The aim of this study is to introduce and evaluate a new approach by using 3D printed anthropomorphic breast phantoms in teaching X-ray mammography techniques Radiologic technologists. For this purpose, a physical anthropomorphic breast phantom is created, based on a computational breast version. The phantom is created by a stereolithography 3D printer. The practical exercises were conducted in three sessions with the participation of radiographers students first, second and third year of training, respectively. A survey was prepared to summarise the participants´ opinion about this new form of training in mammography technique. A total of 83 students were trained with the new approach. From these 52 responded to the survey questions. More than half of the students (71.2%) successfully handled the exercise with the physical breast phantom. The training provoked a substantial number of students to express the belief that incorporating modern methods based on digital technologies into their X-ray device training is essential. The instructor was well prepared and with the needed competence. The experience within this training convinces the future professionals to introduce the new technologies in their routine work, particularly for exercising the compression technique and breast positioning.

We consider the second order differential equation y'' + ω^(2)ρ(x)y = 0 where ω is a positive parameter. The principal concern here is to find conditions on the function ρ^(−1/2)(x), which ensure that the consecutive differences of sequences constructed from the zeros of a nontrivial solution of the equation are regular in sign for ω sufficiently large. In particular, if c_(νk)(α) denotes the k-th positive zero of the general Bessel (cylinder) function C_(ν)(x; α) = J_(ν)(x) cos α−Y_(ν)(x) sin α of order ν, and if |ν| < 1/2, we prove that (−1)^(m)∆^(m+2)c_(νk)(α) > 0 (m = 0, 1, 2, ...; k = 1, 2, ...), where ∆a_(k) = a_(k+1) − a_(k). This type of inequalities was conjectured by Lorch and Szego in 1963. We also show that the differences of the zeros of various orthogonal polynomials with higher degrees possess the sign-regularity.

In this paper, the 1st level general fractional derivatives of arbitrary order are defined and investigated for the first time. We start with a generalization of the Sonin condition for the kernels of the general fractional integrals and derivatives and then specify a set of the kernels that satisfy this condition and posses an integrable singularity of power law type at the origin. The 1st level general fractional derivatives of arbitrary order are integro-differential operators of convolution type with the kernels from this set. They contain both the general fractional derivatives of arbitrary order of the Riemann-Liouville type and the regularized general fractional derivatives of arbitrary order considered in the literature so far. For the 1st level general fractional derivatives of arbitrary order, some important properties including the 1st and the 2nd fundamental theorems of Fractional Calculus are formulated and proved.

The COVID-19 pandemic has struck educational experience systems around the globe. This paper investigates and evaluates the student participants’ perceptions who joined the international exchange seminar on global citizenship and peace held at a University in Hiroshima, Japan. Approximately seventy students and faculty members from nine to ten different universities from around the globe joined this summer program in August 2021 (online) and 2022 (face-to-face). This study is a mixed-method study. The first part consists of a quantitative analysis of BEVI data obtained from the students in the seminar before COVID-19 and after. The research concludes that there are no changes in the way students learn. The second part consists of qualitative data. This data shows the perceptions of students of online teaching versus hybrid teaching. It compares the differences in participants’ perceptions reported in students’ feedback on the programs during and post-COVID-19. Our results confirm prominent differences exist in the students’ perceptions of their learning experience during the pre-pandemic and post-pandemic periods. The findings of this study suggest that universities need to strive and define a meaning and purpose of international seminars, which enables students to experience a high level of intercultural social interaction face-to-face.

In this paper, we analyze the Hawking radiation phenomenon for types of Banados-Teitelboim-Zanelli-like (BTZ-like) black holes. For this purpose, using the Hamilton-Jacobi method, we consider semi-classical WKB approximation to calculate the tunneling probabilities of massive boson particles. For these particles, we use the equation of motion for the Glashow-Weinberg-Salam model. Using quantum tunneling process of charged massive bossons, we compute the corresponding Hawking temperatures. Furthermore, we discuss the effects of rotation parameter on tunneling probability and temperature.

Shown is the derivation of Lorentz-Einstein k-factor in SRT as an amplitude-term of oscillation-differential equations of second order.This case is shown for classical Lorentz-factor as solution of an equation for undamped oscillation as well as the developed theorem as a second solution for advanced SRT of fourth order with an equation for damped oscillation-states.This advanced term allows a calculation for any velocities by real rest mass.Also accelerated coordinate -frames are discussed.

This overview study set out to compare and synthesise the findings of review studies conducted on predicting student academic performance (SAP) in higher education using educational data mining (EDM) methods, EDM algorithms and EDM tools from 2013 to June 2020. It conducted multiple searches for suitable and relevant peer-reviewed articles on two online search engines, on nine online databases, and on two online academic social networks. It, then, selected 26 eligible articles from 2,050 articles. Some of the findings of this overview study are worth mentioning. First, only 2 studies explicitly stated their precise sample sizes with maths and science as the two most mentioned subject areas. Second, 16 review studies had purposes related to either EDM techniques, EDM methods, EDM models, or EDM algorithms employed to predict SAP and student success in the higher education sector. Third, there are six commonly used typologies of input variables reported by 26 review studies, of which student demographics was the most commonly utilised variable for predicting SAP. Fourth and last, seven common EDM algorithms employed for predicting SAP were identified, of which Decision Tree emerged both as the most used algorithm and as the algorithm with the highest prediction accuracy rate for predicting SAP.

Open Education, Open Educational Practices (OEP), and Open Educational Resources (OER) have emerged as significant opportunities for enhancing global sustainability information sharing. However, the creation and sharing of OER, as well as the usage of OEP in Higher Education for Sustainable Development (HESD), remain limited. This study explores the implementation of OEP in HESD, aiming to empower students to co-produce OER on Sustainable Development (SD). This study, drawing on the theoretical approach of the principle of constructive alignment, proposes the development of students’ digital competence in OER production. A two-group pre-test post-test analysis of 409 students (Psychology, Economics, Education, Geography) reveals a significant increase in digital competence over time among students who produced OER on SD, compared to their peers enrolled in courses unrelated to OER content development. We delve into the practical implications for designing OEP in HESD and strategize to support students in their OER production processes.

Pedagogic Conversational Agents (PCAs) are interactive systems that engage the student in a dialogue to teach some domain. They can have the role of teacher, student, or companion, and adopt several shapes. In our previous work, a significant increase of students’ performance when learning programming was found when using PCAs in the teacher role. However, it is not common to find PCAs used in the classrooms. In this paper, it is explored whether teachers would accept PCAs to teach programming better if co-designed with them. An experiment with 35 pre-service Primary Education teachers was carried out during the 2021/2022 academic year to co-design a robotic PCA to teach programming. The experience validates the idea that involving the teachers in the design of the PCA facilitates that they integrate this technology in their classrooms. 97% of the pre-service teachers answered in a survey that they believed that the robot PCA could help children to learn programming and 80% answered that they would like to use them in their classrooms.

Allocations of funding for higher education have typically focused on competition in neoliberal mechanisms. Surprisingly, much less attention has been paid to considering the effect of fund allocations for public goods purposes in neoliberal contexts. This study aims to examine specific funding schemes and determine the influential factors impacting the funding for teaching, research, and public goods intention. Taking Taiwan's Higher Education Sprout Project (HESP) as a unique example, we explored the effect of policy initiatives on public goods transformation. The data was collected from the Ministry of Education and Scopus database. First, the t-test and ANOVA were used to detect the differences between the system and sector; Second, regression analysis was used to determine influential factors for funding allocations; Final, structural equation modeling (SEM) was used to explore the causal effects among the selected variables. The study found that only diversity was shown in private technology groups receiving less HESP funding. The findings suggest that the funding allocation may not affect teaching and research based on sectors and systems. In contrast, this study demonstrates that transforming the public good through special funding can play a critical role in policy intention in neoliberal higher education.

Domestic abuse and stalking in higher education (HE) have been overlooked in research in comparison to sexual harassment and sexual violence. This article reports on survey data from 725 students at a UK university using measures of ‘dating violence’ – physical and psychological violence from an intimate partner – and stalking from a US survey instrument (the Administrator Researcher Campus Climate Collaborative (ARC3) survey). According to this measure, 26% of respondents had been subjected to ‘dating violence’ and 16% to stalking behaviours. However, these findings need to be contextualised within a critical discussion of the use of the ARC3 survey tool in the UK context. The ARC3 questions on ‘dating violence’ focus on physical and ‘psychological violence’; the questions therefore omit further types of domestic abuse under UK definitions. In relation to stalking, US definitions – as captured in the ARC3 survey instrument – define specific behaviours. By contrast, in the UK stalking involves behaviours that engender fear or distress in a pattern of behaviour over time. These differences mean that the ARC3 modules on stalking and ‘dating violence’ would need to be significantly adapted to be suitable for use in the UK context.

To determine the ethical-attitudinal profile of university students in the education career during the pandemic with a tendency towards a new normality. University students of the education career were surveyed online, in an ethical key (axiological attitude, moral attitude and attitude towards new normality). The research was descriptive of univariate hypothesis, with non-probabilistic snowball sampling, reaching a sample of 480 participants. The Ethical-Attitudinal Profile Scale (EPEA) was designed, whose reliability was 0.93 in Lawshe's formula and 0.89 in Cronbach's Alpha. In the axiological attitude, values were obtained more frequently: respect with 79%, sincerity with 73%, prudence with 72%. In the moral attitude, a polar result is contrasted between laxity (67%) and kindness (45%); while, in the attitude towards new normality, there was no spike in frequencies, being distributed more homogeneously between indicators, with a low resilience index. There is an adequate evaluative profile of the university students of the education career despite the context of the pandemic and the trend towards a new normality; having a moral attitude of laxity inferred by the circumstances of uncertainty that are experienced in adverse contexts.

Simulated crime scene investigation is an essential component of forensic science education, but its implementation poses challenges relating to cost, accessibility and breadth of experience. Virtual reality (VR) is an emerging technology which offers exciting prospects for teaching and learning, especially for imparting practical skills. We document here a multidisciplinary experimental study in which a bespoke VR crime scene app was designed and implemented, after which it was tested by both undergraduate student and staff/postgraduate student cohorts. Through both qualitative and quantitative analyses, we demonstrate that VR applications support learning of practical crime scene processing skills. VR-based practical sessions have the potential to add value to forensic science courses through offering cost-effective practical experience and the ability to work in isolation, in a variety of different scenarios. Both user groups reported high levels of satisfaction with the process and reports of adverse effects (motion sickness) were minimal. With reference to user feedback, we proceed to evaluate the scalability and development challenges associated with large-scale implementation of VR as an adjunct to forensic science education.

The objective of this paper is to analyze students’ assessments of the attainment of skills acquired by university graduates enrolled in a Training Programme (TP) to develop entrepreneurial skills and transversal employability competencies. Both of which are vital for the success of today's societies and play an important role in the sustainable development agenda. The TP was a twelve-week programme with six modules combining entrepreneurship training and traditional teaching methods. There were nine editions and 148 students worked in teams preparing business plans to present to consultants and potential investors. The Focal Group method was used to identify competencies and a survey was designed to identify the level to which skills were attained. The results suggest that the students attained both types of skills, acquiring a higher level of proficiency in entrepreneurial skills and those transversal competencies most connected to entrepreneurship. Additionally, different levels of attainment of entrepreneurial skills were found in different groups. We provide new evidence that TPs, as compulsory subjects in the core curriculum of degree programmes, will help accomplish both objectives: the acquisition of entrepreneurial skills and generic university educational competencies. The overall outcome of this research highlights the value added by the TPs.

