The purpose of the study is to control the ratio of programs of different genres when forming the broadcast grid in order to increase and maintain the rating of the channel. In the multichannel environment, television rating control consists of selecting such content, ratings of which are completely restored after advertising. A hybrid approach combining the benefits of semantic training and fuzzy relational equations in simplification of the expert recommendation systems construction is proposed. The problem of retaining the television rating can be attributed to the problems of fuzzy resources control. The increase or decrease trends of the demand and supply are described by primary fuzzy relations. The rule-based solutions of fuzzy relational equations connect significance measures of the primary fuzzy terms. Rules refinement by solving fuzzy relational equations allows avoiding labor-intensive procedures for the generation and selection of expert rules. The solution set generation corresponds to the granulation of the television time, where each solution represents the time slot and the granulated rating of the content. In automated media planning, generation of the weekly TV program in the form of the granular solutions provides the decrease of the time needed for the programming of the channel broadcast grid.

Proposed article deals with analyses on trends of problem-solving robotic applications in manu-facturing, especially in transportations and manipulations. Intelligent agent-based manufacturing systems with robotic agents are observed. Intelligent core of such units must be able to propose the plan of problem-solving in form of strategy. The logical model of adaptive strategies planning for intelligent robotic system is described in form of predicates with presentation of data processing on base of set theory descriptions. Dynamic structure of workspace and possible change of goals are considered as reasons for functional strategies adaptation. Proposed formal descriptions are sup-ported by model of mobile robotic platform, acting in warehouse.

Continuous Distributed Constraint Optimization Problem (C-DCOPs) are a powerful framework to model problems with continuous variables in multi-agent systems. Previous works about C-DCOP algorithms mainly use pseudo-trees to guarantee the anytime property or are without anytime property guarantees. However, there is a risk of privacy leakage in the pseudo-tree due to utility passing between agents. Therefore, based on the basic constraint graph instead of the pseudo-tree, we (i) extend the Maximum Gain Message (MGM) algorithm by combining the local search strategy to solve C-DCOPs, named Continuous MGM (C-MGM), and it’s able to guarantee the monotonicity of the solution quality; (ii) propose a Parallel C-MGM (C-PMGM) algorithm to improve the solution quality through parallel random search; and (iii) introduce the differential search into C-PMGM to design a Parallel Differential Search C-MGM (C-PDSM) algorithm, which constructs a heuristic method to speed up convergence and improve solution quality. Compared to other anytime C-DCOP algorithms using pseudo-trees, the proposed three algorithms can exhibit better performance in avoiding privacy violations. We theoretically prove that the proposed algorithms are the anytime algorithms and empirically demonstrate that our algorithms outperform the state-of-the-art C-DCOP algorithms.

This paper proposes an interpretable geometry solution based on the formal language set of text and diagram. Geometry problems are solved by machines, which still poses challenges in natural language processing and computer vision. Significant progress promotes existing methods in the extraction of geometric formal languages. However, the neglect of the graph structure information in the formal language and the lack of further refinement of the extracted language set can lead to the poor effect of the theorem prediction and affect the accuracy in problem solving. In this paper, the formal language graph is constructed by the extracted formal language set and used to theorem prediction by graph convolutional network. So as to better extract the relationship set of diagram elements, an improved diagram parser was proposed. The test results indicate that the improved method has good results in solving the problem with interpretability geometry.

Use of MS Excel as a platform for teaching simple iterative solution of partial differential equations runs into issues of reliability of the computation because of the large number of calculations required. This article documents the problem and an empirical solution. The cause of this unreliability was found by detailed examination of the numerical results from three simultaneous iterations. Computers of several types from different manufacturers were found to fail occasionally in updating variables in the numerical iteration. A simple work-around is suggested and was tested on several platforms.

