-1 Bundle treatment to reduce mortality from sepsis. Emergency nurses play a vital role in the early screening of sepsis. Studies indicate that mind mapping and In-Situ Simulation (ISS) training not only aid healthcare professionals in reinforcing theoretical knowledge retention but also enhance skills in coordination, task management, and communication during simulation exercises. This, in turn, promotes the effective implementation of various treatments during resuscitation. The combination of theoretical and practical training methods is more effective than a single training approach. In June 2023, our hospital's emergency department conducted training for emergency nurses on sepsis mind mapping combined with ISS.ObjectiveTo explore the effect of mind mapping combined with ISS training in promoting the emergency nurses' implementation of the Hour-1 Bundle in sepsis patients.MethodsUsing mind mapping and ISS training methods, 24 emergency nurses were divided into 6 groups for a 12-week training period. The study compared their pre- and post-training knowledge of sepsis, identification and diagnostic time, Hour-1 Bundle treatment completion rate, and non-technical skill scores. Post-training, the emergency nurses evaluated the effectiveness of the training.ResultsThe scores for sepsis knowledge among emergency nurses before and after training were 44.17 ± 9.21 and 60.42 ± 5.29, respectively. The identification and diagnostic times (hours) were 0.63 ± 0.18 and 0.49 ± 0.13, respectively. The Hour-1 Bundle treatment completion rates were 58.33% and 85.7%, respectively. There was a significant increase in all non-technical skill scores, with statistical significance (P < 0.05, P < 0.001). After two ISS trainings, the SET-M scores progressively increased, indicating a high satisfaction rate among nurses with the mind mapping and ISS training.ConclusionThe combination of mind mapping and ISS training enables emergency nurses to identify sepsis earlier and promotes the effective implementation of the Hour-1 Bundle treatment in sepsis patients, while also enhancing their cognitive understanding of sepsis and non-technical skills.

Analyzin the worth of stocks through fundamental analysis: insights from the Kazakhstan stock exchange (KASE)

The purpose of the article is furnishing recommendations for judicious buy or sell signals conducive to informed investment decisions.The methodology of this article was based on theoretical and empirical research methods: a comprehensive analysis of the value of Kazakhstan stock market, as well as the the utilization of coefficients derived from a multiple regression analysis and the consideration of key value drivers for the KASE Index, as of November 15, 2023.Originality/value of the research: Nowadays there exists a multitude of misconceptions surrounding the practices of security selection and fundamental analysis, predominantly emanating from the fallacious belief that the entirety of available information is accurately incorporated into security prices. Nevertheless, fundamental analysis retains its pivotal role in evaluating the financial robustness of securities, particularly within the realm of long-term investment strategies.Conclusion: Based on the analysis of KASE Index stocks with a focus on Earnings Yield (EY), PE Ratio to Price (PEP ratio) as well as B/P ratio, it was found that KZTO KZ and KEGC KZ shares are fairly priced and it was also found that KCEL KZ and KAP KZ shares have attractive opportunities for investors in the long term. We believe that the information provided is of practical importance for investors and traders who aim to optimise their decision-making process and overall trading strategy.

Artificial Intelligence on Guard Against the Harmful Effects of Deepfakes

&lt;p&gt;&lt;strong&gt;&lt;em&gt;The purpose of the study &lt;/em&gt;&lt;/strong&gt;&lt;em&gt;is to outline the threats posed by modern technologies for creating deepfakes, to confirm the need for legal regulation of their spreading, and to make relatable proposals for recognizing deepfakes at the everyday level, in particular through the use of artificial intelligence.&lt;/em&gt;&lt;/p&gt;&lt;p&gt;&lt;strong&gt;&lt;em&gt;Research methodology.&lt;/em&gt;&lt;/strong&gt;&lt;em&gt; The materials used to prepare this article were compiled using a combination of theoretical and empirical methods, including the analysis of sources that offer information about the role of deepfakes in the media environment and their impact on society as a whole. The analysis of foreign websites with legislative acts made it possible to systematize these sources on the relevant issues, as well as to strengthen the argument for the need to legally regulate the dissemination of such falsifications. The use of these methods, as well as the inductive generalization of the field under study, contributed to the structuring of the necessary material to obtain the relational basis for recognizing deep audiovisual counterfeits.&lt;/em&gt;&lt;/p&gt;&lt;p&gt;&lt;strong&gt;&lt;em&gt;Results&lt;/em&gt;&lt;/strong&gt;&lt;em&gt;. A list of rules that can be used to recognize deepfakes is proposed, and a list of online resources for their detection is reviewed and systematized in order to increase the overall level of media literacy and awareness of threats that negatively affect the mental health of society. &lt;/em&gt;&lt;/p&gt;&lt;p&gt;&lt;strong&gt;&lt;em&gt;Novelty.&lt;/em&gt;&lt;/strong&gt;&lt;em&gt; As a result of the analysis of the sources, as well as their systematization and generalization, recommendations for strengthening critical thinking among the population are proposed, and the need for visual training is emphasized in order not to be deceived by another example of a deep audiovisual fake.&lt;/em&gt;&lt;/p&gt;&lt;p&gt;&lt;strong&gt;&lt;em&gt;Practical significance.&lt;/em&gt;&lt;/strong&gt;&lt;em&gt; The proposed rules can be used both for widespread use in society to develop critical thinking and for the development of a set of competencies and programmatic outcomes in media education disciplines. &lt;/em&gt;&lt;/p&gt;&lt;p&gt;&lt;strong&gt;&lt;em&gt;Key words:&lt;/em&gt;&lt;/strong&gt;&lt;em&gt; deepfake, disinformation, manipulation, media addiction, media literacy, artificial intelligence.&lt;/em&gt;&lt;/p&gt;

Theoretical methods based on linear response theory to simulate dynamics and absorption spectra of molecular polaritons.

In this work, we first derive path integral expressions for the dynamics of molecular polaritons in microcavities. For systems with a large number of molecules in the cavity, i.e., in the thermodynamic limit, it is shown that linear response theory can be employed to describe the molecular response, which can be further modeled by an effective harmonic bath. This leads to analytical path integral expressions for the Dicke model, as well as its extensions that incorporate effects of static disorder and coupling to intramolecular vibrational degrees of freedom. The hierarchical equations of motion are then derived to simulate polariton dynamics and absorption spectra. By further taking advantage of the harmonic nature of both the system and the effective bath, an efficient exact diagonalization method is also obtained. Similar results are also obtained for the Tavis-Cummings model, the rotating-wave approximation of the Dicke model. Utilizing these theoretical findings, we simulate the polariton dynamics and absorption spectra and analyze the critical coupling strength for the superradiant transition in the presence of static disorder and coupling to intramolecular vibrational motion.