Innovative teaching strategies are designing a new and promising landscape in education. They fill up the lessons with creativity and imagination either for the students and teachers. This article addresses an attempt to make easier the approach to science in a non-scientific environment: primary education at university level. Gamification methodologies were combined with flipped classroom in order to free up in-class time and engage the students with the taught courses. A qualitative study was merged with quantitative measures of emotional and motivational parameters. These results were improved with four semi-structured interviews. The results clearly showed a raise in the students' motivational level, an acknowledgment of good teaching practice and an evident enhancement of felt positive emotions toward science teaching and scientific issues.

The digital format opens up new possibilities for interaction with monographic publications. In particular, annotation tools make it possible to broaden the discussion on the content of a book, to suggest new ideas, to report errors or inaccuracies, and to conduct open peer reviews. However, this requires the support of the users who might not yet be familiar with the annotation of digital documents. This paper will give concrete examples and recommendations for exploiting the potential of annotation in academic research and teaching. After presenting the annotation tool of Hypothesis, the article focuses on its use in the context of HIRMEOS (High Integration of Research Monographs in the European Open Science Infrastructure), a project aimed to improve the Open Access digital monograph. The general line and the aims of a post-peer review experiment with the annotation tool, as well as its usage in didactic activities concerning monographic publications are presented and proposed as potential best practices for similar annotation activities.

Students who had been actively engaged in mediated collaborative activities, were asked for their perceptions about the sustainable peer feedback they had received and provided. Their views were then analyzed and categorized in terms of receiver and provider feedback, cognitive feedback and previously acquired feedback to further knowledge about sustainable education processes. A peer supported feedback questionnaire was created and validated, and its categories were correlated. The questionnaire was then aligned with the activities used to foster peer feedback between the pre-service students from the three bachelor’s degrees. The perceptions the students had of the feedback processes were analyzed using defined peer support feedback categories and the results showed a correlation between cognitive feedback and both provider and receiver self-efficacy feedback. In addition, there was a further correlation between both provider and receiver self-efficacy feedback as well as provider and receiver involvement and feedback structure. However, the results also revealed that neither receiver nor provider autonomy support were significant categories for supportive feedback.

Studying concurrent systems is to sort the read/write and control events in the concurrent system according to the order, or in partial order, or in strict order. Because of the concurrency of events and the timeliness of writing events, there will be overlap between events, which requires interval order analysis. A single start and end sequence to represent the entire hierarchical order structure as well as all equivalent spaced order observations.a single sequence of beginnings and endings to represent the entire stratified order structures as well as all equivalent interval order observations. Mazurkiewicz traces and Comtracks are hierarchical traces, but they cannot describe interval traces. In a few sentences of this summary, we can tell the problems (petri interval traces with data), the previous work (Mazurkiewicz traces, Comtracks), the reasons that cannot be solved, and our own solutions (DPN: Petri nets with data, interval traces). This paper focuses on a BE (Beginnings and Endings) sequence representing an equivalent class of runs, or targets. Our goal is to have a BE sequence to represent the entire hierarchical order structure, that is, all equivalent observable interval orders.

We delve into the axion-dilaton model within the supergravity framework, with a specific focus on the intricacies of domain wall construction and stability. Employing holographic vitrification, we unravel the dynamics of domain wall formation in gauge theories featuring periodic vacuum structures. Our model, incorporating a QCD-like axion term and a stabilizing dilaton, undergoes scrutiny for conductivity variations under weak disorder. The investigation reveals the model's resilience, manifesting near-perfect conductivity under mild disorder conditions. However, the rigorous mathematical motivation for the holographic setup demands further elucidation. The scattered nature of our results prompts the necessity for a more systematic interpretation of QCD phenomena and conductivity transitions. This study contributes to the mathematical understanding of the axion-dilaton model's behavior, highlighting the imperative for a refined holographic framework and a more coherent interpretation of observed phenomena.

The COVID-19 pandemic is one of the worst catastrophes that we have faced globally in recent years. It has not only taken its toll on the economic sector but also on the education sector. The social distancing norms that are in place as a direct response to the pandemic have turned conventional classroom teaching into a problematic minefield; as such, students all over the world have been forced into unprecedented situations that have served only to worsen the situation. The current pandemic has given rise to one of the worst crises the 21^st Century has ever seen, resulting in a surge of unemployment. Many companies have taken the route of firing employees or making redundancies, as they cannot afford the monthly reimbursement for staff. While this issue primarily concerns full-time workers, it also carries significant consequences for students – a considerable number of students are required to earn their daily living costs, and, without a job, they cannot pay their educational fees, accommodation costs, or living expenses. This comprehensive study briefly discusses the multitude of problems faced by students in the UK regarding higher education, as a direct result of the coronavirus pandemic. It contains six individual sections: a detailed introduction; the methodological procedures employed; educational disruptions, covering issues from hindrances in field research to examinations and student evaluations; personal problems experienced by students, such as accommodation and loss of income; concerns arising from the global pandemic; and finally, a conclusion and summary of the study’s findings.

Postgraduate research is a massive stumbling block to students who had never had an opportunity of exposure to research methods. A study conducted by the researcher (Costa, 2018) revealed challenges in postgraduate supervision—one of these challenges was lack of exposure to research language by students. Qualitative research and its complexities due to a variety of approaches including rigour determination pose a plethora of challenges to novice researchers. This document presents C.O.S.T.A model as a tool suitable for use by academics and students, with a panoramic view of steps to be taken first to understand foundational concepts and the language of research and secondly to make informed choices on the research methods and design strategy options available for the prospective researcher. Conclusions drawn on the reliability of the model are based on empirical evidence of application of the model observed over a period of 12 months, with some students testifying to have passed their research projects satisfactorily at their respective leading universities in South Africa. Secondary research also provides voluminous sources of success of similar research supervision programmes both in South Africa and abroad.

The high dimensions and governing non linear dynamics in wind farm systems make the design of numerical optimal controllers computationally expensive. A possible pathway to circumvent this challenge lies in finding reduced order models which can accurately embed the existing non linearities. The work here presented applies the ideas motivated by non linear dynamical systems theory - the Koopman Operator - to an innovative algorithm in the context of wind farm systems - Input Output Dynamic Mode Decomposition - to improve on the ability to model the aerodynamic interaction between wind turbines in a wind farm and uncover insights into the existing dynamics. It is shown that a reduced order linear state space model can reproduce the downstream turbine generator power dynamics and reconstruct the upstream turbine wake. It is further shown that the fit can be improved by judiciously choosing the Koopman observables used in the IODMD algorithm without jeopardizing the models ability to rebuild the turbine wake. The extensions to the IODMD algorithm provide an important step towards the design of linear reduced order models which can accurately reproduce the dynamics in a wind farm.

We characterize the form of the order divisor graph of cyclic groups based on the group order. Furthermore, we describe some topological indices of the order divisor graph of cyclic groups, including the Wiener index, Harary index, first Zagreb index, and second Zagreb index.

Most works related to the identification of mathematical nonlinear systems make one suppose that such approaches can always be directly applied to any nonlinear system. This misconception produces a great deal of discouragement when the obtained results are not the expected ones. Thus, the current work hypothesizes that the most information one has about the mathematical structure of the model, the most precise the identification result should be. Therefore, a variant of the Sparse Identification of Nonlinear Dynamics (SINDY) approach is presented to obtain the full mathematical nonlinear model of a high-order system with coupled dynamics, namely, a commercial quadcopter. Furthermore, due to its high sensitivity to inputs, a control system is devised using the identified model to stabilize the quadcopter. This illustrates the effectiveness of the proposed identification method.

The atomic structures of Zn and Na borophosphate glasses were studied by X-ray and neutron diffraction. Peaks assigned to the B−O, P−O, and O−O distances confirm that only BO4 units co-exist with the PO4 tetrahedra. The Zn−O and Na−O coordination numbers are found to be a little larger than four. The narrowest peaks of the Zn−O first-neighbor distances exist for the glasses along a line connecting the Zn(PO3)2 and BPO4 compositions (50 mol% P2O5) which is explained by networks of ZnO4, BO4, and PO4 tetrahedra with twofold coordinated oxygens. Calculated amounts of the available oxygen support this interpretation. Broadened peaks occur for glasses with lower P2O5 contents, consistent with the presence of threefold coordinated oxygens. The two distinct P−O peak components of the Zn and Na borophosphate glasses differ in their relative abundances which is interpreted by Na+ cations that coordinate oxygens in some P−O−B bridges, something not seen for the Zn2+ ions.

In this paper, a robust nonlinear dynamic controller is designed for a wind turbine with a permanent magnet synchronous generator. The wind turbine is subject to variations in all the parameters appearing in its mathematical model. Furthermore, the wind velocity is considered unavailable for direct measurement. This situation is of particular interest in practical applications, where only the nominal parameter values are known, and accurate wind velocity measurement is challenging due to perturbations caused by the turbine itself, even with appropriate sensors. The problem addressed in this work involves tracking the reference angular velocity corresponding to the wind velocity. To achieve accurate tracking, appropriate compensation of the perturbation terms resulting from parameter uncertainties and wind estimation errors is required. To address this problem, an estimator of the wind velocity is utilized, along with high–order sliding mode parameter estimators, to ensure high–performance operation of the turbine.

An in-depth study of the failure of granular materials, which is known as a mechanism to generate defects, can reveal the facts about the origin of the imperfections such as cracks in the carbon anodes. The initiation and propagation of the cracks in the carbon anode, especially the horizontal cracks below the stub-holes, reduce the anode efficiency during the electrolysis process. In order to avoid the formation of cracks in the carbon anodes, the failure analysis of coke aggregates can be employed to determine the appropriate recipe and operating conditions. In this paper, it will be shown that a particular failure mode can be responsible for the crack generation in the carbon anodes. The second-order work criterion is employed to analyze the failure of the coke aggregate specimens and the relationships between the second-order work, the kinetic energy, and the instability of the granular material are investigated. In addition, the coke aggregates are modeled by exploiting the discrete element method (DEM) to reveal the micro-mechanical behavior of the dry coke aggregates during the compaction process. The optimal number of particles required for the failure analysis in the DEM simulations is determined. The effects of the confining pressure and the strain rate as two important compaction process parameters on the failure are studied. The results reveal that increasing the confining pressure enhances the probability of the diffusing mode of the failure in the specimen. On the other hand, the increase of strain rate augments the chance of the strain localization mode of the failure in the specimen.

A new approach is presented to defining the amount of information, in which information is understood as the data about a finite set as a whole, whereas the average length of an integrative code of elements serves as a measure of information. We obtain a formula for the syntropy of reflection, that is, the information that two intersecting finite sets reflect about each other. The specificities of reflection of discrete systems through the combination of their parts are considered, and it is shown that the additive syntropy and entropy of reflection are measures of structural order and chaos. Three information laws have been established: the law of conservation of the sum of chaos and order; information law of reflection; the law of conservation and transformation of information. An assessment of the structural organization and the level of development of discrete systems is presented. It is shown that various measures of information are structural characteristics of integrative codes of elements of discrete systems. The conclusion is made that, from the informational-genetic positions, the synergetic theory of information is primary in relation to the Hartley-Shannon information theory. In the appendix we consider the asymmetry of the mutual reflection of finite sets and the proportionality of arbitrary quantities.

