Demonstrates the postures, exercises, and hygienic value of hatha yoga through explanations and photographs.

This volume contains 45 papers, written by the author alone or in collaboration with the following co-authors: Mumtaz Ali, Said Broumi, Sukanto Bhattacharya, Mamoni Dhar, Irfan Deli, Mincong Deng, Alexandru Gal, Valeri Kroumov, Pabitra Kumar Maji, Maikel Leyva-Vazquez, Feng Liu, Pinaki Majumdar, Munazza Naz, Karina Perez-Teruel, Rıdvan Sahin, A. A. Salama, Muhammad Shabir, Rajshekhar Sunderraman, Luige Vladareanu, Magdalena Vladila, Stefan Vladutescu, Haibin Wang, Hongnian Yu, Yan-Qing Zhang.

This thirteenth volume of Collected Papers is an eclectic tome of 88 papers in various fields of sciences, such as astronomy, biology, calculus, economics, education and administration, game theory, geometry, graph theory, information fusion, decision making, instantaneous physics, quantum physics, neutrosophic logic and set, non-Euclidean geometry, number theory, paradoxes, philosophy of science, scientific research methods, statistics, and others, structured in 17 chapters (Neutrosophic Theory and Applications; Neutrosophic Algebra; Fuzzy Soft Sets; Neutrosophic Sets; Hypersoft Sets; Neutrosophic Semigroups; Neutrosophic Graphs; Superhypergraphs; Plithogeny; (...) Information Fusion; Statistics; Decision Making; Extenics; Instantaneous Physics; Paradoxism; Mathematica; Miscellanea), comprising 965 pages, published between 2005-2022 in different scientific journals, by the author alone or in collaboration with the following 110 co-authors (alphabetically ordered) from 26 countries: Abduallah Gamal, Sania Afzal, Firoz Ahmad, Muhammad Akram, Sheriful Alam, Ali Hamza, Ali H. M. Al-Obaidi, Madeleine Al-Tahan, Assia Bakali, Atiqe Ur Rahman, Sukanto Bhattacharya, Bilal Hadjadji, Robert N. Boyd, Willem K.M. Brauers, Umit Cali, Youcef Chibani, Victor Christianto, Chunxin Bo, Shyamal Dalapati, Mario Dalcín, Arup Kumar Das, Elham Davneshvar, Bijan Davvaz, Irfan Deli, Muhammet Deveci, Mamouni Dhar, R. Dhavaseelan, Balasubramanian Elavarasan, Sara Farooq, Haipeng Wang, Ugur Halden, Le Hoang Son, Hongnian Yu, Qays Hatem Imran, Mayas Ismail, Saeid Jafari, Jun Ye, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Darjan Karabašević, Abdullah Kargın, Vasilios N. Katsikis, Nour Eldeen M. Khalifa, Madad Khan, M. Khoshnevisan, Tapan Kumar Roy, Pinaki Majumdar, Sreepurna Malakar, Masoud Ghods, Minghao Hu, Mingming Chen, Mohamed Abdel-Basset, Mohamed Talea, Mohammad Hamidi, Mohamed Loey, Mihnea Alexandru Moisescu, Muhammad Ihsan, Muhammad Saeed, Muhammad Shabir, Mumtaz Ali, Muzzamal Sitara, Nassim Abbas, Munazza Naz, Giorgio Nordo, Mani Parimala, Ion Pătrașcu, Gabrijela Popović, K. Porselvi, Surapati Pramanik, D. Preethi, Qiang Guo, Riad K. Al-Hamido, Zahra Rostami, Said Broumi, Saima Anis, Muzafer Saračević, Ganeshsree Selvachandran, Selvaraj Ganesan, Shammya Shananda Saha, Marayanagaraj Shanmugapriya, Songtao Shao, Sori Tjandrah Simbolon, Florentin Smarandache, Predrag S. Stanimirović, Dragiša Stanujkić, Raman Sundareswaran, Mehmet Șahin, Ovidiu-Ilie Șandru, Abdulkadir Șengür, Mohamed Talea, Ferhat Taș, Selçuk Topal, Alptekin Ulutaș, Ramalingam Udhayakumar, Yunita Umniyati, J. Vimala, Luige Vlădăreanu, Ştefan Vlăduţescu, Yaman Akbulut, Yanhui Guo, Yong Deng, You He, Young Bae Jun, Wangtao Yuan, Rong Xia, Xiaohong Zhang, Edmundas Kazimieras Zavadskas, Zayen Azzouz Omar, Xiaohong Zhang, Zhirou Ma.‬‬‬‬‬‬‬‬. (shrink)

