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Abstract Mathematical Cognition

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Book Series: Frontiers Research Topics ISSN: 16648714 ISBN: 9782889198160 Year: Pages: 111 DOI: 10.3389/978-2-88919-816-0 Language: English
Publisher: Frontiers Media SA
Subject: Neurology --- Science (General)
Added to DOAB on : 2016-01-19 14:05:46
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Despite the importance of mathematics in our educational systems little is known about how abstract mathematical thinking emerges. Under the uniting thread of mathematical development, we hope to connect researchers from various backgrounds to provide an integrated view of abstract mathematical cognition. Much progress has been made in the last 20 years on how numeracy is acquired. Experimental psychology has brought to light the fact that numerical cognition stems from spatial cognition. The findings from neuroimaging and single cell recording experiments converge to show that numerical representations take place in the intraparietal sulcus. Further research has demonstrated that supplementary neural networks might be recruited to carry out subtasks; for example, the retrieval of arithmetic facts is done by the angular gyrus. Now that the neural networks in charge of basic mathematical cognition are identified, we can move onto the stage where we seek to understand how these basics skills are used to support the acquisition and use of abstract mathematical concepts.

Theory and Applications of Ordered Fuzzy Numbers: A Tribute to Professor Witold Kosiński

Authors: --- --- --- --- et al.
Book Series: Studies in Fuzziness and Soft Computing ISSN: 1434-9922 / 1860-0808 ISBN: 9783319596136 9783319596143 Year: Pages: 322 DOI: https://doi.org/10.1007/978-3-319-59614-3 Language: English
Publisher: Springer Nature
Subject: Mathematics --- Computer Science
Added to DOAB on : 2017-11-24 16:56:25
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This open access book offers comprehensive coverage on Ordered Fuzzy Numbers, providing readers with both the basic information and the necessary expertise to use them in a variety of real-world applications. The respective chapters, written by leading researchers, discuss the main techniques and applications, together with the advantages and shortcomings of these tools in comparison to other fuzzy number representation models. Primarily intended for engineers and researchers in the field of fuzzy arithmetic, the book also offers a valuable source of basic information on fuzzy models and an easy-to-understand reference guide to their applications for advanced undergraduate students, operations researchers, modelers and managers alike.

The Essence of Mathematics Through Elementary Problems

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Book Series: OBP Series in Mathematics ISSN: 2397-1126/2397-1134 ISBN: 9781783746996 9781783747016 Year: DOI: https://doi.org/10.11647/OBP.0168 Language: English
Publisher: Open Book Publishers
Subject: Mathematics
Added to DOAB on : 2019-06-25 18:14:54
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"It is increasingly clear that the shapes of reality – whether of the natural world, or of the built environment – are in some profound sense mathematical. Therefore it would benefit students and educated adults to understand what makes mathematics itself ‘tick’, and to appreciate why its shapes, patterns and formulae provide us with precisely the language we need to make sense of the world around us. The second part of this challenge may require some specialist experience, but the authors of this book concentrate on the first part, and explore the extent to which elementary mathematics allows us all to understand something of the nature of mathematics from the inside.The Essence of Mathematics consists of a sequence of 270 problems – with commentary and full solutions. The reader is assumed to have a reasonable grasp of school mathematics. More importantly, s/he should want to understand something of mathematics beyond the classroom, and be willing to engage with (and to reflect upon) challenging problems that highlight the essence of the discipline.The book consists of six chapters of increasing sophistication (Mental Skills; Arithmetic; Word Problems; Algebra; Geometry; Infinity), with interleaved commentary. The content will appeal to students considering further study of mathematics at university, teachers of mathematics at age 14-18, and anyone who wants to see what this kind of elementary content has to tell us about how mathematics really works."

