Set Theory and How It Is Used

Set theory is a fundamental concept throughout all of mathematics.  This branch of mathematics forms a foundation for other topics.   Intuitively a set is a collection of objects, which are called elements. Although this seems like a simple idea, it has some far-reaching consequences.   Elements The elements of a set can really be anything – numbers, states, cars, people or even other sets are all possibilities for elements. Just about anything that can be collected together may be used to form a set, though there are some things we need to be careful about. Equal Sets Elements of a set are either in a set or not in a set. We may describe a set by a defining property, or we may list the elements in the set. The order that they are listed is not important. So the sets {1, 2, 3} and {1, 3, 2} are equal sets, because they both contain the same elements. Two Special Sets Two sets deserve special mention. The first is the universal set, typically denoted U. This set is all of the elements that we may choose from. This set may be different from one setting to the next. For example, one universal set may be the set of real numbers whereas for another problem the universal set may be the whole numbers {0, 1, 2,...}.   The other set that requires some attention is called the empty set. The empty set is the unique set is the set with no elements. We can write this as { } and denote this set by the symbol ∅. Subsets and the Power Set A collection of some of the elements of a set A is called a subset of A. We say that A is a subset of B if and only if every element of A is also an element of B. If there are a finite number n of elements in a set, then there are a total of 2n subsets of A. This collection of all of the subsets of A is a set that is called the power set of A. Set Operations Just as we can perform operations such as addition - on two numbers to obtain a new number, set theory operations are used to form a set from two other sets. There are a number of operations, but nearly all are composed from the following three operations: Union – A union signifies a bringing together. The union of the sets A and B consists of the elements that are in either A or B.Intersection - An intersection is where two things meet. The intersection of the sets A and B consists of the elements that in both A and B.Complement - The complement of the set A consists of all of the elements in the universal set that are not elements of A. Venn Diagrams One tool that is helpful in depicting the relationship between different sets is called a Venn diagram.  A rectangle represents the universal set for our problem.  Each set is represented with a circle.  If the circles overlap with one another, then this illustrates the intersection of our two sets.   Applications of Set Theory Set theory is used throughout mathematics. It is used as a foundation for many subfields of mathematics. In the areas pertaining to statistics, it is particularly used in probability. Much of the concepts in probability are derived from the consequences of set theory. Indeed, one way to state the axioms of probability involves set theory.

Stem Cell Advocacy Paper Stem Cells - 1123 Words

Stem Cell Advocacy Paper Introduction Stem cells are basically the building blocks of life. Some type of these cells can be engineered into any type of cell in the human body. There are three types of stem cells currently. Adult or somatic stem â€Å"cells can generate replacements for bone and muscle cells that are lost through injury, disease or normal wear and tear.† Another type of stem cells are embryonic stem cells. Embryonic stem cells â€Å"are â€Å"starter cells† that can be coaxed into becoming any of the specialized cells of the body, meaning they are â€Å"pluripotent.† The final type of stem cells are induced-pluripotent stem cells. Induced pluripotent stem cells â€Å"are adult stem cells that have been genetically altered to behave like embryonic stem cells†(National Institute of Health). Due to the advancement in medical technology scientists and doctors alike are now able to use stem cells for a variety of reasons like research and also in patient care. The benefits of this research can lead to the cure of diseases like diabetes, some cancers, and even neurodegenerative diseases like Parkinson’s Disease and spinal cord injuries. The controversy behind stem cells lie from where these stem cells come from. The source of stem cells are plentiful. Some stem cells can come from human embryos that are a few days old. Stem cells can also be engineered in a laboratory setting using the cells from human embryos. Also there are certain stem cells that can be harvested from adults andShow MoreRelatedThe Debate Of Embryonic Stem Cell Research931 Words   |  4 Pages Embryonic stem cell research is the study of stem cells derived from the undifferentiated inner mass cells of a human embryo. For many years now, the ethics of embryonic stem cell research has been argued. 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Big Data for Biopharmaceutical Industry - myassignmenthelp.com