Embryos and microscopes share a long, remarkable history and biologists have always been intrigued to watch how embryos develop under the microscope. Here we discuss the advances in microscopy which have greatly influenced our current understanding of embryogenesis. We highlight the evolution of microscopes and the optical technologies that have been instrumental in studying various developmental processes. These imaging modalities provide mechanistic insights into the dynamic cellular and molecular events which drive lineage commitment and morphogenetic changes in the developing embryo. (...) We begin the journey with a brief history of microscopy to study embryos. First, we review the principles and optics of light, fluorescence, confocal, and electron microscopy which have been key techniques for imaging cellular and molecular events during embryonic development. Next, we discuss recent key imaging modalities such as light‐sheet microscopy, which are suitable for whole embryo imaging. Further, we highlight imaging techniques like multiphoton and super resolution microscopy for beyond light diffraction limit, high resolution imaging. Lastly, we review some of the scattering‐based imaging methods and techniques used for imaging human embryos. (shrink)

If there is one question that has perplexed the best minds in every society, it is how to raise the individuals from their present state to a higher state of existence and perfection? The answers have been tried using different formulations in history: religious, scientific and political. The common factor in all these historical formulations was that they were designed in opposition to each other and therefore left many things unaccounted. The aim of this paper is to explore the idea (...) of self-perfection as a continuous streak of infinite vertical ascension. The paper has elaborated the idea of ‘Verticality’, propounded by Peter Sloterdijk for looking in to the domains of self-perfection and the stages of vertical ascension. For our purpose, we have relied on the example of discipline of Management that has progressively theorized about different aspects and stages of existence. (shrink)

Addressing many social challenges requires both structural and behavioral change. The binary of an i- and s-frame obscures how behavioral science can help foster bottom-up collective action. Adopting a community-frame perspective moves toward a more integrative view of how social change emerges, and how it might be promoted by policymakers and publics in service of addressing challenges like climate change.

Among the means of valid cognition, the one which appears first in every enumeration, which was considered as being the basis of all other means of knowledge and which was considered as a legitimate method of knowledge by all schools of Indian thought is perception (pratyakṣa). With regard to perception, we can naturally expect such questions as ‘what is it to perceive’ or ‘what do we mean when we say that something is perceived’. It is generally believed that the philosophical (...) theories of perceptions are really theories about what we mean by ordinary perceptual statements. In considering our knowledge about the external world, the philosopher tends to consider the way in which perception can and does provide us with the knowledge and the nature, extent and certainty of knowledge it provides us with. It is a well acknowledged fact that perception is the fundamental source of knowledge. In Buddhist epistemology, a systematic discussion on perception is found in the writings of Dignāga’s Pramāṇasamuccaya with vṛitti, who belongs to Yogācāra school of Buddhism of Mahayana tradition. An attempt has been made in this paper to explain and examine critically the first chapter of Pramāṇasamuccaya with vṛitti, i.e., perception with special reference to Non-Buddhist schools, namely Nyāyayikas, Vaiśeṣikas, Sāṁkhyans and Mīmāṁsakas. To explain it, the paper has been divided into three sections. Section I deals with Dignāga’s theory of perception and examination of non-Buddhist school's theory of perception, section II deals with Dignāga’s examination of nature of Perception with reference to non-Buddhists schools and section III deals with conclusion. (shrink)

The application of continuous deep sedation in the treatment of intractable suffering at the end of life continues to be tied to a number of concerns that have negated its use in palliative care. Part of the resistance towards use of this treatment option of last resort has been the continued association of CDS with physician-associated suicide and/or euthanasia, which is compounded by a lack clinical guidelines and a failure to cite this treatment under the aegis of a palliative care (...) approach. I argue that reinstituting a palliative care-inspired approach that includes a holistic review of the patient’s situation and the engagement of a multidisciplinary team guided by clearly defined practice requirements that have been lacking amongst many prevailing guidelines will overcome prevailing objections to this practice and allow for the legitimization of this process. (shrink)