The continuing public health issue known as COVID-19 (the 2019 Novel Corona virus infection) has a global emphasis. Despite (or perhaps because of) the fact that there are significant gaps in our understanding of COVID-19 epidemiology, transmission dynamics, research methods, and management breakout poses a new kind of global hazard. The good news is that there is currently enough knowledge about the epidemic process to allow for the creation of mathematical forecasting models. We modify a conventional SEIR epidemic model to the unique dynamic compartments and epidemic features of COVID 19 as it spreads in a population with a diverse age structure. Although many US states and other nations around the world followed lockdown and reopening processes, we perform some analysis on using some techniques of the epidemic course. A new perspective of fractional calculus known as piecewise derivatives of fractional order is used to study the proposed model. Sufficient conditions are established to show the existence theory. In addition, a numerical scheme based on Newton’s polynomials is established to simulate the approximate solutions of the proposed model by using various fractional orders. Some real data results are also shown with comparison of the numerical results.

Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto optimal solutions have led to a wide range of new applications related to optimal and feedback control which results in new challenges such as expensive models or real-time applicability. Since the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview over recent developments in accelerating multiobjective optimal control for complex problems where either PDE constraints are present or where a feedback behavior has to be achieved. In the first case, surrogate models yield significant speed-ups. Besides classical meta-modeling techniques for multiobjective optimization, a promising alternative for control problems is to introduce a surrogate model for the system dynamics. In the case of real-time requirements, various promising model predictive control approaches have been proposed, using either fast online solvers or offline-online decomposition. We also briefly comment on dimension reduction in many-objective optimization problems as another technique for reducing the numerical effort.

In the study of materials and macromolecules by first-principle methods, the bond order is a useful tool to represent molecules, bulk materials and interfaces in terms of simple chemical concepts. Despite the availability of several methods to compute the bond order, most applications have been limited to small systems because a high spatial resolution of the wave function and an all-electron representation of the electron density are typically required. Both limitations are critical for large-scale atomistic calculations, even within approximate density-functional theory (DFT) approaches. In this work we describe our methodology to quickly compute delocalization indices for all atomic pairs, while keeping the same representation of the wave function used in most compute-intensive DFT calculations on high-performance computing equipments. We describe our implementation into a post-processing tool, designed to work with Quantum ESPRESSO, a popular open-source DFT package. In this way we recover a description in terms of covalent bonds from a representation of wave function containing no explicit information about atomic types and positions.

On-chip integration of two-dimensional (2D) materials with unique structures and distinctive properties endow integrated devices with new functionalities and improved performance. With a high flexibility in modifying its properties and a strong compatibility with various integrated platforms, graphene oxide (GO) becomes an attractive 2D material for implementing functional hybrid integrated devices. Here, we demonstrate novel functionalities that go beyond the capabilities of conventional photonic integrated circuits, by harnessing the photo-thermal effects in 2D GO films integrated onto them. These include all-optical control and switching, optical power limiting, and non-reciprocal light transmission. The 2D layered GO films are on-chip integrated with precise control of their thicknesses and sizes. Benefitting from the broadband response of 2D GO films, all the three functionalities feature a very wide operational bandwidth. By fitting the experimental results with theory, we also extract the changes in material properties induced by the photo-thermal effects, which reveal interesting insights about 2D GO films. These results highlight the versatility of 2D GO films in implementing functional integrated photonic devices for a range of applications.

As various services have been generating large scale graphs to represent multiple relationships between objects, studies have been conducted to obtain subgraphs with particular patterns. In this paper, we propose a distributed query processing method to efficiently search a subgraph for a large graph on Spark. To reduce unnecessary processing costs, the search order is determined by filtering scores using the probability distribution. The partitioned queries are searched in parallel in the distributed graph of each slave node according to the search order, and the local search results obtained from each slave node are combined and returned. The query is partitioned in triplets based on the determined search order. The performance of the proposed method is compared with the performance of existing methods to demonstrate its superiority.

A classical origin for the Bohmian quantum potential, as that potential term arises in the quantum mechanical treatment of black holes and Einstein-Rosen (ER) bridges, can be based on 4th-order extensions of Einstein's equations. In Bohm's ontological interpretation, black hole radiation, and the analogous tunneling process of quantum transmission through an ER bridge, are classically allowed if the dynamics are modified to include such a quantum potential. The 4th-order extension of general relativity required to generate the quantum potential is given by adding quadratic curvature terms with coefficients that maintain a fixed ratio, as their magnitudes approach zero. Quantum transmission through the classically non-traversable bridge is replaced by classical transmission through a traversable wormhole. If entangled particles are connected by a Planck-width ER bridge, as conjectured by Maldacena and Susskind, then the classical wormhole transmission effect gives the ontological nonlocal connection between the particles posited in Bohm's interpretation of their entanglement. It is hypothesized that higher-derivative extensions of classical gravity can account for the nonlocal part of the quantum potential generally.

Elucidating physicochemical processes in the degradation of pollutants may optimize their removal from water sources. This work presents a set of elementary steps in the photocatalytic degradation of carbamazepine (CBZ), assuming a steady state approximation in an Advanced Oxidation Process (AOP) combining short-wave ultraviolet radiation (UVC), homogeneous reagent (H₂O₂) and heterogeneous (TiO₂) catalyst. Elementary steps include excitation of both reagent/catalysts by UVC photons, adsorption of CBZ on the excited TiO₂, or its oxidation by hydroxyl radicals. Assuming the steady state approximation on the intermediate products (excited TiO₂, CBZ- excited TiO₂ complex, and hydroxyl radicals), leads to rate laws for degradation of CBZ, in which UVC radiation, TiO₂, and H₂O₂ are pseudo first order at all concentrations or intensities having no direct influence on CBZ pseudo-order, whereas CBZ shifts from pseudo first order at low concentrations to pseudo-zero order at high concentrations. Several experiments to test the mechanism were conducted, by varying CBZ, H₂O₂, and TiO₂ concentrations, and UVC radiation intensities. Measured results indeed fit the suggested mechanism for the first three, but irradiation intensity appears to shift CBZ influence from pseudo-second to pseudo-first order with increased intensities. Corrected elementary steps are proposed to fit the results.

We study the tight focusing properties of generic bright and dark HyOPS beams in the presence of primary coma. The role of the polarization singularity index and handedness of the polarization of the HyOPS beams on the focused structure has been discussed. Results have been presented for the total intensity, component intensities, and component phase distributions for left-, and right-handed bright and dark star and lemon types singularities. The presence of primary coma distorted the focal plane intensity distributions for both positive and negative index generic C-points. Coma is known to disturb the circular symmetry of the focal plane intensity distribution. Similarly in tight focusing polarization is known to disturb the symmetry. Therefore, a beam with structured and inhomogeneous polarization distribution tightly focused under the influence of coma is a fit case to study. It is found that the presence of primary coma aberration in the focusing system produces a positional shift of the high-intensity peaks and a reduction of the intensity on one side of the center. As the strength of the primary coma increases, the focal plane intensity distributions shift more and more toward the right from the initial position. Unlike the scalar vortex case, in the case of HyOPS beams, the focal plane intensity distribution undergoes rotation, as the helicity of the HyOPS beams is inverted, in addition to shifting. All the component phase distributions are found to be embedded with phase vortices of charge ±1.

Proteomic analysis revealed the preservation of many proteins in the “Heslington brain” (which is at least 2,600-year-old brain tissue uncovered within the skull excavated in 2008 from a pit in Heslington, Yorkshire, England). Five of these proteins (“main proteins”), heavy, medium, and light neurofilament proteins (NFH, NFM, and NFL), glial fibrillary acidic protein (GFAP), and myelin basic (MBP) protein are engaged in the formation non-amyloid protein aggregates, such as intermediate filaments and myelin sheath. We used a wide spectrum of bioinformatics tools to evaluate the prevalence of functional disorder in several related sets of proteins, such as “main proteins” and their 44 interactors, as well as all other protein identified in the Heslington brain. These analyses revealed that all five “main proteins”, half of their interactors and almost one third of the Heslington brain proteins are expected to be mostly disordered. Furthermore, most of the remaining proteins are expected to contain sizable disordered regions. This is in contrary the expected substantial (if not complete) elimination of the disordered proteins from the Heslington brain. Therefore, it seems that the intrinsic disorder of NFH, NFM, NFL, GFAP, and MBP, their interactors and many other proteins might play a crucial role in preserving the Heslington brain by forming tightly folded brain protein aggregates, in which different parts are glued together via the disorder-to-order transitions.

A stochastic dominance (SD) relation can be defined by two different perspectives: One from the view of distributions, and the other one from the view of expected utilities. In early days, Fishburn investigated SD from the view of distributions and we refer this perspective as Fishburn’s SD. One of his many results was the development of fractional-order SD for continuous distributions. However, discrete fractional-order SD may not be generalized directly since some properties of fractional calculus do not have a discrete counterpart. In this paper, we develop a discrete analogue of fractional-order SD from the view of distributions. We generalize the order of SD by Lizama’s fractional delta operator, show the preservation of SD hierarchy, and formulate the utility classes that are congruent with our SD relations. This work brings a message that some results of discrete SD cannot be generalized directly from continuous SD. We characterize the difference between discrete and continuous fractional-order SD, as well as the way to handle them.

In this paper, existence and stability results of non-local integro-differential equation with Hilfer derivative of order ω∈(1,2) have been investigated. In this derivative is applied in RLC circuit equation of various fractional order. To proposed problem the existence solutions are derived using Schaefer’s fixed point theorem and the Banach contraction principle is using for uniqueness results. To demonstrate the effectiveness and applicability of our theoretical conclusions and two-step Lagrange polynomial interpolation were used to solve four numerical results.

To reveal the influence of variables such as entrepreneurial learning, entrepreneurial inspiration, and incubation resources on students' entrepreneurial intentions in vocational colleges, this study took vocational colleges in Zhejiang Province, a province with a strong entrepreneurial climate in China, as an example. The study used a questionnaire to obtain data, and 614 valid questionnaires were collected from seven vocational colleges. The study divided entrepreneurship education into three dimensions: entrepreneurial learning, entrepreneurial inspiration, and incubation resources, and used structural equation modeling to investigate the influence of entrepreneurship education on entrepreneurial intentions while introducing entrepreneurial efficacy as a mediating variable to examine the influence mechanism of entrepreneurship education on entrepreneurial intentions of higher education students. The results showed that entrepreneurial learning, entrepreneurial inspiration, incubation resources, and entrepreneurial efficacy were all significantly and positively correlated with entrepreneurial intentions and that entrepreneurial efficacy mediated between the two dimensions of entrepreneurship education (entrepreneurial learning and entrepreneurial inspiration) and entrepreneurial intentions. Therefore, to enhance the effectiveness of entrepreneurship education in vocational institutions, we should stimulate students' sense of entrepreneurial efficacy, strengthen their entrepreneurial learning and inspire them to start their businesses. In turn, university incubation resources can be developed and utilized to enhance students' entrepreneurial confidence and intentions.