Building the Foundation: Whole Numbers in the Primary Grades: The 23rd ICMI Study

Authors: ---
Book Series: New ICMI Study Series ISSN: 1387-6872 ISBN: 9783319635545 9783319635552 Year: Pages: 536 DOI: https://doi.org/10.1007/978-3-319-63555-2 Language: English
Publisher: Springer Nature Grant: International Commission on Mathematical Instruction (ICMI); International Mathematical Union (IMU)
Subject: Education --- Mathematics
Added to DOAB on : 2018-06-22 15:48:51
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This twenty-third ICMI Study addresses for the first time mathematics teaching and learning in the primary school (and pre-school) setting, while also taking international perspectives, socio-cultural diversity and institutional constraints into account. One of the main challenges of designing the first ICMI primary school study of this kind is the complex nature of mathematics at the early level. Accordingly, a focus area that is central to the discussion was chosen, together with a number of related questions. The broad area of Whole Number Arithmetic (WNA), including operations and relations and arithmetic word problems, forms the core content of all primary mathematics curricula. The study of this core content area is often regarded as foundational for later mathematics learning. However, the principles and main goals of instruction on the foundational concepts and skills in WNA are far from universally agreed upon, and practice varies substantially from country to country. As such, this study presents a meta-level analysis and synthesis of what is currently known about WNA, providing a useful base from which to gauge gaps and shortcomings, as well as an opportunity to learn from the practices of different countries and contexts.

Symmetry in Graph Theory

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ISBN: 9783038976585 Year: Pages: 340 DOI: 10.3390/books978-3-03897-659-2 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Mathematics --- Science (General)
Added to DOAB on : 2019-03-21 15:50:41
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This book contains the successful invited submissions to a Special Issue of Symmetry on the subject of ""Graph Theory"". Although symmetry has always played an important role in Graph Theory, in recent years, this role has increased significantly in several branches of this field, including but not limited to Gromov hyperbolic graphs, the metric dimension of graphs, domination theory, and topological indices. This Special Issue includes contributions addressing new results on these topics, both from a theoretical and an applied point of view.

Computer Algebra in Scientific Computing

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ISBN: 9783039217304 9783039217311 Year: Pages: 160 DOI: 10.3390/books978-3-03921-731-1 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Computer Science
Added to DOAB on : 2019-12-09 11:49:16
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Although scientific computing is very often associated with numeric computations, the use of computer algebra methods in scientific computing has obtained considerable attention in the last two decades. Computer algebra methods are especially suitable for parametric analysis of the key properties of systems arising in scientific computing. The expression-based computational answers generally provided by these methods are very appealing as they directly relate properties to parameters and speed up testing and tuning of mathematical models through all their possible behaviors. This book contains 8 original research articles dealing with a broad range of topics, ranging from algorithms, data structures, and implementation techniques for high-performance sparse multivariate polynomial arithmetic over the integers and rational numbers over methods for certifying the isolated zeros of polynomial systems to computer algebra problems in quantum computing.

Wind Turbine Power Optimization Technology

Authors: ---
ISBN: 9783039289332 / 9783039289349 Year: Pages: 138 DOI: 10.3390/books978-3-03928-934-9 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- General and Civil Engineering
Added to DOAB on : 2020-06-09 16:38:57
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Wind turbines are one of the most promising renewable energy technologies, and this motivates fertile research activity about developments in power optimization. This topic covers a wide range of aspects, from the research on aerodynamics and control design to the industrial applications about on-site wind turbine performance control and monitoring. This Special Issue collects seven research papers about several innovative aspects of the multi-faceted topic of wind turbine power optimization technology. The seven research papers deal respectively with the aerodynamic optimization of wind turbine blades through Gurney flaps; optimization of blade design for large offshore wind turbines; control design optimization of large wind turbines through the analysis of the competing objectives of energy yield maximization and fatigue loads minimization; design optimization of a tension leg platform for floating wind turbines; innovative methods for the assessment of wind turbine optimization technologies operating on site; optimization of multiple wake interactions modeling through the introduction of a mixing coefficient in the energy balance method; and optimization of the dynamic stall control of vertical-axis wind turbines through plasma actuators. This Special Issue presents remarkable research activities in the timely subject of wind turbine power optimization technology, covering various aspects. The collection is believed to be beneficial to readers and contribute to the wind power industry.

New types of Neutrosophic Set/Logic/Probability, Neutrosophic Over-/Under-/Off-Set, Neutrosophic Refined Set, and their Extension to Plithogenic Set/Logic/Probability, with Applications