The present paper takes a critical posthumanist lens to study the consequences of rapid urbanisation of the Chinese landscape as presented in the short story ‘Good Hunting’, by Ken Liu. One of the main characters in the story is Yan, a huli jing (fox-spirit), whose ability to switch between her fox and human forms is severely impaired by the loss of remnant nature in China, and the subsequent erosion of the qi from the soil. It is not just the natural (...) landscape that undergoes a transformation during urbanisation – the remnants of nature do not remain untouched by this process. Beings like Yan, who continue to inhabit the place that used to be their home, do not remain the same that they were pre-urbanisation. The city changes them, moulds them in ways hitherto inconceivable, and they undergo this transmogrification of their bodies and their self in order to survive. The article draws out the historical relationship between urban spaces and (post)human bodies, with a specific focus on the Chinese body, drawing parallels between the ideals associated with the city and juxtaposing them with what it means to be posthuman. The paper also interrogates Yan’s status as a liminal entity before and after Hong Kong’s transformation, and her use of liminality as a survival strategy. (shrink)

Roots and Routes are related to each other but in life, self, culture and society we sometimes forget this. We become either prisoners of closed roots or rootless routes. The introduction to this book tries to overcome such closure and imprisonment and discusses many contributions of this volume. It tries to create pathways of going beyond one and many create alternative planetary futures.

Kingdom of God is a familiar and dominant discourse in religion, society and the world. It is also a dominant framing for thinking about a good society here on Earth. But the discourse of Kingdom of God is many a time locked in a discourse of power. In dominant versions of political theology, it is linked to violence. In this essay, an attempt is made to rethink Kingdom of God as Gardens of God. There is also an interlinked attempt to (...) rethink the discourse of Ramrajya to Ramvana where there is an attempt to transform violence to non-violence. (shrink)

Hate speech has spread more rapidly through the daily use of technology and, most notably, by sharing your opinions or feelings on social media in a negative aspect. Although numerous works have been carried out in detecting hate speeches in English, German, and other languages, very few works have been carried out in the context of the Bengali language. In contrast, millions of people communicate on social media in Bengali. The few existing works that have been carried out need improvements (...) in both accuracy and interpretability. This article proposed encoder–decoder-based machine learning model, a popular tool in NLP, to classify user’s Bengali comments from Facebook pages. A dataset of 7,425 Bengali comments, consisting of seven distinct categories of hate speeches, was used to train and evaluate our model. For extracting and encoding local features from the comments, 1D convolutional layers were used. Finally, the attention mechanism, LSTM, and GRU-based decoders have been used for predicting hate speech categories. Among the three encoder–decoder algorithms, attention-based decoder obtained the best accuracy (77%). (shrink)

With its promise of personal improvement, physical well-being and spiritual enrichment, yoga is enjoying a resurgence in popularity at the turn of the third millennium. To unravel the mystery of the discipline, its philosophies and relevance in contemporary life, the original text of the Yoga Sutras of Patanjali must be explored. This book offers the first accessible translation and commentary on Patanjali's Yoga Sutras. An introductory section examines the multidimensional aspects of yoga as philosophy, psychology, science, and religion, as well (...) as exploring popular versions of yoga in the West. The core of the book offers a new translation of the entire text of the Yoga Sutras, in a language that is clear and comprehensible to students. Commentaries are presented to highlight the meaning of various statements and key themes are outlined via sectional summaries. A full glossary of key words and names is also provided. Concluding chapters look at yoga in contemporary life, revealing the popularity of yoga in the 21st century through Star Wars, and exploring yoga's connection to health and science, contrasting yoga's holistic view of healing with that of the limited view of present day medical science. Sample physical, breathing and meditation exercises are provided. An Introduction to Yoga Philosophy offers a comprehensive introduction to the Yoga Sutras text of Patanjali to all students and interested readers of Indian philosophy and religion, world religions, east-west psychology, and mysticism. (shrink)