Purpose: Now traditional lecture-based teaching and learning have been affected by the COVID-19. The objectives of this article are to design the novel educational technique called ‘dynamic-based learning’ (DBL) that provides the combination of online teaching-learning methods and student’s creativity, to evaluate primary dynamic-based learning function, and to propose dynamic-based learning for higher education. Methods: DBL composes of four steps, including, preparation, homework, classroom, and evaluation, which was designed, and taught in medical and dental schools. Online support materials included mobile phone, email, Facebook Messenger, Line Messenger, Cisco Webex, and Zoom Meetings applications were recruited for this novel method. Results: A total of 32 third-year medical students and 26 sixth-year dental students was treated by DBL similarly. three subjects, including, Innovation in Dentistry, Basic Medical Research, and Principles of Pathology and Forensic Medicine were selected in this article. The results showed students could create their knowledge, ideas, and creativity during the online classes.Conclusion: DBL can be used as an alternative learning mode during the COVID-19 crisis. The benefits of DBL also include high flexibility, dynamic process, active learning, and high creativity. DBL should be tested with other disciplines such as engineering school, laws school, health sciences school, and should be compared with other traditional teaching and learning modes in the future. This method may support the global higher education systems to move forward the COVID-19 pandemic to set a novel standard of a future normal.

Urban settings are increasingly faced with challenges across natural and engineered environmental systems, threatening the sustainability of urban centers where >50% of the world's population resides. The pressures of aging infrastructure, water and air pollution, and environmental justice exemplify the growing need for urban professionals to employ complex scientific reasoning across disciplines where they can effectively address the multi-faceted issues of urban sustainability. Here we present an innovative model for preparing the next generation of public, private, and academic leaders to address complex problems in urban sustainability. Specifically, we outline the design and implementation of an integrated, adaptable graduate training program, with the goals of science leadership, curriculum relevancy, community impact, broader applicability, recruitment into science, technology, engineering and mathematics (STEM) programs and careers, and program sustainability. This program addresses human-ecosystem challenges using a transdisciplinary approach to produce scientific products in partnership with local communities, businesses, industries, scientists, and policy makers, while providing a mechanism to understand and overcome contemporary societal challenges. Students receive rigorous training in their home disciplines, coupled with training across disciplinary lines and developmental experiences, to prepare them to communicate, collaborate, and innovate in a variety of contexts. Training success is evaluated across measurable competency domains including problem definition, research methods, communication, collaboration, and problem-solving. After three years the program expanded relationships across fields and professions, successfully established 18 internship opportunities with community partners, created a new dual-title PhD program open to students in 5 academic departments, and facilitated the co-production of knowledge with external partners. This model bridges the gaps between research, education, and application, providing an integrated, rigorous graduate training program that fosters collaborative problem-solving between STEM graduate students and the broader community of professionals conducting sustainability work in a post-industrial urban setting.

The Bologna Process and the European Higher Education area require the application of new active methodologies in the classroom that place the student at the center of his or her learning process. In the present work we analyze the application of a Service-Learning methodology in the context of a Final Degree Dissertation (FDD) in the degree in Environmental Sciences at the University of Extremadura (Spain). The project deals with an isolated Kichwa community in Ecuador and involves the development of alternative science education materials for the capacitation of in-service science teachers. This paper evaluates how an FDD carried out according to self-learning (SL) principles can help in the acquisition of so-called soft skills and how these can be focused in the promotion of the Sustainable Development Goal (SDG) knowledge and achievement. To this end, a qualitative study of the experience and a deep evaluation, followed by a final reflection, were carried out. According to the preliminary results, we can conclude that Higher Education should include SDGs in its teaching praxis and could do this successfully using the SL methodology.

Education is an imperative key to driving sustainability and gender equity. In addition to addressing well-known female deficiencies in leadership training, it is really important to develop initiatives in sustainable leadership education for women to acquire skills, competencies and tools on leadership and to increase their self-perceptions. The purpose of this study is to assess a Women’s Leadership Program for university students. The sample consisted of 50 students enrolled in the program. A mixed-method approach was applied. Quantitative methods with a survey were conducted to evaluate the training and the achievement of leadership skills. In the data analysis, a descriptive statistics variance analysis, using a Welch statistic and T2 Dunnett test, was applied. Qualitative research methods were conducted through three focus groups to evaluate personal changes in their own-perceptions and self-confidence. Results suggest that the female students in the program reached a level of leadership knowledge with practical tools for their future. The program inspired them and confirmed changes in their personal capacities or self-confidence, including reflection about facing challenges in the work environment. The findings support the effectiveness of the specific education in breaking two barriers shown by the literature for women to getting a managerial position: lack of training and female self-confidence.

The impact of instructional guidance on learning outcomes in higher biomedical education is subject of intense debate. There is the teacher-centered or traditional way of teaching (TT) and, on the other side, the notion that students learn best under minimal guidance (problem-based learning, PBL). Although the benefits of PBL are well-known, there are aspects susceptible to improvement. Hence, a format merging TT and PBL (hybrid-PBL, h-PBL) may advance education in biomedical sciences. Here, we systematically reviewed studies that employed h-PBL in higher biomedical education compared to TT and/or pure PBL. We found that h-PBL resulted in better overall students’ performance and perception than TT or pure PBL. These findings encourage more research on investigating the pedagogical benefits of h-PBL and posit an eclectic system in which the pedagogical tools from TT and PBL are used cooperatively in the best interest of the education and satisfaction of the students.

Transcription factors (TFs) are proteins that recognize specific DNA fragments in order to decode the genome and ensure its optimal functioning. TFs work at the local and global scales by specifying cell type, cell growth and death, cell migration, organization and timely tasks. We investigate the structure of DNA-binding motifs with the theory of finitely generated groups. The DNA ‘word’ in the binding domain -the motif- may be seen as the generator of a finitely generated group Fdna on four letters, the bases A, T, G and C. It is shown that, most of the time, the DNA-binding motifs have subgroup structure close to free groups of rank three or less, a property that we call ‘syntactical freedom’. Such a property is associated to the aperiodicity of the motif when it is seen as a substitution sequence. Examples are provided for the major families of TFs such as leucine zipper factors, zinc finger factors, homeo-domain factors, etc. We also discuss the exceptions to the existence of such a DNA syntactical rule and their functional role. This includes the TATA box in the promoter region of some genes, the single nucleotide markers (SNP) and the motifs of some genes of ubiquitous role in transcription and regulation.

As a matter of course, the first gene must be formed in the absence of gene. On the other hand, many biopolymers including gene are produced under the genetic system in extant organisms. Thus far, no idea explaining how the first gene was formed in the absence of gene, has been proposed except the idea based on the GADV hypothesis. GADV means four amino acids; Gly [G], Ala [A], Asp [D] and Val [V]. In this article, a reliable answer to the question, how the first gene was generated, is provided. The idea is as follows. The first gene (genetic information) was formed by random joining of anticodons, GNCs, which were carried by primeval anticodon stem-loop (AntiC-SL) tRNAs produced during repeated cycles of random joining of nucleotides and degradation of oligonucleotides. However, it might be difficult for many persons to accept the idea, because tRNAs and metabolic pathways using various proteins, which are produced under genetic functions, must be used to form the first gene. Then, it is reconsidered based on definition of genetic information and minimum necessary things to generate the first gene in this article, how the first gene was generated. Consequently, it could be reconfirmed that five prototypes of members (genetic code, tRNA, metabolism, cell structure and protein) composing the fundamental life system, except gene, are certainly necessary to generate the first gene. Namely, it can be concluded that the first gene was formed through nucleotide metabolism with immature [GADV]-proteins, primeval AntiC-SL tRNA formation with immature [GADV]-proteins, formations of single-stranded (GNC)n codon sequence by random joining of anticodons, GNCs, carried by AntiC-SL tRNAs, double-stranded (ds)-(GNC)n RNA and maturation of an immature [GADV]-protein, which was produced from one strand of the ds-RNA. Thus, the first gene was formed using the five primitive or prototypes of members, which were produced in the absence of gene. There would be no other way for generating the first gene.

The aim of the present work is to explore a different non-traditional approach to higher dimensional spacetime which differs from the usual approaches such as large extra space dimensions, warped extra space dimensions and multiple extra time dimensions. This approach will be referred to as "Dynamic" higher dimensional spacetime. By this term will be introduced a new kind of higher dimensional spacetime (more than the usual 3+1 dimensions), which behaves dynamically in the sense that time is not a fixed dimension but is the extra plus one dimension to the spatial dimensions of the phenomenon we are studying. For a higher dimensional phenomenon, the lower dimensional time will behave as space and the new time will be a plus one dimension, meaning if we study a 3-dimensional phenomenon then time is the usual 4th dimension but if we are studying a 4-dimensional phenomenon then its time will be an extra 5th dimension and for this phenomenon the 4th dimension will behave as space. All spatial dimensions are indistinguishable from each other and behave in the exact same way, which means that the important parameter is not the dimension we are studying (for example the 4th or the 5th) but the number of dimensions in which a phenomenon can interact and how higher dimensional phenomena interact with lower ones. This non-traditional approach to higher dimensional spacetime may appear confusing at first but will become clearer in the rest of the paper. For this reason, we will first associate the time dimension with propagation relative to space dimensions and change orthogonal to them in order to give the reader a better intuition. Following that, we will describe how higher - dimensional phenomena would appear to us, the 3 - dimensional observer and try to set some guidelines on how we should mathematically model higher - dimensional phenomena in order for us to make accurate predictions of their behaviour. Then we will express the general framework of a "Dynamic" higher - dimensional spacetime and turn our gaze to 4+1 – dimensional phenomena. We will explore how a mass term arises for 4 – dimensional waves by generalizing the frequency – speed – wavelength relation of 3D waves and give a basic description on a possible way to describe a 4+1 – dimensional disturbance in a scalar Energy Field in order to make accurate predictions on our 3+1 dimensional plane. In this framework we will derive the Klein – Gordon equation by generalizing the wave equation and ignoring all lower than 4+1 - dimensional disturbances and compere our mass term findings with the Klein – Gordon equation mass term and with results from gravity – induced quantum interference experiments. Lastly, we will describe how a "Dynamic" 5 - dimensional spacetime would appear in a 3D observer and examine whether our findings are compatible with quantum mechanics and the special theory of relativity.

This study presents finite-time synchronization of chaotic fractional order systems with disturbance uncertainty and unknown time delay. First, a PID sliding surface is presented. Then, for the finite-time synchronization of the master and slave systems, a robust sliding-adaptive control method is provided. Update rules have been retrieved to estimate the system parameters by using the Lyapunov function while establishing the stability of the suggested mechanism and assuring the convergence of errors to zero. The proposed approach was used to solve the fractional order system of Gensou-Tsei with time-varying parameters, and the simulation results show that the presented approach performs well.

We investigate numerically the interactions of in-phase Airy beams modulated by a fundamental Gaussian beam and fourth-order diffraction in Kerr nonlinear media. Directly numerical simulations show that normal (anomalous) fourth-order diffractions and in-phase (out-of-phase) Gaussian beam affect the interactions of solitons generated from Airy beams in unique manners. Different from previous results that interactions between in-phase (out-of-phase) conventional beams are always attractive (repulsive), many anomalous interactions of Airy beams are obtained. Stable bound states of breathing Airy soliton pairs can be formed with the help of fourth-order diffraction and fundamental Gaussian beam.