Generative artificial intelligence tools are flourishing across various sciences, particularly in the educational domain. ChatGPT, with its versions 3.5 and 4.0, stands out for its multilingual capabilities, catering to both students and educators. This research aimed to evaluate the performance differences between these versions, and importantly, to compare the accuracy of ChatGPT's responses in English versus Arabic. In our study, we presented ChatGPT with 39 chemistry problems related to 6th-7th grade curriculum, including twenty-five open questions and fourteen multiple-choice questions. Each response was categorized as accurate, partially accurate, or inaccurate. Our analysis, focused on trends across versions and languages, revealed significant enhancements in version 4.0, particularly in its ability to process Arabic. However, despite these improvements, our findings indicate that responses in English consistently outperformed those in Arabic in terms of accuracy. In light of this discrepancy, we suggest that ChatGPT either incorporates additional Arabic databases into its training regimen or develops a code that adopts the following strategy to ensure more accurate responses in science education: questions should first be translated from Arabic to English, addressed, and then retranslated into Arabic before being presented to the user. This approach takes advantage of the greater accuracy of responses in English to benefit Arabic-speaking users, and it may also improve outcomes for speakers of other languages who experience less precise answers in the fields of chemistry or science education.

High-fidelity patient simulation (HFPS) is widely used in professional training to enhance students’ competence in clinical management. Problem-solving (PS) and clinical reasoning (CR) skills are essential to developing students in professional competence in safe and effective care. These two skills should be initiated at the early training. However, little is known about the effects of HFPS on developing PS and CR skills in first year undergraduate students. Therefore, this pre- and post-experimental study aimed to investigate the effects of HFPS on development of PS and CR skills in first-year nursing students. The students were required to go through four sessions, preparation, pre-briefing and orientation, simulation role-playing, and debriefing, for the HFPS. The study utilized the Problem-Solving Inventory (PSI) and the Nurses Clinical Reasoning Scale (NCRS) to measure problem-solving and clinical reasoning abilities before and after HFPS. Bivariate analysis, one-sample t-test, and independent t-test were performed to evaluate the performance of the PS and CR skills at the two study periods. One hundred eighty-nine students were recruited, with a mean age of 20.56 years, and 73% were female students. The analytic results showed that the PSI, particularly in domains of Problem-Solving Confidence (PSC) (p<0.001) and overall PS (p<0.001), and the CR (p<0.001) had significant improvement after HFPS. The study concluded that HFPS is an effective innovative method to significantly improve students’ problem-solving and clinical reasoning abilities. Nurse educators play an important role in providing explicit learning instructions in a simulation guideline that directs and guides students to learn at each stage of HFPS. Students should take more initiative and engage in their learning through HFPS to enhance their competence in knowledge and higher intellectual skills for personal and professional developments.

Backgrounds: The field of Artificial Intelligence (AI) has seen a major shift in recent years due to the development of new Machine Learning (ML) models such as Generative Pre-trained Transformer (GPT) and AI which are progressively becoming part our everyday lives. GPT has achieved previously unheard-of levels of accuracy in most computerized language processing tasks and their chat-based variations. Aim: The aim of this study was to investigate the problem-solving abilities of ChatGPT using two sets of verbal insight problems, with a known performance level established by a sample of human participants. Material and Methods: A total of 30 problems labelled as “practice problems” and “transfer problems”, as listed by Ansburg and Dominowski (2000), were administered to ChatGPT. The answers provided by ChatGPT received a score of "0" for each problem answered incorrectly and a score of "1" for each correct response, as per the correct solution specified in Ansburg and Dominowski's (2000) study. The highest score that could be attributed to both the practice and transfer problems was 15 out of 15. In order to compare ChatGPT performance to the performance to that of human subjects, the solution rate for each problem (based on a sample of 20 subjects) was used, as indicated by Ansburg and Dominowski (2000). Results: The study highlighted that ChatGPT can be trained in out-of-the-box thinking and demonstrated potential in solving verbal insight problems. The global performance of ChatGPT equalled the most probable outcome for the human sample in both practice problems and transfer problems as well as upon their combination. Additionally, ChatGPT answer combinations were among the 5% of most probable outcomes for the human sample both when considering practice problems and pooled problem sets. These findings demonstrate that ChatGPT performance on both set of problems was in line with the mean rate of success of human subjects, indicating that it performed reasonably well. Conclusions: The use of transformer architecture and self-attention in ChatGPT may have helped to prioritize inputs while predicting, contributing to its potential in verbal insight problem-solving. ChatGPT has shown potential in solving insight problems, thus highlighting the importance of incorporating AI in psychological research. However, it is acknowledged that open challenges still exist. Indeed, further research is needed to fully understand the capabilities and limitations of AI in insight problem-solving.