Agrarian environments have to be comprehended as being part of a biophysical and social environment that includes the urban and the nonurban, the arable and the nonarable, and other areas that are integrally linked to the world of agriculture and environment and their allied socioeconomic relations. This article examines the responses of rice biotechnologists located in selected Indian public agricultural institutes under the aegis of the State Agricultural University and the Indian Council of Agricultural Research on questions such as “How (...) is GM (genetically modified) technology perceived by rice biotechnologists and under what limiting conditions is it being pursued in rice biotechnology research? Is there a consensus among rice biotechnologists over the application of GM technology? What are the complexities of the GM policy? and What are the implications of intellectual property rights on GM-based research and how scientists are responding to such institutional norms?”. (shrink)

Background: Digital technologies such as smartphones, tablets and laptops have become a mainstay part of nearly every household and are gradually being integrated into the lives of both adults and children. We aim to determine the extent of exposure and usage of digital technology by children in their daily activities and to understand the transition in technological preferences and attitudes over the generation. Methods: A cross-sectional study was conducted on 400 children aged 05-12 years living in Prayagraj city of Uttar (...) Pradesh, India, using a pretested interview schedule. Descriptive and bivariate statistics were used for data analysis. The phenomenological method was used to understand respondents’ viewpoints about their preferences and attitudes related to technology. Results: An overwhelming majority of households have television followed by digital cameras, laptops, tablets, kindle and video games such as Playstation. Nearly half of children began to use digital devices from the age of 7 to 8 years. Nearly two-third of the children learnt to use digital devices on their own, and about 12% of them reported often practicing media multitasking. Over the generation, differences are noted in terms of possession, use and perception regarding digital technology. Conclusion: The availability of media content on such devices influences the screen time of children of all ages. The study underscores the importance of parental monitoring and devising a policy to regulate the ownership of digital devices and to reduce screen time to less than two hours per day, especially during early childhood. (shrink)

"Darshanika Cintan ke Vividha Āyāma" (Diverse dimensions of philosophical thinking), is a compilation book of various research articles in which the discursive diversity of philosophy is reflected. On the one hand, it pursues the basic problems of philosophy, such as the relevance of philosophy, the nature and justification of metaphysics, the metaphysical analysis of the nature of value, etc., while on the other hand, it Is involved in the analysis and testing of the concept of life-world, globalization and multiculturalism, environmental (...) ethics and applied ethics etc. Proper analysis and evaluation of the most important problems of Indian epistemology, for example, the idea of syntax (Vākyārtha Vicāra), Prāmanyavāda , and the issue of evidential implication (Pramānatarabhāva), has been heuristically presented. Some lively topics of contemporary Indian philosophy like Logical conclusion of Manvendra Nath Roy's materialism, Kant's influence on contemporary Indian philosophy, Post-independence Indian philosophical thinking, and the future form of Indian philosophy are included. There is a unique combination of linguistic beauty and clarity, systematic presentation, critical attitude and philosophical insight in the writings of the author duo. This is undoubtedly a valuable work which deserves to be welcomed by teachers, scholars and students of philosophy. (shrink)

With the technological evolutionary advent, a vision-based approach presents the remote measuring approach for the analysis of vibration. The structure vibration test and model parameter identification in the detection of the structure of the bridge evaluation occupies the important position. The bridge structure to operate safely and reliably is ensured, according to the geological data of qixiashan lead-zinc mine and engineering actual situation, with the aid of international mining software Surpac. To build the 3D visualization model of the application of (...) visualization in mine production are discussed. The results show that the final solid model of -425 stope can accurately display the spatial form of each layer of stope through rotation, amplification and movement. The proposed system is effectually able to perform cutting, volume calculation and roaming in any direction, which has certain guiding significance for mine production management. An accuracy value of 98.75%, the sensitivity of 99%, specificity of 99.64% and PPV of 99.89% are achieved using the proposed 3D modelling and visualization algorithm for vibration signal processing and management. (shrink)