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ISBN: 9783039219384 9783039219391 Year: Pages: 714 DOI: 10.3390/books978-3-03921-939-1 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- General and Civil Engineering
Added to DOAB on : 2019-12-09 16:39:37
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This book contains 37 papers by 73 renowned experts from 13 countries around the world, on following topics: neutrosophic set; neutrosophic rings; neutrosophic quadruple rings; idempotents; neutrosophic extended triplet group; hypergroup; semihypergroup; neutrosophic extended triplet group; neutrosophic extended triplet semihypergroup and hypergroup; neutrosophic offset; uninorm; neutrosophic offuninorm and offnorm; neutrosophic offconorm; implicator; prospector; n-person cooperative game; ordinary single-valued neutrosophic (co)topology; ordinary single-valued neutrosophic subspace; ?-level; ordinary single-valued neutrosophic neighborhood system; ordinary single-valued neutrosophic base and subbase; fuzzy numbers; neutrosophic numbers; neutrosophic symmetric scenarios; performance indicators; financial assets; neutrosophic extended triplet group; neutrosophic quadruple numbers; refined neutrosophic numbers; refined neutrosophic quadruple numbers; multigranulation neutrosophic rough set; nondual; two universes; multiattribute group decision making; nonstandard analysis; extended nonstandard analysis; monad; binad; left monad closed to the right; right monad closed to the left; pierced binad; unpierced binad; nonstandard neutrosophic mobinad set; neutrosophic topology; nonstandard neutrosophic topology; visual tracking; neutrosophic weight; objectness; weighted multiple instance learning; neutrosophic triangular norms; residuated lattices; representable neutrosophic t-norms; De Morgan neutrosophic triples; neutrosophic residual implications; infinitely ?-distributive; probabilistic neutrosophic hesitant fuzzy set; decision-making; Choquet integral; e-marketing; Internet of Things; neutrosophic set; multicriteria decision making techniques; uncertainty modeling; neutrosophic goal programming approach; shale gas water management system.