In this paper, a system of searching for optimal paths is developed and concreted on a FPGA. It is based on a memristive emulator, used as a delay element, by configuring the test graph as a memristor network. A parallel algorithm is applied to reduce computing time and increase efficiency. The operation of the algorithm in Matlab is checked beforehand and then exported to two different Intel FPGAs: a DE0-Nano board and an Arria 10 GX 220 FPGA. In both cases reliable results are obtained quickly and conveniently, even for the case of a 300x300 nodes maze.

The Gestalt psychologists’ theory of insight problem-solving was based on a direct parallelism between perceptual experience and higher-order forms of cognition (e.g., problem-solving). Simi-larly to the sudden recognition of an ambiguous figure, they contended that problem-solving in-volves a restructuring of one's initial representation of the problem’s elements, leading to a sud-den leap of understanding phenomenologically indexed by the "Aha!" feeling. Over the last centu-ry, different scholars discussed the validity of the Gestalt psychologists’ perspective foremost us-ing the behavioral measures available at the time. However, in the last 2 decades, scientists gained a deeper understanding of insight problem-solving due to the advancements in cognitive neuroscience. This review aims to provide a retrospective reading of Gestalt theory based on the knowledge accrued by adopting novel paradigms and investigating their neurophysiological correlates. Among several key points that the Gestalt psychologists underscored, we focus specif-ically on the role of the visual system in marking a discrete switch of knowledge into awareness, as well as the perceptual experience and the holistic standpoints. While the main goal of this paper is to read the previous theory in light of new evidence, we also hope to initiate an academic dis-cussion and encourage further research about the points we raise.

This paper addresses the difficulty of balancing real-time response and low power consumption in intelligent manhole cover application scenarios. It proposes a method to distinguish normal and abnormal events by segmenting the boundary where the acceleration of the intelligent manhole cover deviates from a set threshold and lasts for a certain period, based on the difference in vibration patterns of the intelligent manhole cover when a normal event and an abnormal event occur. This paper uses digital output motion sensor data autonomous data fusion to implement the pattern mentioned above recognition algorithm, which reduces the MCU computing and working time and the overall power consumption of the system while meeting the real-time response requirements. The test results demonstrate that the method has a high rate of anomaly recognition accuracy. The method ensures the system's real-time response capability, and the actual low power consumption test demonstrates that the device can operate continuously for 9.5 years. The low power consumption index exceeds the requirements of the existing national standard, thereby resolving the issue that it is challenging to balance intelligent manhole cover abnormality recognition and low power consumption.

Research has shown that hands-on projects promote stem education, namely, via problem-solving. CanSat, literally 'satellite in a can', is a stem educational project promoted by the European Space Agency. This paper addresses this issue by researching this STEM project, which demonstrates how problem-solving can be achieved in secondary-level students within the framework of the CanSat. We use qualitative techniques of data collection and analysis. The results showed that students use sophisticated thinking strategies to process information within this interdisciplinary project: (a) cognitive testing, cognitive organization, cognitive regulation, and monitoring, in addition to computer language and physical–mathematical calculations, are cognitive and metacognitive behavior strategies revealed in the CanSat; (b) problem-solving was suggested as a specific model, where students’ higher cognitive and metacognitive ordering processes deepen in project development; (c) computational, lateral, or divergent and convergent thinking were detected as thinking types of students associated with and mobilized in the course of problem-solving, The findings of this research have practical implications for STEM education in space science. Hands-on projects using problem-solving are an essential strategy to promote STEM education. Additionally, they are a starting point to promote meaningful learning and new thinking types.