Let $m$ and $n$ be the fixed positive integers. Suppose $\mathcal{A}$ is a von Neuman algebra with no central summands of type $I_{1}$ and $L_{m}$ be a Lie type higher derivation i.e., an additive (linear) map $L_{m} :\mathcal{A}\to \mathcal{A}$ such that \begin{equation}\label{def2} \[L_{m}(p_{n}(\mathfrak{S}_{1},\mathfrak{S}_{2},\cdots,\mathfrak{S}_{n}))=\sum_{l_1+l_2+\cdots+l_n=m}p_{n}\big(L_{l_1}(\mathfrak{S}_{1}),L_{l_2}(\mathfrak{S}_{2}),\cdots,L_{l_n}(\mathfrak{S}_{n})\big)\] %L_{m}(p_{n}(\mathfrak{S}_{1},\mathfrak{S}_{2},\cdots,\mathfrak{S}_{n}))=\sum_{l_1+l_2+\cdots+l_n=m}p_{n}\big(L_{l_1}(\mathfrak{S}_{1}),L_{l_2}(\mathfrak{S}_{2}),\cdots,L_{l_n}(\mathfrak{S}_{n})\big)\nonumber \end{equation} for all $\mathfrak{S}_{1},\mathfrak{S}_{2},\cdots,\mathfrak{S}_{n}\in \mathcal{A}$. In the present paper, we study Lie type higher derivations on von Neuman algebras and prove that every additive Lie type higher derivation on $\mathcal{A}$ has a standard form at zero product as well as at projection product. Further, we discuss some more related results.

Anyon is collective excitation of two dimensional electron gas subjected to strong magnetic field, carrying fractional charges and exotic statistical character beyond fermion and boson. So far, anyons with serial fractional charges only exist in fractional quantum Hall effect. It is still a challenge to find new serial of fractional charges in other physical system and develop an unified mathematical physics theory based on the same root. Here a topological path fusion theory of propagating electrons in magnetic flux lattice is proposed to explore the physical origin of fractional charges based on a generalization of Feynman's path integral theory and Thurston's train track theory. This mathematical physics theory generated the existed serial of fractional charges in fractional quantum Hall effect and predicted new serial of fractional charges. A serial of irrational charges are predicted in one dimensional lattice of magnetic fluxes. Fractionally charged anyons are also generated in two dimensional and three dimensional lattice of train tracks of electric currents, revealing an exact correspondence between knot lattice model and train track model. A new explanation for the modular symmetry of complex Hall conductance and composite fermion in fractional quantum Hall effect is also derived from this topological path fusion theory. Experimental observation of anyon in three dimensions can be realized by constructing three dimensional interlocking magnetic fluxes or mapping magnetic fluxes into forbidden zones in multi-connected space filled by solid state material. A photonic crystal with porous nano-structures is a promising system for detecting fractional charges and paves a new way for topological quantum computation.

Brazil, Russia, China, India, and the Republic of South Africa (BRICS) represent developing economies facing different energy and economic development challenges. The current study aims to forecast energy consumption in BRICS at aggregate and disaggregate levels using the annual time series data set from 1992 to 2019 and to compare results obtained from a set of models. The time-series data are from the British Petroleum (BP-2019) Statistical Review of World Energy. The forecasting methodology bases on a novel Fractional-order Grey Model (FGM) with different order parameters. This study contributes to the literature by comparing the forecasting accuracy and the forecasting ability of the FGM(1,1) with traditional ones, like standard GM(1,1) and ARIMA(1,1,1) models. Also, it illustrates the view of BRICS's nexus of energy consumption at aggregate and disaggregates levels using the latest available data set, which will provide a reliable and broader perspective. The Diebold-Mariano test results confirmed the equal predictive ability of FGM(1,1) for a specific range of order parameters and the ARIMA(1,1,1) model and the usefulness of both approaches for energy consumption efficient forecasting.

Reverse order laws for generalized inverses of matrix products is a classic object of study in the theory of generalized inverses. One of the well-known reverse order laws for a matrix product $AB$ is $(AB)^{(i,\ldots,j)} = B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$, where $(\cdot)^{(i,\ldots,j)}$ denotes an $\{i,\ldots, j\}$-generalized inverse of matrix. Because $\{i,\ldots, j\}$-generalized inverse of a singular matrix is unique, the relationships between both sides of the reverse order law can be divided into four situations for consideration. This paper provides a thorough coverage of the reverse order laws for $\{i,\ldots, j\}$-generalized inverses of $AB$, from the development of background and preliminary tools to the collection of miscellaneous formulas and facts on the reverse order laws in one place with cogent introduction and references for further study. We begin with the introduction of a linear mixed model $y = AB\beta + A\gamma + \epsilon$ and the presentation of two least-squares methodologies to estimate the fixed parameter vector $\beta$ in the model, and the description of connections between the two types of least-squares estimators and the reverse order laws for generalized inverses of $AB$. We then prepare some valued matrix analysis tools, including a general theory on linear or nonlinear matrix identities, a group of expansion formulas for calculating ranks of block matrices, two groups of explicit formulas for calculating the maximum and minimum ranks of $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$, as well as necessary and sufficient conditions for $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$ to be invariant with respect to the choice of $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$. We then present a unified approach to the 512 matrix set inclusion problems associated with the above reverse order laws for the eight commonly-used types of generalized inverses of $A$, $B$, and $AB$ through use of the definitions of generalized inverses, the block matrix method (BMM), the matrix rank method (MRM), the matrix equation method (MEM), and various algebraic calculations of matrices.

In this paper, we give the Galois adjunction form of the regular relation, and by using residuated mapping, we find the connection between it and order-generating set. Furthermore, we obtain the equivalent conclusion of "regular". In addition, by using the specialization order of topological space and the lower approximate operator in the rough set, we find a continuous homeomorphic mapping from a regular space to a Alexandrov topological space

Resonant light scattering by mesoscale dielectric spheres has received enormous attention and found many interesting applications. The recently emerged field of Mesotronics provides novel opportunities for wavelength-scaled optics and new fundamental aspects are still being uncovered. It has recently been demonstrated that high-order Mie resonances can be excited in homogeneous low-dissipation mesoscale dielectric spheres, leading to the generation of intense magnetic fields. This Letter describes a simple and effective way to drastically enhance the superresonance effect. Proof-of-principle results for the first time show that yet one more novel phenomenon of increasing the intensity of the magnetic field without changing the resonant Mie size parameter of the sphere by introducing an air cavity. In such a dielectric cenosphere (from two Greek words “kenos” - hollow and “sphaira” - sphere), by correct choosing of the air cavity size, it is possible to increase the intensity of the electromagnetic fields at the poles of the sphere by an order of magnitude due to increasing of amplitude of resonant partial wave coefficient.

The efficiency of a new composite material of the layered double hydroxide (LDH) of ZnMgAl and rice husk biochar (RHB) for the removal of Cu(II) and Pb(II) ions from synthetic wastewater was investigated in this study. The images of scanning electron microscope showed extremely fine crystalline LDH particles decorated on the rough surface of the RHB while the succesful formation of the composite adsorbent (LDH/RHB) was confirmed by the corresponding energy dispersive X-ray and the Fourier-transform infrared spectroscopy. An equilibrium contact time of 30 and 15 min for Cu2+ and Pb2+, respectively, was proposed for the optimum performance of the batch adsorption process. The dose of the LDH/RHB adsorbent was optimized at 0.4 g yielding maximum adsorption capacities of 117 and 124 mg g-1 for Cu2+ and Pb2+, respectively, with corresponding maximum removal efficiencies of nearly 94% and 99%. The initial meta concentrations was optimized at 50 or 60 mg L-1 corresponding to maximum removal efficiencies or adsorption capacities. For the changing initial metal’s concentration, the removal efficiencies remained unchanged for up to 50 mg L-1 and decreased by about 50% by increasing the initial concentrations from 50 to 100 mg L-1. The adsorption capacities observed a linear increasing trend by increasing the initial concentrations from 5 to 60 mg L-1 and remained unchanged afterward up to 100 mg L-1. A solution pH of 6.0 yielded optimum results with an increasing trend in adsorption capacities and percentage removal by changing the solution pH from 2.0 to 7.0. Based on the best-fit of the pseudo second-order kinetic model to the experimental data, the chemisorption was suggested to be the controlling mechanism of adsorption. The fitting of the Langmuir model suggested a monolayer sorption of Cu2+ and Pb2+ in addition to a heterogeneous adsorption as supported by the fitting of the Temkin isotherm. The application of the Dubinin–Radushkevich isotherm proposed a physical adsorption (mean free energy of adsorption less than 8 kJ mol−1) of both heavy metal ions on the surface of the LDH/RHB adsorbent.

The operation status of manufacturing equipment is directly related to the reliability of the operation of manufacturing equipment and the continuity of operation of the production system. Based on the analysis of the operation status of manufacturing equipment and its characteristics, it is proposed that the concept of assessing the operation status of manufacturing equipment can be realized by applying real-time acquisition of accurate inspection data of important parts of weak motion units and comparing them with their motion status evaluation criteria. Through the study of the application characteristics of fractional-order calculus theory, a differential data fusion model based on the fractional-order differential operator is established. The advantages of Internet of Things (IoT）technology and fractional order differential fusion algorithm are integrated to obtain real-time high-precision data of the operating parameters of manufacturing equipment, and the research objective of operating condition assessment of manufacturing equipment is realized. The feasibility and effectiveness of the method are verified by the application of the method in machining center operation status assessment.

A comprehensive presentation of a variety of biologically sounding properties of genomes is present; chloroplast genomes are used as a biological matter. Triplet frequency composition is the general issue standing behind the properties. Besides, the new alignment-free error-tolerant method of sequences comparison highly efficient for in/del mismatches is present, for transposons search. Triplet frequency dictionaries determined for a genome, or for a part of that latter were studied through various clustering techniques. The interplay between triplet composition and function reveals on tRNA genes unambiguously shows the prevalence of the function encoded in tRNA gene over the phylogeny: the genes gather into the clusters comprising the genes encoding the same amino acid; more exactly, few gene families exhibit fine cluster pattern corresponding the synonymous codons of amino acid. Previously reported symmetry in chloroplast genomes is shown for a set of gymnosperm: that is mirror symmetry, rotational symmetry, and the second Chargaff's parity rule asymmetry. A family of transposons was found in gymnosperm chloroplast genomes. This family is revealed through the novel comparison method based on convolution calculation, for a set of DNA sequences.

To quantify the time-varying reproduction number (Rt) for Malaysia using the COVID-19 incidence data., we used data the from the Johns Hopkins University Center for Systems Science and Engineering (JHU CCSE) Coronavirus repository. Day 1 was taken from the first assumed local transmission of COVID-19. Data was split into four intervals: a) Interval 1: from Day 1 to Day 10 MCO 1, b) Interval 2: from Day 1 to Day 10 MCO 2, c) Interval 3: from Day 1 to Day 10 MCO 3 and d) Interval 4: from Day 1 to Day 10 MCO 4. We estimated the Rt using the EpiEstim package. The means for Rt at Day 1, Day 5 and Day 10 for all MCOs ranged between 0.665 to 1.147. The average Rt gradually decreased in MCO 1 and MCO 2. However, Rt increased in MCO 3 before stabilized around 0.8 in MCO 4. MCO 1 and MCO 2 which were stricter coincide with the gradual reduction of Rt. However, the more relaxed MCO 3 and MCO 4 correspond to a slight increase in the Rt before it stabilized.