This article presents a novel control approach, hybrid neuro-fuzzy, for the load frequency control of a four-area interconnected power system. The advantage of this controller is that it can handle nonlinearities, and at the same time, it is faster than other existing controllers. The effectiveness of the proposed controller in increasing the damping of local and inter-area modes of oscillation is demonstrated in a four-area interconnected power system. Areas 1 and 2 consist of a thermal reheat power plant, whereas Areas (...) 3 and 4 consist of a hydropower plant. Performance evaluation is carried out by using fuzzy, artificial neural network, adaptive neuro-fuzzy inference system, and conventional proportional and integral control approaches. Four different models with different controllers are developed and simulated, and performance evaluations are carried out with said controllers. The result shows that the intelligent HNF controller has improved dynamic response and is at the same time faster than ANN, fuzzy, and conventional PI controllers. (shrink)

It has become essential to create and apply new media in visual communication design due to social media existence. This study aims to investigate the role of innovative applications of new media in visual communication design in educational institutions. Traditional media design in visual communication lacks to disseminate information more effectively, which requires innovative change. Therefore, this study attempts to highlight the role of innovative application of new media in visual communication by considering visual expression design with information technology, flexible (...) layout, diversified modes of transmission, and interactivity of integration. For this purpose, this study adopted a quantitative research approach in which a cross-sectional research design is followed. A questionnaire survey is carried out to collect data from educational institutions in China. Partial Least Square-Structural Equation Modeling is used for data analysis. Results of the study indicated that innovative applications of new media have central importance in visual communication. However, resistance to innovative change has a negative role in the relationship between innovative applications of new media and visual communication design. Results of the study highlighted that visual expression design with IT, flexible layout, diversified modes of transmission, and interactivity of integration have a positive effect on visual communication design. Therefore, among the educational intuitions of China, implementing innovative applications related to the new media can lead to visual communication design. The results of this study provided several insights for the practitioners to promote communication methods among educational institutions. (shrink)

In this work, we explore modeling of wormholes in framework of f(R, T) gravity with the functional form f(R,T)=R+αR2+λT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f(R, T)= R+\alpha R^2 +\lambda T$$\end{document}, where R and T are the Ricci scalar and trace of energy-momentum tensor respectively, α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document} and λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda$$\end{document} are arbitrary constants. Using the equation of state (EoS) pr=ωρ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} (...) \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p_r=\omega \rho$$\end{document} and shape function b(r)=r0arar0,(0shrink)

This essay reads John Locke’s Two Treatises through its nonhuman animal presences, especially the emblematic figures of cattle and “noxious creatures” like “lyons,” “tygers,” and wolves. It argues that the real ground of Lockean human equality is an ongoing practice of subjugating nonhuman animals, and not any attribute of the human species as such. More specifically, the Lockean social compact founded on this equality relies on a “dominion covenant,” an existential “agreement” in which God lends the power of dominion to (...) man and any threats to this order require punishment. This dynamic enables violence toward humans, in the name of their humanity, if they do not properly exert their power of dominion. Critics have connected Locke’s theory of property to indigenous dispossession and his theory of punishment to carceral systems; both processes, I argue, intimately rely on the dominion covenant. Lockean racism is the fulfillment of, and not a deviation from, his account of human equality. (shrink)

In this paper, I discuss the ethical underpinnings to the anthropological analysis of age and reproductive decline in the ‘management’ of infertility, by suggesting that assisted reproductive technologies ‘use’ age and reproductive decline to further endanger women’s bodies by subjecting it to disaggregation into parts that do not belong to them anymore. Here, the category of age becomes a malleable concept to manipulate women seeking fertility management. In ethnographic findings from two Indian ART clinics, amongst women aged between 20 and (...) 35 years visiting an IVF/art clinic in Hyderabad city in South India, and women above 50 years of age visiting an IVF/art clinic in Hisar in North India—reproductive bodies are similarly disaggregated. In case of younger women, the treatment is fixated on rescuing eggs that may be in ‘decline’, and in case of older women, the aim is to engineer a viable pregnancy. Thus, the constant focus on eggs and wombs in infertility treatment creates a body that is not only not whole but also completely without agency. Age becomes a category that has rhetorical value to ‘push’ or persuade women into particular forms of fertility management through infertility medicine. I undertake a problematization of the egg and the uterus through the identification of the recurring motif of the menstrual cycle within IVF treatment to suggest that bodily holism is not part of ART discourse that unethically thrives on promoting technological intrusions to promote its use and normalization. (shrink)

The paper develops value based management guidelines from the famous Indian treatise on management, Kautilya's Arthashastra. Guidelines are given for individual components of a total framework in detail, which include guidelines for organizational philosophy, value based leadership, internal corporate culture, accomplishment of corporate purpose and feedback from stakeholders.