Problem solving is one of the most important components of the human cognition that affects for ages the progress of the human society. Mathematical modelling is a special type of problem solving concerning problems related to science or everyday life situations. The present study is a review of the author’s earlier works on problem solving and mathematical modelling from the scope of Education. Its real goal is that it presents in a systematic way and in a few pages only the results of many years research on the subject. This helps the reader to get a comprehensive idea about a very important topic belonging to the core of Mathematics Education, which is very useful to those wanting to study deeper the subject and get directions for further research in the area.

Urban design is a complex problem-solving activity that commonly requires the aid of a variety of methods to support the process and enhance the quality of the outcomes. How to help designers with adequate methods to deal with ill-defined urban problems constitutes a major challenge in the urban design domain. In this regard, the use of urban design patterns is considered as a method that can contribute to urban design problem-solving. However, this tool was never investigated to understand its role in the task-related activities that take place during the design process by designers working in team, and its effect on the creativity of the final design outcome as perceived by urban designers and students. Therefore, an empirical research based on a controlled experiment was carried out to explore the aid provided by design patterns during the conceptual stages of the process. The study contributed to gain a better insight into the main design activities derived from the use of patterns as problem-solving tools, and to unveil their contribution to urban design. Implications for design practice and design education are discussed.

Students with disabilities are often framed as “the problem” and have limited opportunities to engage in standards based mathematics, leading to persistent underachievement. In this paper, we investigate a research divide between mathematics educational research for students with and without disabilities, a divide with significant differences in the theoretical orientations and research methodologies used to understand learners. Based on an analysis of 149 mathematics educational research articles published between 2013 and 2015, we found significant differences between articles focused on learners with and without disabilities. For those with disabilities, mathematical problem solving was understood primarily from behavioral and information processing theoretical perspectives, while for those without disabilities, problem solving was understood primarily through constructivist and sociocultural perspectives. While 86% of research on problem-solving including students with disabilities was quantitative, only 35% of research on students without disabilities was quantitative. Fifty percent of problem-solving research on students without disabilities was qualitative, compared to only 6% of research on students with disabilities. Problem solving, then, is studied in very different ways for learners with and without disabilities. Students without disabilities are studied through close analysis of learning, often individual. Students with disabilities are most often studied quantitatively, in groups, with little analysis of individual thinking. By offering only a limited range of methods and theoretical orientations, this research divide reifies deficit constructions of students with disabilities.

Purpose: This study investigates the implementation and impact of maker culture—viewed as a tool for developing green digital skills—in higher education institutions in Hong Kong. Maker culture, a collaborative educational approach, embraces students’ capacity for self-paced, autonomous learning and applies this knowledge to creative problem-solving and innovation, key aspects of sustainability education. Methods: An empirical study was conducted, focusing on the experiences of teachers in the higher education sector in Hong Kong. Eight individuals were interviewed to gain insights into their perceptions and experiences with maker education within sustainability contexts. The sample was limited to ensure cross-sectional comparability and direct weighting of teachers’ experiences within a singular, complementary educational setting. Results: The findings provide valuable insights into the benefits and challenges of integrating maker education into traditional educational systems to foster green digital skills. It became evident that adequate resources, effective teachers, and improved administrative systems play significant roles in the successful implementation of this approach. Conclusion: Maker education, as a tool for developing green digital skills, offers a promising alternative to traditional performance-based studies. It has the potential to lead to a future of education that is creative, innovative, and student-directed, fostering sustainability competences. Therefore, despite the challenges, with the right support and resources, the integration of maker culture into educational systems could significantly transform teaching and learning processes, advancing sustainability education.

