Products related to Polynomial:
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Sparse Polynomial Approximation of High-Dimensional Functions
Over seventy years ago, Richard Bellman coined the term "the curse of dimensionality" to describe phenomena and computational challenges that arise in high dimensions.These challenges, in tandem with the ubiquity of high-dimensional functions in real-world applications, have led to a lengthy, focused research effort on high-dimensional approximation—that is, the development of methods for approximating functions of many variables accurately and efficiently from data.This book provides an in-depth treatment of one of the latest installments in this long and ongoing story: sparse polynomial approximation methods.These methods have emerged as useful tools for various high-dimensional approximation tasks arising in a range of applications in computational science and engineering.It begins with a comprehensive overview of best s-term polynomial approximation theory for holomorphic, high-dimensional functions, as well as a detailed survey of applications to parametric differential equations.It then describes methods for computing sparse polynomial approximations, focusing on least squares and compressed sensing techniques. Sparse Polynomial Approximation of High-Dimensional Functions presents the first comprehensive and unified treatment of polynomial approximation techniques that can mitigate the curse of dimensionality in high-dimensional approximation, including least squares and compressed sensing.It develops main concepts in a mathematically rigorous manner, with full proofs given wherever possible, and it contains many numerical examples, each accompanied by downloadable code.The authors provide an extensive bibliography of over 350 relevant references, with an additional annotated bibliography available on the book's companion website (www.sparse-hd-book.com). This text is aimed at graduate students, postdoctoral fellows, and researchers in mathematics, computer science, and engineering who are interested in high-dimensional polynomial approximation techniques.
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Industrial Automation and Robotics : Techniques and Applications
This book discusses the radical technological changes occurring due to Industry 4.0, with a focus on offering a better understanding of the Fourth Industrial Revolution.It also presents a detailed analysis of interdisciplinary knowledge, numerical modeling and simulation, and the application of cyber–physical systems, where information technology and physical devices create synergic systems leading to unprecedented efficiency.The book focuses on industrial applications of automation and robotics.It covers recent developments and trends occurring in both computer-aided manufacturing techniques, as well as computer-aided assembly techniques.Robots using embedded systems and artificial intelligence applications are also covered.Industrial Automation and Robotics: Techniques and Applications offers theoretical results, practical solutions, and guidelines that are valuable for both researchers and those working in the area of engineering.
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Food Engineering Automation with Robotics and AI
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Robotics and Automation in Healthcare : Advanced Applications
The recent pandemic has forced researchers to adapt technologies such as robotics and AI in the healthcare field.This book, Robotics and Automation in Healthcare: Advanced Applications, explores these new technologies by focusing on important issues related to the employment of robotics and automation in healthcare, such as in medical diagnosis, treatment, and surgery. The volume reviews wireless charging of implantable pacemakers, considers smart bot design for library building of medical colleges, and discusses strain distribution in biomechanical systems.Other topics included in the book are medical imaging, drone technology, 3D printing, and image processing techniques.The application and importance of actuators in medical devices, especially during surgery, is discussed, as are wearable devices for pre-identification of seizure development.The volume also looks at a decision support system for detection of suitable robots and early detection of diseases with the support of image processing techniques.The application of nano-robots in healthcare is also explored. Providing advanced information and insight into robotics, wearable devices, and applications of image processing in healthcare field, this volume will be helpful to those in communications and electronics engineering as well as those at the forefront of smart technology in healthcare.
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What is the difference between a polynomial and a polynomial function?
A polynomial is an algebraic expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication, but not division or roots. A polynomial function, on the other hand, is a specific type of function that can be defined by a polynomial expression. In other words, a polynomial function is a function that can be expressed as a polynomial. So, while a polynomial is simply an algebraic expression, a polynomial function is a specific type of mathematical function.
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What are polynomial functions?
Polynomial functions are mathematical functions that can be expressed as a sum of terms, where each term is a constant multiplied by a variable raised to a non-negative integer power. These functions can have multiple terms, each with a different power of the variable. Polynomial functions are continuous and smooth, and they can be used to model a wide range of real-world phenomena. They are commonly used in algebra, calculus, and other branches of mathematics to analyze and solve various problems.
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How difficult is a study of robotics and automation?
The study of robotics and automation can be challenging due to its interdisciplinary nature, requiring knowledge in fields such as mechanical engineering, electrical engineering, computer science, and control systems. Additionally, the rapid advancements in technology and the need to stay updated with the latest developments can add to the complexity of the study. However, with dedication, problem-solving skills, and a strong foundation in mathematics and physics, students can overcome these challenges and excel in the field of robotics and automation.
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What is double polynomial division?
Double polynomial division is a method used to divide one polynomial by another polynomial. It involves dividing the leading term of the dividend by the leading term of the divisor to determine the first term of the quotient. This process is repeated for each subsequent term until the entire dividend is divided by the divisor. The result is a quotient and a remainder, if any.