Question: Discuss about theBig Data in Manufacturing for Biopharmaceutical Industry. Answer: Introduction The big data analysis can enhance the business operations irrespective of industry and the industry size. The impact of big data is enhancing day by day and the industries like IT industry, the biopharmaceutical industry is gaining the profit. The report will highlight the big data effects, will showcase how the managers can handle the business operations with much ease, ten revolutionary ways by which the big data can bring in the revolution will be detailed along with the case study of the semiconductor industry. Advancement of the incorporation of IT services, operational systems and the Industrie 4.0 technology The Industrie 4.0 is a technology adopted by the Government of Germany and they have a plan to fully automatize the factories of Germany. Big data is utilized to optimize the production schedules and this production is based on the supplier, clients, cost constraints and the availability of machines (Lee, Kao Yang, 2014). The German suppliers and the German manufacturers are planning to use the Industrie 4.0 for the embellishment of their company. Big data analysis can increase the productivity; can ease the manufacturing procedures as all the manufacturing units will work digitally. Showcase the demand of the product, the productivity and overview of plant performance on multiple metrics and catering service and support to customers The finding from the latest survey of LNS Research and MESA International demonstrates that the big data has the capability to provide the quality service that is capable to benefits the manufacturing industry. Integration of advanced analytics across the Six Sigma DMAIC DMAIC driven improvement program has the capability to furnish the manufacturing industry aspects from all sides (Lee et al., 2013). The program highlights the production workflow, can facilitate the customers to great extent. Greater visibility accuracy in detecting the performance of the suppliers timely The big data analysis techniques can help to get an overall on sight of all the business procedures, the employees can get an overview of the workflow so that can help them to keep track of every bit of data flow (Hazen et al., 2014). The big data analysis can help them to maintain the product quality, can help to manage the accuracy in delivery of the products, and can help to accomplish the goal or complete the products within the stipulated time. Measurement of traceability and compliance to the machine level Due to use of the sensors, the operation management team can get a general overview of all the operations currently being undertaken by the enterprise (Jagadish et al., 2014). The advanced analytics can enhance the quality; can enhance the workflow of the production center. Selling off most profitable customized configurations of products that enhances profitable services For the complex manufacturers, the well-customized product orders can cater them the enhanced production process (Dubey et al., 2016). With the aid of advanced analysis of the big data the manufacturers can sell their products with the minimum impact to the prevalent production schedules to the shop floor level, machine scheduling and the staffing. Break down of compliance systems and quality management With the aid of big data, the manufacturers can get more strategies to advance their business process can enhance the quality of the project or the product they deal with (Zhong et al., 2017). The managers and the management team can get rid of the soiled quality management; they can even get rid of the compliance systems. Daily production impacts on financial performance Big data together with the advanced analytics can unite and facilitates the productivity of the enterprise (Tao et al., 2017). The management team can detect the machine level if they get to know the factory floor plan is executing with full efficiency or not, based on that they can take the best strategic decision to scale the business activities of their enterprise. Strategic service and a contribution to customers goals The manufacturers can detect the customers shopping behaviors or the shopping patterns, with the aid of big data, the managers can keep track of the wish list of the employees, all these aspects can help the enterprises to learn the latest market trends and the customers demands and in this way the big data can facilitate both the customers and the organizations (Noh Park, 2014). Augmentation of the efficiency, productivity of biopharmaceutical production The IT services can facilitate the biopharmaceutical production and in this way, the purity of the ingredients can greatly flourish. The IT aspects and big data