Complex problem-solving (CPS) tasks have become an increasingly popular tool for understand-ing and assessing cognitive ability. These tasks have been repeatedly shown to be predictors of academic and workplace success above and beyond traditional measures of general intelligence and fluid intelligence. To date, there has been little exploration of the underlying mechanisms that drive this additional predictive utility. In this study, we examined the role of a variety of non-cognitive personality and investment traits that could drive performance on CPS tasks. Adult participants (n = 152) were recruited via M-Turk and completed a battery of personality and in-vestment trait measures, a measure of general mental ability, and a 61-trial microworlds-style CPS task. Generalised linear mixed-effects models revealed a wide variety of personality and in-vestment traits influenced task performance above and beyond general mental ability. Specifical-ly, two clusters of traits emerged as important determinants of performance: one cluster that in-fluenced the capacity to deal with the introduction of system randomness (Conscientiousness and Extraversion) and one cluster that influenced the capacity to deal with the introduction of system delays (NFC, Learning Goal Orientation, and Intellect). These findings suggest that CPS tasks do capture more than just general mental ability and may be good predictors of academic and workplace success because they tap into both cognitive ability and the motivation and willingness to engage in cognitive exploration and mental effort.

There have been a vast number of studies on reading strategies from different angles performed at various age levels. However, the COVID-19 pandemic has brought a challenge to students´ lives, especially at the university level where they have to struggle with reading many materials online and offline. Therefore, this study investigated the levels of three different strategies of metacognitive awareness: global reading strategy, problem-solving strategy, and support reading strategy among 192 Slovak freshmen university students in a Business English class during the COVID-19 pandemic. The findings reveal that the students used problem-solving strategies the most, followed by global and support reading strategies the least. The results also indicate a difference between male and female students at individual levels of reading strategies. The study proposes a set of recommendations with an alliance of COVID-19 learning environment based on the results such as taking notes while reading and highlighting the most important information with an emphasis on details or showing the importance of previewing the text, asking questions/making predictions about the text, and most importantly paying attention to self-regulation practices in a new school environment.

Because of hyper complexity, difficulty to define, multiple stakeholders with conflicting perspectives, and lack of clear-cut solutions, wicked problems necessitate innovative and adaptive strategies. Operations Research has been a valuable tool for managers to make informed decisions for years. However, as we face increasingly complex and messy problems, it has become apparent that relying solely on either hard or soft OR approaches is no longer sufficient. We need to explore more innovative methodologies to address these wicked problems effectively. This study has bridged the research gap by proposing a structured process encompassing a subdivision-based problem structuring method for defining the wicked problem, a multi-attribute decision-making (MADM) for prioritizing sub-problems, and a hard OR technique, data envelopment analysis (DEA) for tackling one of the most critical sub-divisions. The proposed methodology, implemented in a case study, focuses on a higher education institution experiencing a decline in student admissions and involves five steps. First, a diverse group of stakeholders is formed to ensure comprehensive consideration of perspectives. Second, the wicked problem is defined, considering long-term consequences, multiple stakeholders, and qualitative stakeholder opinions. Third, a hierarchical structure is created to break down the wicked problem into manageable sub-problems. Fourth, a multi-criteria decision-making (MCDM) method prioritizes sub-problems. Finally, the sub-problems are addressed one by one using a combination of soft and hard OR tools. The findings highlight the benefits of integrating hard and soft OR approaches. The article concludes with reflections on the implications of using a combined OR approach to tackle wicked problems in higher education and beyond.