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Robots, Automation and the Innovation Economy
Cascades of new technologies and innovations are entering our lives so fast that it is difficult for us to adapt to one innovation before the next becomes embedded into our everyday lives.What happens when the changes brought by technology are so profound that they affect all aspects of our lives?This book explores the potential impact of artificial intelligence (AI) and intelligent robots on individuals, organizations and society, specifically examining the impact on jobs and workplaces in the future.It provides an understanding of how we can adapt to changes that appear like flocks of black swans. Five key areas are unpacked in the book: automation, AI, (the significance of AI technology), innovation, competence transformation, and the fact that the pace of change is so rapid that it outstrips our ability to adapt to consecutive changes.The main objective is to show how AI will change society and how we as individuals and society must adapt in order to survive what the author terms ‘robot shock’, together with its consequences and after-effects.It offers a greater understanding of resistance to change and how we need to adopt strategies for adapting to major changes.Each of the book’s six chapters also contains policy inputs, framed as propositions, that are intended specifically for decision-makers.The book concludes by offering possible strategies for overcoming the negative effects of ‘robot shock’. The book intends to send a message to leaders of institutions, decision-makers and anyone attempting to understand and explain how we – as a social system – can succeed in tackling the many major challenges and crises faced by humanity.
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Technology Innovation in Manufacturing
This text identifies and discusses different technology innovation initiatives (TIIs) such as entrepreneurial capability, technology infrastructure capability, organizational culture and climate, and government initiatives.It further evaluates the relationship between various technology innovation initiatives and manufacturing performances using multi-criteria decision-making techniques such as fuzzy set theory (FST), structural equation modeling (SEM), and analytic hierarchy process (AHP).It will serve as an ideal reference text for graduate students and academic researchers in the field of industrial engineering, manufacturing engineering, mechanical engineering, automotive engineering. This book:• Discusses technology innovation initiatives such as entrepreneurial capability, technology infrastructure capability, and organizational culture. • Highlights technology innovation-strategy model in assisting manufacturing industries for enhancing their performance in today’s competitive environment. • Examines the effect of technology innovation initiatives on the performance of manufacturing industries. • Covers multi-criteria decision-making techniques such as fuzzy set theory, structural equation modeling, and analytic hierarchy process. • Explores the validation of fuzzy-based technology innovation model through structural equation modeling.
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Technology and Innovation Management
Technology and Innovation Management is one of the most sought-after courses offered like MBA or PGDM in Business Schools and various Technology Institutes, today.This book, written with deep ingrained practical insights and well-researched theoretical foundations integrates people, processes and technology to achieve maximum economic benefits to society.The book is designed to be a compendium for students and managers, who wish to understand technology and innovation management to the core.The book explains the relationship between technology innovation and strategy in a simplified manner.Keeping Indian education framework in mind, this book details on practices and principles that are easy to implement.The theories are simple to grasp, and anecdotal stories on Technology and Innovation implementations make it a student-friendly edition, to help achieve success in exams as well as in the professional front.It further explains the core principles of Technology and Innovation Management.S-Curve and the Segment Zero Principle, adopting industry 4.0 and innovation 4.0 to make India a smart and intelligent manufacturing hub in the era of fourth industrial revolution, design thinking for solving complex business problems along with the role and contribution of Government in Technology Development.
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Mediating Innovation Policy Delivery : The Regional Innovation Centres of Ontario
Report cards and academic scholarship have been critical of innovation policy in Canada.But what if these reports have done a profound injustice to the story of knowledge-driven economic reinvention and the actual transformation taking place in the country?Spotlighting what is happening in cities and regions across Ontario, Mediating Innovation Policy Delivery argues that it is far more nuanced and exciting than what has been captured in scorecards and report cards.The book explores the intermediary institutions, the organizational brokers at the frontline of Canada’s innovation race, that are shepherding the process of economic reinvention in regions large and small. The book draws on case studies to explore three central themes.The first is about innovation, innovation policy, and their delivery systems.The second is that of regions as the frontlines of technological and socioeconomic change in the Canadian federation.The third covers the role of intermediary institutions as innovation platforms, highlighting their triumphs and tribulations as they strategically navigate through the shifting currents of change.The book’s main lessons apply not just to Ontario and Canada but also to other industrialized democracies worldwide.Ultimately, the book advances our knowledge of organizational instruments of innovation policy delivery that operate at the strategic interface between the state, market, and society.
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What is a polynomial space?
A polynomial space is a vector space whose elements are polynomials. In other words, it is a set of all polynomials of a certain degree, along with the operations of addition and scalar multiplication. The dimension of a polynomial space is determined by the highest degree of the polynomials in the space. Polynomial spaces are commonly used in mathematics and engineering to represent and manipulate functions and data.
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Is 2x a polynomial function?
Yes, 2x is a polynomial function. A polynomial function is a function that can be expressed as a sum of terms, where each term is a constant multiplied by a variable raised to a non-negative integer power. In the case of 2x, it can be written as 2x^1, which fits the definition of a polynomial function.
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"Is my polynomial function correct?"
To determine if your polynomial function is correct, you should first check if it satisfies the given conditions or constraints. Then, you can verify if the function produces the expected output for a range of input values. Additionally, you can compare your function with other known correct polynomial functions to see if they match. If your function meets all these criteria, it is likely correct. However, it's always a good idea to double-check your work and seek feedback from others to ensure accuracy.
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What is the polynomial form?
The polynomial form is a mathematical expression consisting of variables, coefficients, and exponents. It is a sum of terms, where each term is a variable raised to a non-negative integer power, multiplied by a coefficient. The polynomial form is used to represent various mathematical functions and equations, and it can be manipulated through operations such as addition, subtraction, multiplication, and division. The degree of a polynomial is determined by the highest exponent of the variables present in the expression.
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