When a rotary machine is running, from which the acquired vibro-acoustic signals enable to reveal its operation status and health condition. The study proposed a DSP-based adaptive angular-velocity Vold-Kalman filtering order tracking (AV2KF_OT) algorithm with an online real-time nature for signal interpretation and machine condition monitoring. Theoretical derivation and numerical implementation of computation schemes are briefly introduced. An online real-time monitoring system based on the AV2KF_OT algorithm, which was implemented through both a digital signal processor and a user interface coded by using LabVIEW, was developed. Two experimental tasks were applied to justify the proposed technique, including (i) the detection of startup on the fluid-induced whirl performed through a journal-bearing rotor rig, and (ii) the separation of close orders from the measured signals of a multifunction transmission-element ball-bearing bench.

Time series data having low signal-to-noise ratio, non-stationarity and non-linearity are commonly seen in high-frequency stock trading, where the objective is to increase the likelihood of profit by taking advantage of tiny discrepancies in prices and trading on them quickly and in huge quantities. For this purpose, it is essential to apply a trading method that is capable of fast and accurate prediction from such time series data. In this paper, we develop an online time series forecasting method for high-frequency trading (HFT) by integrating three neural network deep learning models, i.e., Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU) and Transformer; and we abbreviate the new method to online LGT or O-LGT. The key innovation underlying our method is its efficient storage management, which enables super-fast computing. Specifically, when computing the forecast for the immediate future time, we use only the output calculated from the previous trading data (rather than the previous trading data themselves) together with the current trading data. Thus, the computing involves updating only the current data into the process. We evaluate the performance of O-LGT by analyzing the high-frequency Limit Order Book (LOB) data from the China market. It shows that our model in most cases achieves similar speed with much higher accuracy than the conventional fast supervised learning models for HFT. However, with a slight sacrifice in accuracy, O-LGT is approximately 40 times faster than the existing high-accuracy neural network models for the LOB data in China market.

Despite the successes earned in cataloguing and finding the role of the most of molecular components in living matter, the “biochemical and molecular” perspective, popular in biology, medicine and genetics, is unable to give account for crucial topics as the faculty of living systems to “feel”, to “perceive” what a given stimulus implies (means, indeed) for their survival. Condensed matter physics too, if bounded to a local, short-range, and perturbative approach, fails dramatically. This is also due to the role commonly assigned to water – actually the main constituent of living matter – deemed for long time to be merely chemical (as “solvent” or a reactant/product). Nonetheless, today many evidences show how living matter can be right conceived as a super-structured coherent water-based matrix, suggesting that the characterization of bio(electro)chemical and physical processes undertaken at molecular level in living matter, would let us unable to answer a question like this: what allows an amoeba, moreover without any neurons, to “know” to get closer to a nutrient or escape away from a toxin? I propose that to pursue such a fundamental inquiry it’s necessary an essentially relational approach, that is: to consider the living being at its grounding as the outcome of a physical history of relationships where symmetry-breakings, dissipation and coherence yield the emergence of the living state of matter, conceivable only as a time-dependent open process, and not as a portraited “body”. The effective tools to build up such an approach may be retrieved in far-from-equilibrium thermodynamics (TD), symmetry-breakings and gauge-fields theory, science of complexity, within the framework of a Quantum Field Theory. Indeed, within a field-view of matter, and of water especially, as it has been developed by a Quantum Electrodynamic (QED) description of condensed matter, it’s possible to give account for a physical basis too such an epistemologically elusive, though crucial, feature of living systems (i.e.: perception and meaning). The emerging landscape allows some important meditations about adaptation, evolution, ecodynamics, and about different conceptions of complexity and “information” in living realm. Furthermore, some neuroscientific themes like consciousness, qualia and their links to artificial intelligence could be supplied with due insights.

We shall discuss three methods of inverse Laplace transforms. A Sinc-Thiele approxi- mation, a pure Sinc, and a Sinc-Gaussian based method. The two last Sinc related methods are exact methods of inverse Laplace transforms which allow us a numerical approximation using Sinc methods. The inverse Laplace transform converges exponentially and does not use Bromwich contours for computations. We apply the three methods to Mittag-Leffler functions incorporating one, two, and three parameters. The three parameter Mittag-Leffler function represents Prabhakar’s function. The exact Sinc methods are used to solve fractional differential equations of constant and variable differentiation order.

This study aimed to explore what factors affect teachers’ acceptance and instructional use of ICT in Chinese higher vocational colleges. Grounded in the modified UTAUT model, the current study investigated the direct and indirect effects of teachers’ performance expectancy, effort expectancy, external conditions, and behavioral intentions on using ICT in teaching. A total of 6087 teachers from 219 vocational colleges in 28 provinces in China participated in a large-scale survey. Structural equation modeling revealed that the teachers’ psychological perceptions (including performance expectancy, effort expectancy, and intention to use ICT technology) and the external support conditions (including professional development support, infrastructures, the climate of organizational reform and innovation, and teacher performance assessment mechanisms) significantly directly affect the use of ICT in Chinese higher vocational college teachers’ teaching practice. Moreover, this study confirmed the mediating role of teachers’ intention to use ICT in teaching in the relationship between teachers’ psychological perceptions and ICT instructional usage behavior. However, there were differences in the significance of these variables in the chain effect of teachers’ intention to use ICT. These findings expand our understanding of the factors influencing ICT use in teaching among VET teachers in China and thus provide practical implications for higher vocational college managers to promote teachers’ ICT teaching behaviors.

We introduce and discuss a generalization of the classical multi-objective optimization to pairs of functions. This procedure is referred to as bi-multi-objective optimization. A justification of this general optimization procedure is presented, related both to multi-objective optimization under ambiguity concerning individual preferences and to Pareto optimality for a family of preferences with nontransitive indifference. Incidentally, the binary relation naturally associated to a bi-multi-objective optimization problem is represented by a finite bi-multi-utility, which generalizes to the nontransitive case the classical finite multi-utility representation. An important application is presented to Markowitz portfolio selection under ambiguity concerning both the vector of returns and the covariance matrix.

Transportation is the primary consumer of oil, accounting for a significant portion of global energy consumption (34%) and CO2 emissions (40%). Electrifying road transportation is crucial to mitigate the effects of global warming. The abundant potential of renewable energy sources like solar and wind is hindered by their intermittent nature and incongruity with peak energy demands. This calls for the development of sophisticated energy storage solutions. Metal-air batteries (MABs), emerging as viable alternatives to lithium-ion batteries (LIBs), have attracted considerable attention due to their promising applications in the transportation sector. Despite substantial progress in MAB development over the past two decades, overcoming critical challenges such as electrolyte decomposition, carbon cathode degradation, anodic dendrite growth, and air impurities remains essential for their commercial viability. This mini-review provides a comprehensive overview of MAB fundamentals and the challenges associated with their development. The insights presented in this review serve to illuminate the current landscape and future prospects of MABs in the transportation sector.

Selection of appropriate friction factors is paramount for accurate prediction of key flow characteristics in gas–liquid two-phase flows. In this work, experimental investigation of vertical air and oil (with viscosities up to 200 mPa s) flow in a 0.060-m ID pipe is reported. Superficial air and oil velocity ranges utilized are from 22.37 to 59.06 m/s and 0.05 to 0.16 m/s respectively. The influence of estimation of interfacial friction factor on accurate determination of film thickness, void fraction and pressure gradient was investigated using a two-fluid model. The results indicated that the two-fluid model is capable of accurately predicting flow characteristics. Further, it reveals that the best performing correlations are the Belt et al. and Ambrosini et al. correlations.

University-Business partnership for collaborative curriculum design, development and delivery is possibly the less explored dimension of University Business Collaboration (UBC). Even if some models for curricular design and development might be available, scarce information exists on how the partnership is constructed, the new curricula are designed, developed and how they are implemented. This article intends to present and discuss the experience obtained during a three-year European funded Project, namely Think4Jobs. This project exemplifies the significance and benefits of UBC in the design, development and delivery of curricula that meet the evolving demands of the labour market while promoting Critical Thinking (CT) as a foundational 21st century skill to contribute to graduates' employability. Think4Jobs project brought together a multidisciplinary team of researchers and business organisations from five European countries (Germany, Greece, Lithuania, Portugal and Romania) with interests in promoting and developing CT and mitigating eventual competence gaps. The project's success was attributed to key practices, including defining a common conceptualization of CT, employing participatory co-design, and providing common training for university and business partners. Clear objectives, explicit roles, effective communication, and ongoing evaluation further enhanced the collaboration. Experiential learning, real-work problems, and case studies reinforced the curricula, bridging the gap between academia and the labour market. By embracing these insights, future UBC initiatives can empower graduates with the necessary skills to stand out in an ever-changing labour market, contributing to enhanced education and successful careers.

We introduce the linear subgroup of volume-preserving diffeomorphism as the underlying symmetry to construct an action within the effective field theory framework and the Schwinger-Keldish formalism. The formulated action is posited to effectively incorporate dissipative effects into the Navier-Stokes equations.

In this paper, we compare the performance between systems of ordinary and (Caputo) fractional differential equations depicting the susceptible-exposed-infectious-recovered (SEIR) models of diseases. In order to understand the origins of both approaches as mean-field approximations of integer and fractional stochastic processes, we introduce the fractional differential equations as approximations of some type of fractional nonlinear birth--death processes. Then, we examine validity of the two approaches against empirical courses of epidemics; we fit both of them to case counts of three measles epidemics that occurred during the pre-vaccination era in three different locations. While FDEs appear more flexible in fitting empirical data, our ODEs offered better fits to two out of three data sets. Important differences in transient dynamics between these modeling approaches are discussed.

This paper investigates the application of blended learning in undergraduate translation classes to enhance the effective incorporation of technology in teaching. Blended learning is the combination of face-to-face instruction with online learning, which provides students with a flexible and diverse learning environment for developing technological proficiency. Using a case study methodology, this research examines the translation undergraduate program at the University of Jeddah, which implemented blended learning as its primary instructional framework starting in 2021. The study aims to explore the advantages and challenges associated with the adoption of blended learning in translation classes while offering practical suggestions that could help in its implementation. The findings show several advantages of integrating blended learning into undergraduate translation classes. Firstly, the students could benefit from a flexible learning environment that accommodates their individual learning preferences and schedules. Secondly, It also helps to promote active engagement and interaction which nurture collaborative learning opportunities among students. Thirdly and lastly, blended learning provides a platform for students to develop their technological skills, which become crucial in today's digital age. Despite this, the study also points out significant challenges that need to be addressed. These important challenges include the required planning and preparation involved in creating effective online components, ensuring equitable access to technology and the internet, and adapting teaching and learning approaches to optimise the blended learning experience.To sum up, this paper contributes to the understanding of blended learning in the context of undergraduate translation classes.

Abstract: Discussed is an expansion of SRT to fourth-order of space-time including any velocities and possible negative kinetic energies by real rest mass in analogy of the model amplitude of enforced damped oscillation. This paper serves an introduction to developed SRT including superluminar translating velocities without tachyons or imaginary restmass. Focused is on those parts, which develop the elaborated lorentz-transformations. Discussed are the problems of this theory.