mining make the entire production simple and easy and thus the employees of the enterprise can increase the productivity of the products, even they can analyses the parameters well (Venkatesh, Delgado, Patel, 2017). Based on the analysis the vaccines yield can get increased by 50%. The heavy expenses can cut down due to the advent of the IT services and the big data mining. Case Study: Case Study based on Big Data Analytics to enhance Smart Manufacturing and its role in Semiconductor Manufacturing Smart Manufacturing (SM) is the term basically used to enhance the business operations via linking physical capabilities along with the cyber capabilities and integration of various aspects of the system. SM with the aid of big data can embellish the business operations to the next level (Chen Zhang, 2017). The enhancement is not limited to a specific industry but it covers all the industries and semiconductor manufacturing is one of them. The semiconductor industry is portrayed in the report by the following parameters that are by precise processing prerequisites, highly complicated procedures and the problems associated with manufacturing the data quality (Yin Kaynak, 2015). The analytical solution deployment showcases that the SME is needed to identify the robust solutions. By incorporating SME the faults within can be detected and possible solutions can be suggested to mitigate and the faults occurrence. Various me3thods involving the data quality improvement along with SME inc orporation can enhance and facilitate and ease the productivity and these vital components of the analytics roadmap for SM (Bi Cochran, 2017). Thus Smart Manufacturing can embellish semiconductor manufacturing procedures to a greater extent. Conclusion It can be concluded from the above discourse that the big data analysis can enhance every sector of the business organizations, can solve all the faulty issues occurring within, it can facilitate the biopharmaceutical industry as well as the chemical industry in semiconductor manufacturing; the Smart Manufacturing concepts have been highlighted in the report to support the big data benefits. The big data can aids the organizations can keep track of the customers' data, their wish list can be well traced, thus the shopping behavior and the shopping patterns can be analyzed, thus the enterprise can learn the customers' demands and the current market scenario. The big data mining can help in accessing the data really fast with ease and simplicity and big data can help to fully automatize the system of the enterprises. All these aspects of big data in manufacturing have been highlighted and have been explained in details. References Bi, Z., Cochran, D. (2014). Big data analytics with applications.Journal of Management Analytics,1(4), 249-265. Chen, C. P., Zhang, C. Y. (2014). Data-intensive applications, challenges, techniques and technologies: A survey on Big Data.Information Sciences,275, 314-347. Dubey, R., Gunasekaran, A., Childe, S. J., Wamba, S. F., Papadopoulos, T. (2016). The impact of big data on world-class sustainable manufacturing.The International Journal of Advanced Manufacturing Technology,84(1-4), 631-645. Hazen, B. T., Boone, C. A., Ezell, J. D., Jones-Farmer, L. A. (2014). Data quality for data science, predictive analytics, and big data in supply chain management: An introduction to the problem and suggestions for research and applications.International Journal of Production Economics,154, 72-80. Jagadish, H. V., Gehrke, J., Labrinidis, A., Papakonstantinou, Y., Patel, J. M., Ramakrishnan, R., Shahabi, C. (2014). Big data and its technical challenges.Communications of the ACM,57(7), 86-94. Lee, J., Kao, H. A., Yang, S. (2014). Service innovation and smart analytics for industry 4.0 and big data environment.Procedia Cirp,16, 3-8. Lee, J., Lapira, E., Bagheri, B., Kao, H. A. (2013). Recent advances and trends in predictive manufacturing systems in big data environment.Manufacturing Letters,1(1), 38-41. Noh, K. S., Park, S. (2014). An exploratory study on application plan of big data to manufacturing execution system.Journal of Digital Convergence,12(1), 305-311. Tao, F., Zhang, L., Nee, A. Y. C., Pickl, S. W. (2016). Editorial for the special issue on big data and cloud technology for manufacturing. Venkatesh, M., Delgado, C., Patel, P. (2017). Mitigating Supply Chain Risk for Sustainability Using Big Data Knowledge: Evidence from the Manufacturing Supply Chain.World Academy of Science, Engineering and Technology, International Journal of Environmental and Ecological Engineering,4(5). Yin, S., Kaynak, O. (2015). Big data for modern industry: challenges and trends [point of view].Proceedings of the IEEE,103(2), 143-146. Zhong, R. Y., Lan, S., Xu, C., Dai, Q., Huang, G. Q. (2016). Visualization of RFID-enabled shopfloor logistics Big Data in Cloud Manufacturing.The International Journal of Advanced Manufacturing Technology,84(1-4), 5-16.