The present era of the Internet of Things (IoT) having intelligent functionalities in solving problems pertaining to realtime mission-critical systems has brought an immense revolution in diverse fields including healthcare and navigation systems. However, to the best of our knowledge, the potential of IoT has not been fully exploited yet in the field of the energy sector. We argue that there is an immense need to shift the traditional mission-critical electric power system architecture to IoT-based fully orchestrated architecture in order to increase efficiency, as billions of investment is reserved for the energy sector globally. Since network orchestration deals with auomating the interaction between multiple components involved to execute a particular service, therefore, scheduling the relevant processes within strict deadlines becomes the core pillar of the architecture. The mission-critical systems with urgent task execution often suffer from issues of missing task deadlines. In this study, we present a novel IoT task orchestration architecture for efficient energy management of a nanogrid system that focuses on minimizing the use of nonrenewable energy resources and maximizing the use of renewable energy resources. Moreover, major components of IoT task orchestration such as task mapping and task scheduling are also enhanced using NLP and PSO optimization modules. The proposed task scheduling algorithm incorporates the optimized surplus time, and efficiently executes the energy management-related tasks contemplating to their types. The study utilizes sensors to obtain data from physical IoT devices, including photovoltaic (PV), Energy Storage System (ESS), and diesel generator (DG). The performance of the proposed model is evaluated using data set of nanogrid houses. The outcomes revealed that IoT-task orchestration has played a pivotal role in efficient energy management for nanogrid mission-critical system. Furthermore, the comparison with state-of-the-art scheduling algorithms showed that the task starvation rate is reduced to 16% and 12% when compared with RR and FEF algorithms, respectively.

Mild Cognitive Impairment (MCI) is a clinical syndrome characterized by a moderate decline in one or more cognitive functions with a preserved autonomy in daily life activities [1]. MCI exhibits cognitive, behavioral, psychological symptoms [2]. The executive functions (EFs) are a set of key functions for everyday life and physical and mental health; and allow adapting the behavior to external changes [3-5]. Higher-level executive functions develop from basic EFs (inhibition, working memory, attentional control, and cognitive flexibility). They are planning, reasoning, problem- solving, and fluid intelligence (Gf) [3]. This systematic review investigates the relationship between higher-level executive functions and healthy and pathological aging, assuming the role of executive functions deficits as a predictor of cognitive decline. The systematic review was conducted according to the PRISMA Statement [6-7]. A total of 73 studies were identified. The results indicate that 65.8% of the studies confirm significant EFs alterations in MCI (100% problem solving, 71.4% fluid intelligence, 56.8% planning, 50% reasoning). These results seem to highlight a strong prevalence of higher-level executive functions deficits in MCI elderly than in healthy elderly.

This article presents a description of a new method for solving the factorization problem, based on the gradient descent algorithm. This approach demonstrates significant improvements in efficiency compared to traditional methods proposed in previous research. This article describes a new method for solving the factorization problem, based on the gradient descent algorithm, and demonstrates the transition from algebraic methods to approaches based on functional analysis. The proposed approach not only improves the efficiency of solving the problem but also allows the application of computational algorithms of functional analysis, opening new possibilities for research and optimization.

Digital competence is one of the 8 key competences for life-long learning developed by the European Commission, and is requisite for personal fulfilment and development, active citizenship, social inclusion and employment in the knowledge society. To accompany young learners in the development of the competence, and to guarantee optimal implementation of ICTs, it is necessary that teachers are, in turn, literate. We had 43 Secondary School teachers in initial training to assess their own level of competence in the 21 sub-competences in 5 areas identified by the DIGCOMP project, using the rubrics provided in the Common Framework for Digital Competence of Teachers (Spanish Ministry of Education). Overall, pre-service teachers' conceptions about their level of Digital Competence was low (Initial). Students scored highest in Information, which refers mostly to the operations they performed while being students. Secondly, in Safety and Communication, excluding Protection of Digital Data and Preservation of the Digital Identity. Lowest values were achieved in Content Creation and Problem Solving, the dimensions most closely related with the inclusion of ICTs to transform teaching-learning processes. The knowledge or skills they exhibit are largely self-taught and, so, we perceive an urgent need to purposefully incorporate relational and didactic aspects of ICT integration.