Keywords

single-valued neutrosophic soft number and its operations --- SVN soft weighted arithmetic averaging operator --- SVN soft weighted geometric averaging operator --- decision-making --- optimization solution --- sampling plan --- producer’s risk’ --- consumer’s risk --- sample size --- decision making --- neutrosophic set --- Q-neutrosophic set --- Q-neutrosophic soft set --- soft set --- Neutrosophic compound orthogonal neural network --- Neutrosophic number --- Neutrosophic function --- Function approximation --- triangular neutrosophic cubic fuzzy number --- Einstein t-norm --- arithmetic averaging operator --- Multi-attribute decision making --- numerical application --- neutrosophic statistical interval method --- classical statistics --- fuzzy logic --- producer’s risk --- consumer’s risk --- neutrosophic cubic weighted geometric operator (NCWG) --- neutrosophic cubic ordered weighted geometric operator (NCOWG) --- neutrosophic cubic Einstein weighted geometric operator (NCEWG) --- neutrosophic cubic Einstein ordered weighted geometric operator (NCEOWG) --- multi-attribute decision making --- single-valued neutrosophic set --- aggregation --- TOPSIS --- single-valued neutrosophic linguistic set --- distance measure --- combined weighted average --- MAGDM --- low-carbon supplier selection --- weighted geometric operator --- weighted average operator --- neutrosophic cubic sets --- multi-attribute decision-making (MADM) --- neutrosophic cubic hybrid weighted arithmetic and geometric aggregation operator (NCHWAGA) --- neutrosophic sets --- cubic sets --- soft sets --- neutrosophic cubic soft sets --- neutrosophic cubic soft expert system --- multicriteria decision-making --- neutrosophic extended triplet group --- generalized neutrosophic extended triplet group --- quasi-completely regular semigroup --- clifford semigroup --- prostate cancer --- neutrosophic statistics --- dietary fat level --- neutrosophic regression --- neutrosophic correlation --- single valued neutrosophic sets --- logarithmic operational laws --- logarithmic aggregation operators --- MCGDM problems --- complex neutrosophic set --- complex neutrosophic soft expert set --- fuzzy parameterized single valued neutrosophic soft expert set --- single valued neutrosophic set --- soft expert set --- decision making --- membership function --- neutrosophic set --- neutrosophic soft rough --- relations --- rough set approximation --- soft set --- neutrosophic time series --- triangular neutrosophic number --- neutrosophic logical relationship --- neutrosophic logical relationship groups --- smart port --- simplified neutrosophic set --- single-valued neutrosophic set --- exponential similarity measure --- port evaluation --- nonstandard analysis --- extended nonstandard analysis --- open and closed monads to the left/right --- pierced and unpierced binads --- MoBiNad set --- infinitesimals --- infinities --- nonstandard reals --- standard reals --- nonstandard neutrosophic lattices of first type (as poset) and second type (as algebraic structure), nonstandard neutrosophic logic --- extended nonstandard neutrosophic logic --- nonstandard arithmetic operations --- nonstandard unit interval --- nonstandard neutrosophic infimum --- nonstandard neutrosophic supremum --- intuitionistic fuzzy parameters --- uncertainty modeling --- neutrosophic goal programming approach --- shale gas water management system --- e-marketing --- Internet of Things --- neutrsophic set --- multi-criteria decision making techniques --- probabilistic neutrosophic hesitant fuzzy set (PNHFS) --- decision-making --- Choquet integral --- neutrosophic extended triplet group --- neutrosophic quadruple numbers --- neutrosophic set --- BNHWA aggregation operator --- BNHOWA aggregation operator --- BNHHA aggregation operator --- score function --- accuracy function --- certainty function --- group decision making --- non-standard analysis --- extended non-standard analysis --- monad --- binad --- left monad closed to the right --- right monad closed to the left --- pierced binad --- unpierced binad --- non-standard neutrosophic mobinad set --- neutrosophic topology --- non-standard neutrosophic topology --- neutrosophic sets --- neutrosophic triangular norms --- residuated lattices --- representable neutrosophic t-norms --- De Morgan neutrosophic triples --- neutrosophic residual implications --- infinitely ?-distributive --- visual tracking --- neutrosophic weight --- objectness --- weighted multiple instance learning --- supply chain sustainability metrics --- plithogeny --- aggregation operations --- neutrosophic set --- quality function deployment --- multi-granulation neutrosophic rough set --- non-dual --- two universes --- multi-attribute group decision making --- neutrosophic extended triplet group --- neutrosophic quadruple numbers --- refined neutrosophic numbers --- refined neutrosophic quadruple numbers --- neutrosophic set --- fuzzy numbers --- neutrosophic numbers --- neutrosophic symmetric scenarios --- performance indicators --- financial assets --- simplified neutrosophic hesitant fuzzy set --- multi-attribute decision-making --- maximizing deviation --- TOPSIS --- single valued neutrosophic set --- covering --- symmetric relation --- graph representation --- matrix representation --- paper defect diagnosis --- ordinary single valued neutrosophic (co)topology --- ordinary single valued neutrosophic subspace --- ?-level --- ordinary single valued neutrosophic neighborhood system --- ordinary single valued neutrosophic base --- ordinary single valued neutrosophic subbase --- neutrosophic offset --- uninorm --- neutrosophic offuninorm --- neutrosophic offnorm --- neutrosophic offconorm --- implicator --- prospector --- n-person cooperative game --- hypergroup --- semihypergroup --- neutrosophic extended triplet group --- neutrosophic extended triplet semihypergroup (NET-semihypergroup) --- NET-hypergroup --- neutrosophic rings --- neutrosophic quadruple rings --- idempotents --- neutrosophic extended triplet group --- neutrosophic set

Multiple-Criteria Decision-Making (MCDM) Techniques for Business Processes Information Management

Authors: --- ---
ISBN: 9783038976424 Year: Pages: 320 DOI: 10.3390/books978-3-03897-643-1 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- General and Civil Engineering
Added to DOAB on : 2019-03-08 11:42:05
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Information management is a common paradigm in modern decision-making. A wide range of decision-making techniques have been proposed in the literature to model complex business and engineering processes. In this Special Issue, 16 selected and peer-reviewed original research articles contribute to business information management in various current real-world problems by proposing crisp or uncertain multiple-criteria decision-making (MCDM) models and techniques, mostly including multi-attribute decision-making (MADM) approaches, in addition to a single paper proposing an interactive multi-objective decision-making (MODM) approach. Particular attention is devoted to information aggregation operators; 65% of papers dealt with this item. The topics of this Special Issue gained attention in Europe and Asia. A total of 48 authors from seven countries contributed to this Issue. The papers are mainly concentrated in three application areas: supplier selection and rational order allocation, the evaluation and selection of goods or facilities, and personnel selection/partner selection. A number of new approaches are proposed that are expected to attract great interest from the research community.