Nonlocal theories are gaining prominence because they can solve problems which lead to unphysical conclusions in standard models. This study presents a novel fractional boundary element method (BEM) solution for nonlinear nonlocal thermoelastic problems of anisotropic fibrous polymer nanomaterials. This broad BEM solution combines two solutions: anisotropic fibrous polymer nanomaterials problem solution and nonlinear nonlocal thermoelasticity problem solution. The nonlinear nonlocal thermoelasticity problem solution divides the displacement field into complementary component and particular component. The overall displacement is generated using the boundary element technique, which is the solution to a Navier type problem, while the particular displacement is derived using local radial point. The New Modified Shift-Splitting (NMSS) approach, which reduces memory and processing time requirements, was used to solve linear systems created by BEM. Figures demonstrate the numerical findings, which show the effects of fractional and graded parameters on the thermal stresses of nonlinear nonlocal thermoelastic problems of anisotropic fibrous polymer nanomaterials. The numerical results indicate the consistency and efficiency of the proposed methodology.

Estimation of core and surface temperature is one of the crucial functionalities of the lithium-ion Battery Management System (BMS) towards providing effective thermal management, fault detection and operational safety. While, it is impractical to measure core temperature using physical sensors, implementing a complex estimation strategy in on-board low-cost BMS is challenging due to high computational cost and the cost of implementation. Typically, a temperature estimation scheme consists of a heat generation model and a heat transfer model. Several researchers have already proposed ranges of thermal models having different levels of accuracy and complexity. Broadly, there are first-order and second-order heat capacitor-resistor-based thermal models of lithium-ion batteries (LIBs) for core and surface temperature estimation. This paper deals with a detailed comparative study between these two models using extensive laboratory test data and simulation study to access suitability in online prediction and onboard BMS. The aim is to guide whether it’s worth investing towards developing a second-order model instead of a first-order model with respect to prediction accuracy considering modelling complexity, experiments required and the computational cost. Both the thermal models along with the parameter estimation scheme are modelled and simulated using MATLAB/Simulink environment. Models are validated using laboratory test data of a cylindrical 18650 LIB cell. Further, a Kalman Filter with appropriate process and measurement noise levels are used to estimate the core temperature in terms of measured surface and ambient temperatures. Results from the first-order model and second-order models are analyzed for comparison purposes.

Nowadays, the European Union and the governments of the different countries have focused on the development of the Sustainable Development Goals (SDG) and the 2030 agenda, something that has been translated into education itself. Video Games, Gamification, and Game Based Learning have become different strategies and tools to enhance the learning process and some of the growing approaches used by teachers to develop sustainable education in the classrooms. This research aims to analyze the characteristics to promote sustainability in education using games and technology, specifically its learning benefits for Higher Education. A systematic review of the literature was conducted following the PRISMA methodology. At first, 2025 documents were found which, after the filtering phases, the number of articles has been reduced to nine, which subsequently were analyzed in depth. The results indicated that among the benefits of the use of games mediated by technologies are the following: it favors education for sustainability and it promotes the educational inclusion and the work of various social skills such as collaborative and cooperative work. Also, showed an increase of the number of publications between 2019 and 2023, reflecting the growing interest in the topic. However, there are some research gap in this field.

Cavitation resulting from underwater explosions in compressible multiphase or multicomp-onent flows presents significant challenges due to the dynamic nature of shock-cavitation-structure interactions, as well as the complex and discontinuous nature of the involved interfaces. Achieving accurate resolution of interfaces between different phases or components, in the presence of shocks, cavitating regions, and structural interactions, is crucial for modeling such problems. Furthermore, pressure convergence in simulations involving shock-cavitation-structure interactions requires accurate algorithms. In this research paper, we employ the diffuse interface method, also known as the interface capturing scheme, to investigate cavitation in various underwater explosion test cases near different surfaces; free surface and a rigid surface. The simulations are conducted using the Unstructured Compressible Navier-Stokes (UCNS3D) finite volume framework employing central-weighted essentially non-oscillatory (CWENO) reconstruction schemes, utilising the five-equation diffuse interface family of methods. Quantitative comparisons are made between the performance of both models. Additionally, we examine the effects of cavitation as a secondary loading source on structures, and evaluate the ability of the CWENO schemes to accurately capture and resolve material interfaces between fluids with minimal numerical dissipation or smearing. The results are compared with existing high-order methods and experimental data, where possible, to demonstrate the robustness of the CWENO schemes in simulating cavitation bubble dynamics, as well as their limitations within the current implementation of interface capturing.

In this paper it is shown that mathematical description of strain, constitutive law and dynamics obtained by direct replacement of integer order derivatives with Caputo or Riemann-Liouville fractional order partial derivatives, having integral representation on finite interval, in case of a guitar string, is nonobjective. The basic idea is that different observers, using this type of descriptions, obtain different results which cannot be reconciled, i.e. transformed into each other using only formulas that link the coordinates of the same point in two fixed orthogonal reference frames and formulas that link the numbers representing the same moment of time in two different choices of the origin of time measuring. This is not an academic curiosity! It is rather a problem: which one of the obtained results is correct?

We study the influence of high-order twisting phases on polarization states and optical angular momentum of a vector light field with locally linear polarization and a hybrid state of polarization (SoP). The initial SoP of a twisted vector optical field (TVOF) modulated by the high-order twisting phase possesses various symmetric distributions. The propagating properties of a high-order TVOF with locally linear polarization and hybrid SoP are explored, including the intensity compression, expansion, and conversion between the linear and circular polarization components. In particular, orbital angular momentum (OAM) appears in a high-order TVOF during propagation where no OAM exists in the initial field. The variation of OAM distribution in cross-section becomes more frequent with the increase of the twisting phase order. In addition, a non-symmetric OAM distribution appears in an anisotropic TVOF, leading to the rotation of the beam around the propagation axis during propagation. These results provide a new approach for optical field manipulation in a high-order TVOF.

In this paper the D 3 dihedral logistic map of fractional order is introduced. The map 1 presents a dihedral symmetry D 3 . It is numerically shown that the construction and interpretation 2 of the bifurcation diagram versus the fractional order require special attention. The system stability 3 is determined and the problem of hidden attractors is analyzed. Also, analytical and numerical 4 results show that the chaotic attractor of integer order, with D 3 symmetries, looses its symmetry 5 in the fractional-order variant.

Though there have been works highlighting the advantages and disadvantages of online learning, no study focused on university-level economics students. None of the studies explored students' opinions about improving the quality and effectiveness of online classes. Many used questionable samples, closed-ended questions, and all those researches were carried out at the beginning of online classes. In this paper, we overcome these limitations of earlier studies. Using a convenience sampling technique and open-ended questions, we collect data from 154 university-level economics students after being exposed to the online class for a year. Some advantages of online classes are: students can do classes from home without being exposed to health risks, easily accessible, flexible class schedule, students remained connected with the study, it saves costs, reduce the likelihood of semester loss, easy to understand, less stressful, and learning new technologies. Major problems from students' perspectives include network problems, difficulties in understanding the topic, unsuitable for mathematical courses, concentration problem, class not interactive, financial constraint, adverse health impacts, device issues, power outages, unfamiliarity with digital technology, internet problem, and unfixed class-schedule. Disadvantages outnumbered advantages. Students made several suggestions to improve the quality and effectiveness of online classes. Some of the vital suggestions are: using state-of-the-art digital tools, recording and uploading lectures, resolving internet issues, holding classes regularly, higher efforts to make the topics easier, resolving network issues, lowering class duration, institutional support, implementing a fixed class schedule, and introducing online evaluation system.

In this paper, we present a new parametric class of optimal fourth-order iterative methods to estimate the solutions of nonlinear equations. After the convergence analysis, we study the stability of this class by using the tools of complex discrete dynamics. This allows us to select those elements of the class with lower dependence on initial estimations. We verify by means of numerical tests that the stable members on quadratic polynomials perform better than the unstable ones, when applied to other non-polynomial functions. We also compare the performance of the best elements of the family with known methods, such as the schemes by Newton or Chun, among others, showing robust and stable behaviour.

There is a great need to develop research-based models for supporting collaboration between educational institutions. Collaboration models are needed, for example, to assist the transition from lower educational level to higher education or from higher education to work life. In this research, collaboration was conducted through a joint upper-secondary school and university course that addressed global challenges by using a project-based learning approach. There is a shortage of research exploring students’ perceptions of collaboration. Therefore, the main purpose of this qualitative case study is to explore the relevance of the joint course for students and university students. The research was guided by the following research question: What kind of relevance did the students experience in the joint project-based learning course? The data was gathered using questionnaires, interviews, and reflective study reports. The data was analyzed via theory-based content analysis where research-oriented relevance model was used as the analysis framework. The analysis framework enabled categorizing experienced relevance on individual, vocational and societal dimensions. Altogether, the analysis produced 7 relevance categories for upper-secondary students and 9 for university students. According to the analysis, upper-secondary school students felt that the course offered the most on an individual relevance dimension whereas university students experienced the vocational relevance dimension most diverse. As the main conclusion, this research produced new insights on the experienced relevance of upper-secondary level and higher education cooperation from the students’ point of view. The acquired knowledge can be useful for everyone developing new cross-institutional cooperation models.

Collatz conjecture (3x+1 problem) is a natural phenomenon in set theory that may be reconstructed using known combinatorics and order theory. Construction begins by selecting a specific order isomorphism with a bijectional order-embedding. Mapping by 3x+1 induces a unique property to only members of the mapped embedding. Under selective congruence from recursive division by two, that complex controls sequence behavior. This demonstration uses an order isomorphism consisting of two linear orders: the (1) odd positive integers and the always odd (2) Rule 50 Jacobsthal numbers, as the embedding. The argument proceeds by cardinality. When the order isomorphism is mapped under 3x+1, all Rule 50 Jacobsthal numbers are mapped to all the powers of four. This one-to-one correspondence guarantees that every odd integer is assigned to a Rule 50 Jacobsthal number, and subsequently, to a power of four. To align this construction with the conjecture, expand the set to all positive integers by showing that: (1) the powers of four embed the powers of two, in a natural way, and (2) the unique factorization of any positive even integer, not congruent to a power of two, is simply an odd integer, once the factorized power of two is divided out. In other words, if the initial choice for a positive integer is not congruent to a power of two, then recursion continues until a Rule 50 Jacobsthal number (guaranteed by cardinality) is attained. Since this value mapped by 3x+1 is always a power of four, repeated division by two will always send the sequence to one. Because this same process occurs for any choice of positive integer, Collatz conjecture is true.

The paper focuses on the admissibility problem of descriptor fractional-order systems (DFOSs). The alternate admissibility criteria are addressed for DFOSs with order in (0,2) which involve a non-strict linear matrix inequality (LMI) method and a strict LMI method, respectively. The forms of non-strict and strict LMIs are brand-new and distinguished with the existing literature, which fill the gaps of studies for admissibility. These approaches are available to the order in (0,2) without separating the order ranges into (0,1) and [1,2). In addition, a method involved least real decision variables in terms of strict LMIs is derived which is more convenient to process the practical solution. Three numerical examples are given to illustrate the validity of proposed results.

We analyze different approaches to quantum gravity. It is stressed that nonperturbative methods to quantise gravity and the usage of diffeomorphism-invariant variables are very important. We pay attention on the Wheeler--DeWitt equation in the framework of canonical quantum gravity. The Wheeler--DeWitt equation is presented in the first order formalism with the hope that this form can solve some problems such as singularities and the ordering. Also, there is a problem of defining the time.