Work-related thoughts in off-job time have been studied extensively in occupational health psychology and related fields. We provide a focused review of research on overcommitment – a component within the effort-reward imbalance model – and aim to connect this line of research to the most commonly studied aspects of work-related rumination. Drawing on this integrative review, we analyze survey data on ten facets of work-related rumination, namely (1) overcommitment, (2) psychological detachment, (3) affective rumination, (4) problem-solving pondering, (5) positive work reflection, (6) negative work reflection, (7) distraction, (8) cognitive irritation, (9) emotional irritation, and (10) inability to recover. First, we leverage exploratory factor analysis to self-report survey data from 357 employees to calibrate overcommitment items and to position overcommitment within the nomological net of work-related rumination constructs. Second, we leverage confirmatory factor analysis to self-report survey data from 388 employees to provide a more specific test of uniqueness vs. overlap among these constructs. Third, we apply relative weight analysis to quantify the unique criterion-related validity of each work-related rumination facet regarding (1) physical fatigue, (2) cognitive fatigue, (3) emotional fatigue, (4) burnout, (5) psychosomatic complaints, and (6) satisfaction with life. Our results suggest that several measures of work-related rumination (e.g., overcommitment and cognitive irritation) can be used interchangeably. Emotional irritation and affective rumination emerge as the strongest unique predictors of fatigue, burnout, psychosomatic complaints, and satisfaction with life. Our study assists researchers in making informed decisions on selecting scales for their research and paves the way for integrating research on effort-reward imbalance and work-related rumination.

Solving Linear equations with large number of variable contains many computations to be performed either iteratively or recursively. Thus it consumes more time when implemented in a sequential manner. There are many ways to solve the linear equations such as Gaussian elimination, Cholesky factorization, LU factorization, QR factorization. But even these methods when implemented on a sequential platform yield slower results as compared to a parallel platform where the time consumption is reduced considerably due to concurrent execution of instructions. The above mentioned linear equation solving methods can be implemented on the parallel platform using the direct approaches such as pipelining or 1D and 2D Partitioning approach. Vedic mathematics is a very ancient approach for solving mathematical problems. These Vedic mathematical approaches are well known for quicker and faster computation of mathematical problems. Vedic Mathematics provides a very different outlook towards the approach of solving linear Equation on parallel platform. It could be considered as a better approach for reducing space consumption and minimizing the number of algebraic operations involved in solving linear equation. In future Vedic Mathematics might serve as a viable solution for solving linear equation on parallel platform.

A new framework in quantum chemistry has been proposed recently ("An approach to first principles electronic structure calculation by symbolic-numeric computation'' by A. Kikuchi). It is based on the modern technique of computational algebraic geometry, viz. the symbolic computation of polynomial systems. Although this framework belongs to molecular orbital theory, it fully adopts the symbolic method. The analytic integrals in the secular equations are approximated by the polynomials. The indeterminate variables of polynomials represent the wave-functions and other parameters for the optimization, such as atomic positions and contraction coefficients of atomic orbitals. Then the symbolic computation digests and decomposes the polynomials into a tame form of the set of equations, to which numerical computations are easily applied. The key technique is Grröbner basis theory, by which one can investigate the electronic structure by unraveling the entangled relations of the involved variables. In this article, at first, we demonstrate the featured result of this new theory. Next, we expound the mathematical basics concerning computational algebraic geometry, which are necessitated in our study. We will see how highly abstract ideas of polynomial algebra would be applied to the solution of the definite problems in quantum mechanics. We solve simple problems in "quantum chemistry in algebraic variety'' by means of algebraic approach. Finally, we review several topics related to polynomial computation, whereby we shall have an outlook for the future direction of the research.