Keywords

multi-criteria decision-making --- group decision-making --- subcontractor evaluation --- MCDM --- MADM --- fuzzy sets --- fuzzy EDAS --- multi-attribute decision making --- projection model --- bi-directional projection model --- Pythagorean uncertain linguistic variable --- rough number --- rough weighted aggregated sum product assessment (WASPAS) --- rough analytical hierarchical process (AHP) --- multiple criteria decision making (MCDM) --- supplier --- supplier selection --- order allocation --- multiobjective optimization --- interactive approach --- desirability function --- Pythagorean fuzzy set --- Muirhead mean --- multiple criteria group decision-making --- multiple attributes decision-making --- group decision-making --- unbalanced linguistic set --- prioritized average operator --- maximizing deviation model --- Pythagorean fuzzy set --- Muirhead mean --- interaction operational laws --- multi-attribute group decision-making --- green supplier --- rough ANP --- trapezoidal fuzzy number --- rough boundary interval --- evidence theory --- trust interval --- multiple attribute decision making --- linguistic cubic variable --- Dombi operations --- linguistic cubic variable Dombi weighted arithmetic average (LCVDWAA) operator --- linguistic cubic variable Dombi weighted geometric average (LCVDWGA) operator --- single-valued linguistic neutrosophic interval linguistic number --- score function --- weighted aggregation operator --- decision making --- multiple attribute decision making --- nonnegative normal neutrosophic number --- aggregation operator --- multi-criteria decision-making --- multi-hesitant fuzzy sets --- aggregation operators --- hesitant probabilistic fuzzy element (HPFE) --- Einstein operations --- hesitant probabilistic fuzzy Einstein aggregation operators --- multiple attribute decision making (MADM). --- ANFIS --- warehouse --- queuing systems --- logistics --- uncertain group decision-making support systems --- multiple criteria decision-making --- reliable group decision-making --- interval multiplicative preference relations --- rough sets --- binary discernibility matrices --- deterministic finite automata --- multiple-criteria decision-making (MCDM) --- multi-attribute decision-making (MADM) --- fuzzy sets --- neutrosophic sets --- rough sets --- aggregation operators --- adaptive neuro-fuzzy inference system (ANFIS)

Stochastic Processes with Applications

Authors: --- ---
ISBN: 9783039217281 9783039217298 Year: Pages: 284 DOI: 10.3390/books978-3-03921-729-8 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-12-09 16:10:12
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Stochastic processes have wide relevance in mathematics both for theoretical aspects and for their numerous real-world applications in various domains. They represent a very active research field which is attracting the growing interest of scientists from a range of disciplines.This Special Issue aims to present a collection of current contributions concerning various topics related to stochastic processes and their applications. In particular, the focus here is on applications of stochastic processes as models of dynamic phenomena in research areas certain to be of interest, such as economics, statistical physics, queuing theory, biology, theoretical neurobiology, and reliability theory. Various contributions dealing with theoretical issues on stochastic processes are also included.

Keywords

fusion estimation --- sensor networks --- random parameter matrices --- multiplicative noises --- random delays --- realized volatility --- forecast combinations --- structural breaks --- arithmetic progressions --- first Chebyshev function --- products of primes --- regularly varying functions --- slowly varying functions --- mixed Gaussian process --- small deviations --- exact asymptotics --- loan interest rate regulation --- diffusion model --- first passage time (FPT) --- continuous-time Markov chains --- catastrophes --- bounds --- birth-death process --- rate of convergence --- double-ended queues --- time-non-homogeneous birth-death processes --- catastrophes --- repairs --- transient probabilities --- periodic intensity functions --- time-non-homogeneous jump-diffusion processes --- transition densities --- first-passage-time --- lognormal diffusion process --- exogenous factors --- growth curves --- maximum likelihood estimation --- asymptotic distribution --- first-passage time --- inverse first-passage problem --- diffusion --- mixture of Gaussian laws --- rate of convergence --- total variation distance --- Wasserstein distance --- weighted quadratic variation --- non-Markovian queue --- general bulk service --- multiple vacation --- breakdown and repair --- stand-by server --- re-service --- discrete time stochastic model --- first-passage time --- time between inspections --- host-parasite interaction --- nematode infection --- nonhomogeneous Poisson process --- seasonal environment --- Strang–Marchuk splitting approach --- Cohen and Grossberg neural networks --- random impulses --- mean square stability --- fractional differential-difference equations --- fractional queues --- fractional birth-death processes --- busy period --- two-dimensional signature --- multi-state network --- totally positive of order 2 --- stochastic order --- stochastic process --- reliability --- stochastic orders --- scale family of distributions --- proportional hazard rates --- differential entropy

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