The semi-logarithmic plot of the cumulative number of cases of epidemics resembles the response of a first-order systems for a step load. This similarity was utilized to develop a first order model that can be used for extracting information about the dynamics of infectious disease epidemics. The developed model was validated using COVID-19 data of China. It was also heuristically fitted to other 13 countries. Obtained results indicated that the model can reliably forecasts the number of infected person, epidemic growth speed towards steady-state condition (process time constant, T), and time to reach steady-state condition (4T). The developed model will help public health authorities in developing more effective control strategies of epidemics.

In this effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics. Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical engineering applications. Classical projection-based model reduction methods generate reduced systems by projecting full-order differential operators into low-dimensional subspaces. However, these techniques usually lead to severe instabilities in the presence of highly nonlinear dynamics, which dramatically deteriorates the accuracy of the reduced-order models. In contrast, our new framework exploits linear multistep networks, based on implicit Adams-Moulton schemes, to construct the reduced system. The advantage is that the method optimally approximates the full order model in the low-dimensional space with a given supervised learning task. Moreover, our approach is non-intrusive, such that it can be applied to other complex nonlinear dynamical systems with sophisticated legacy codes. We demonstrate the performance of our method through the numerical simulation of a two-dimensional flow past a circular cylinder with Reynolds number Re = 100. The results reveal that the new data-driven model is significantly more accurate than standard projection-based approaches

An overview of the chemical compounds forming the rare smectic T phases is cited with references to the historical context. Thermodynamics (transition temperatures, enthalpies) along with the factors (stereochemical constraints, electrostatic interactions, aliphatic chain stacking, intermolecular forces) contributing to the adoption of tetragonal scaffolds are also discussed. Characteristic optical microscopy textures and x-rays diffraction patterns are presented. In parallel, a comparison of the geometrical parameters such as distances between atoms, molecular areas, volumes, and lattice parameters with the closest two-dimensional and three-dimensional organizations, is performed.

Below T_CO=157 K the quasi-one-dimensional charge-transfer salt (TMTTF)_2SbF_6 undergoes a pronounced phase transition to a charge-ordered ground state. We have explored the non-linear and photoconductive behavior as a function of applied voltage, laser pulse energy and temperature. Besides a decay of the photoconductive signal in a double exponential fashion in the millisecond range, we discover current oscillations in the kHz range induced by the application of short laser pulses. While the resonance frequencies do not depend on voltage or laser intensity and vary only slightly with temperature, the amplitude changes linearly with the laser intensity and voltage. The findings are discussed and compared to comparable phenomena in other low-dimensional electron systems.

We discuss the optimal control formulation for enhancement and denoising of satellite multiband images and propose to take it in the form of an L1-control problem for quasi-linear parabolic equation with non-local p[u]-Laplacian and with a cost functional of a tracking type. The main characteristic feature of the considered class of parabolic problems is the fact that the variable exponent p(t,x) and the anisotropic diffusion tensor D(t,x) are not well predefined a priori, but instead these characteristic non-locally depend on a solution of this problem, i.e., pu=p(t,x,u) and Du=D(t,x,u). We prove the existence of optimal pairs with sparse L1-controls using for that the indirect approach and a special family of approximation problems.

The entropy and charge distributions have been calculated for a simple model of polyelectrolytes attached to the surface of DNA using a field-theoretic method that includes fluctuations to the lowest one-loop order beyond mean-field theory. Experiments have revealed correlation-driven behavior of DNA in charged solutions, including charge inversion and condensation. In our model, the condensed polyelectrolytes are taken to be doubly charged dimers of length comparable to the distance between sites along the phosphate chains. Within this lattice-gas model, each adsorption site is assumed to have either a vacancy or a positively-charged dimer attached with the dimer oriented either parallel or perpendicular to the double helix DNA chain. We find that the inclusion of the fluctuation terms decreases the entropy by ∼50% in the weak binding regime. There, the bound dimer concentration is low because the dimers are repelled from the DNA molecule, which competes with the chemical potential driving them from the solution to the DNA surface. Surprisingly, this decrease in entropy due to correlations is so significant that it overcompensates for the entropy increase at the mean field level, so that the total entropy is even lower than in the absence of interactions between lattice sites. As a bonus, we present a transparent exposition of the methods used that could be useful to students and others wishing to use this formulation to extend this calculation to more realistic models.

This paper presents a brief account and rationale for implementation of competency-based learning in any form of management and leadership development programmes in South Africa. The fact that competency-based learning (CBL), also known as outcomes-based learning has been scrapped from the schooling system in South Africa is unfortunate as this method enhances critical thinking skills and practical problem-solving skills. This paper presents CBL as a model of meta-cognitive approach to learning that integrates both theory and practice into experiential learning through six dimensions, namely, active learning, constructive learning, cumulative learning, goal-oriented learning, learner-centred and curriculum design strategies. In the advent of the fast-paced global economy, managers and leaders need to seek those business schools that value real-time practical approach to curriculum for relevance and to maximize shareholder value through human resource development. This brief presentation ends by recommending an approach through CBL that fosters three critical pillars of leadership development, namely: intellectual, behavioural and emotional agenda.

Maze navigation using one or more robots has become a recurring challenge in scientific literature and real life practice, with fleets having to find faster and better ways to navigate environments such as a travel hub (e.g. airports) or to evacuate a disaster zone. Many methods have been used to solve this issue, including the implementation of a variety of sensors and other signal receiving systems. Most interestingly, camera-based techniques have increasingly become more popular in this kind of applications, given their robustness and scalability. In this paper, we have implemented an end-to-end strategy to address this scenario, allowing a robot to solve a maze in an autonomous way, by using computer vision and path planning. In addition, this robot shares the generated knowledge to another by means of communication protocols, having to adapt its mechanical characteristics to be able to solve the same challenge. The paper presents experimental validation of the four components of this solution, namely camera calibration, maze mapping, path planning and robot communication. Finally, we present the integration and functionality of these methods applied in a pair of NAO robots.

The major goal of this work is to present a novel fractional temperature-dependent boundary element model (BEM) for solving thermoelastic wave propagation problems in smart nanomaterials. The computing performance of the suggested methodology was demonstrated by using stable communication avoiding S-step – generalized minimal residual method (SCAS-GMRES) to solve discretized linear BEM systems. The benefits of SCAS-GMRES are investigated and compared to those of other iterative techniques. The numerical results are graphed to demonstrate the influence of fractional, piezoelectric, and length scale characteristics on total force-stresses. These findings also demonstrate that the BEM methodology is practical, feasible, effective, and has superiority over domain methods. The results of the present paper help to develop the industrial uses of smart nanomaterials.

In this empirical article, we argue that, while emergency remote teaching (ERT) may have achieved its goal of saving the academic years during the COVID-19 pandemic, it also constructed unintended pedagogical consequences that were possibly overlooked at the time of advocating it. The research question that the article attempted to answer is, what unintended pedagogical consequences did students and lecturers suffer because of the move to ERT at rural-based universities (RBUs) in South Africa? Drawing on students' and lecturers’ lived experiences of ERT, this article foregrounds unintended pedagogical consequences that arose at one RBU in South Africa during the transition from face-to-face teaching to ERT. Underpinned by the tenets of critical realism philosophy, as well as student integration theory, in-depth interviews with three lecturers and six students were conducted. The findings of the study indicate that home conditions, individual characteristics, pre-COVID-19 blended learning experiences, university training and support, and teaching, learning, and assessment practices and policies altogether contributed to the construction of unintended pedagogical consequences of ERT presented in this article. These consequences include (1) exclusion of low-income students in active teaching and learning, (2) equipping middle-class students with better chances of success than working-class students. (3) distressing female students and lecturers more than their male counterparts, and (4) unproductive assessment practices. This study may be beneficial to academics and policymakers from similar contexts in their plight to continue with remote teaching and assessment (RTA) beyond the pandemic.

In this study, the partial least squares regression (PLSR) models were developed using no pre-processing, traditional preprocessing, multi-preprocessing 5 range, multi-preprocessing 3 range, genetic algorithm (GA), and successive projection algorithm (SPA) to assess the higher heating value (HHV) and ultimate analysis of grounded biomass for energy usage employing near-infrared (NIR) spectroscopy. A novel approach was utilized based on the assumption that using multiple pretreatment methods across different sections in the entire NIR wavenumber range would enhance the performance of the model. The performance of the model obtained from 200 biomass samples for HHV and 120 samples for ultimate analysis was compared, and the best model was selected based on the coefficient of determination of validation set, root mean square error of prediction, and the ratio of prediction to deviation values. Based on model performance results, the proposed HHV model from GA-PLSR, and the N and O models from the mul-ti-preprocessing PLSR 5 range method could be used for most applications, including research, whereas the C and H models from GA-PLSR performance is fair and applicable only for rough screening. The overall findings highlight that the multi-preprocessing 5-range method, which was attempted as a novel approach in this study to develop the PLSR model, demonstrated better accuracy for HHV, C, N, and O, improving by 4.1839%, 8.1842%, 3.7587%, and 35.9404%, respec-tively. Therefore, it can be considered a reliable and non-destructive alternative method for rap-idly assessing biomass properties for energy usage and can also be used effectively in biomass trading. However, due to the smaller number of samples used in the model development, more samples are needed to update the model for a robust application.

The emotional dimension in education has become increasingly important in recent decades. Enhancing the emotional dimension of prospective teachers in science subjects is higher education stuff responsibility. The implementation of active methodologies could modify the traditional student-teacher roles that are encouraged by the educational policies implemented in the Bologna Process. The principal aim of this work is to describe a Project Based Learning methodology and to introduce it as potential resource for the emotional and cognitive improvement of 19 prospective primary teachers enrolled in a scientific subject. This is a qualitative study with a transversal sustainability approach in the context of a research line focused on Higher Education for Sustainable Development. A questionnaire was designed and filled by the students at two different times, before and after implementation of the activity. The initial feedback from students was surprisingly enthusiastic by the fact that they were working with rockets, despite of this is not a common emotion in the science field. The results show the emotional improvement of prospective teachers after the implementation. It is concluded that a correct science education is necessary during the training of teachers taking into account their emotional dimension and the social repercussion due to the future transmission.

This note reconsiders a matrix equality $A_1A_2^{-}A_3A_4^{-}A_5 = A$ composed by six matrices of appropriate sizes, where $A_2^{-}$ and $A_4^{-}$ are generalized inverses of $A_2$ and $A_4$, respectively, and solves a selection of matrix set inclusion problems associated with various mixed reverse order laws for generalized inverses of products of two, three, and four matrices by means of this equality and its variations.

Environmental responsibility and economic benefits have promoted the development of closed-loop supply chain (CLSC), and shortages and channels are considered to be two important issues in CLSC. This paper explores ordering and channel decisions in CLSC with new and differentiated remanufactured products, and considers the price and sales effort-dependent demands, as well as the proportion of emergency orders determined by emergency order costs and backorder losses, and establishes an integrated and decentralized CLSC game models. We introduce a stochastic sales effort, which affects two types of products. Numerical results show that sales effort and the order quantity of new and remanufactured products exhibit concave and convex functions, respectively. Wherein, the upper limit of sales effort has a greater impact on supply chain decisions. High sales efforts can serve as a means of coordinating dispersed supply chains. Moreover, in different cases, decisions of integrated channel are better than those of decentralized channel. Finally, whether the supply chain adopts an emergency order strategy depends on the relative cost of emergency orders and out of stock costs. According to the research in this article, some management insights are also provided.