How does one give voice to the unspeakable, inhuman violence that shapes the present, and what remains of humanity in its wake? Adriana Cavarero offers an answer that roots human speech in embodied vulnerability, in contrast to philosophical emphases on disembodied rationality. In the face of what she calls horrorism, which puts humans in proximity to animality, she calls for resuscitating vocality, and therefore humanity, from loss. This article reads Kafka’s short story “A Report to an Academy” – which structurally (...) resembles a slave narrative and concerns a kidnapped ape who learns to speak – to extend Cavarero’s emphasis on vulnerability while challenging her humanism. In Kafka, modern horror’s locus is not animality but the abstract human, and it projects the unstable distinction between voice and noise onto blackened humans and nonhuman animals. (shrink)

Social media is the preferred communication platform for today’s youth, yet little is known of how online intergender communication is shaped by social identity norms. Drawing from the Social Identity and Deindividuation Effects (SIDE) approach, we argue that through depersonalization, online interactions are marked by the salience of social identities and identity performance conforming to perceived norms of behavior (traditional as well as developing). We specifically look at discursive terms and their meaning-making as a strategic performance of gender in uncontrolled (...) social media interactions. We examined a corpus of 442 comments from selected public Indian Facebook pages in two phases over a span of 1 year (2020–2021). Thematic discourse analysis revealed established (#mansplaining, pseudofeminism) and emerging (choice feminism, MGTOW, #fuckboi etc.) discursive strategies within the major themes on feminism and antifeminism, men’s rights, intersectional feminism, and sexual behavior. These meaningful terms are used to modulate identity performance in a heavily contested space, reflecting both consolidation as well as mobilization functions, as proposed by SIDE. The findings highlight that intergender communication on social media is both dependent on existing offline norms, while challenging the same to create new discourses of gender. (shrink)

This essay explores the humanistic dimensions of the unparalleled world-wide pandemic caused by Covid-19. Using both western and eastern sources, it seeks to draw wisdom from this tragedy – but also apply wisdom to it. Reflecting on the historical moment ensconcing this pandemic, and the fundamental metaphysical implications of Covid-19, this essay has three parts: (1) Precipice of History-Nature: This Historical Moment surrounding Covid-19; (2) Implications of a Pandemic for the nature of Nature and God; (3) Implications of a Pandemic (...) for Death, Predestination, Higher Faith – and likely Results. Viewing this moment as portentous in its anticipation of a new age, this essay uses the notion of a temporized precipice, to situate this pandemic historically. Drawing from western (Heidegger, Russell, Augustine, Catherine of Sienna, Epictetus, Plato, and Plotinus), and Indian (Gandhi, Vivekananda, and the Bhagavadgītā) sources, this essay offers both idealistic and realistic views of the likely results of Covid-19. (shrink)

One of the fundamental themes in economic theory is the study of the role of prices in achieving an optimal allocation of resources in a competitive, decentralized economy. The book begins with a review of the basic results on the rigorous elaboration of the Walras-Pareto theory in the context of a static economy with many agents. It summarizes some subsequent research in which the limits of the price-mechanism as a successful coordination device are recognized. When economic activity is allowed with (...) no pre-assigned terminal period, the two fundamental theorems linking competitive equilibrium allocations to Pareto optimality are challenged and the question of decentralization is carefully re-examined. With incomplete markets, and sequential trading, the concept of a Radner equilibrium is next introduced, and some of the striking properties of this are summarized. In a large economy with random shocks to preferences and/or endowments of individual agents, the implications of the celebrated laws of probability theory are explored. This book provides a clear and comprehensive analysis of the efficiency properties of general equilibrium, with many agents and an expanded list of commodities. It will be of particular interest to postgraduate and doctorate students of economic theory as well as scholars on Walrasian equilibrium, Pareto optimality and uncertainty theories. (shrink)