Trends and Challenges in Cognitive Modeling
An Interdisciplinary Approach Towards Thinking, Memory, and Decision-Making Simulations
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This introductory chapter presents some background and context for some of the techniques and approaches to cognitive modeling and simulations. It includes the summarizing ideas drawn for the contributed chapt...
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An Interdisciplinary Approach Towards Thinking, Memory, and Decision-Making Simulations
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New mathematical tools often lead to new engineering applications. Although it is often difficult to foresee what innovations might result from such tools, we’ll begin by looking at potential applications resu...
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The chapter describes our approach, i.e., the multivariate power substitution and its variations, illustrated by many interesting examples involving commonly used special functions along with applications of the ...
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In this chapter, we continue to present results that arise from approaches introduced in the last two chapters. The integral identities appearing here involve, in particular, the Lerch transcendent, the logari...
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The integral identities in this chapter involve a very important function in mathematical sciences, viz. the Riemann zeta function ζ(s) and the related Hurwitz zeta function ζ(s, α). See also references Apostol (...
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This first chapter introduces the Generalized Method of Exhaustion (GME) to represent a definite integral as an exact convergent series; it is not an approximation method such as the trapezoidal rule or Simpson’s...
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In this chapter we present additional variants of the multivariate power substitution with more applications, triple and quadruple integrals, and the Owen T-function (Brychkov and Savischenko, Integr Transf Sp...
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The integral identities in this chapter comprise the exponential integral function Ei ( x ...
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What is mathematics? What do mathematicians do? Do they discover or do they invent mathematics? Artificial Intelligence (AI) is permeating all realms of human endeavors, prompting the question as to whether mathe...
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Mathematical modeling and analysis of system behavior are at the core of the development of high-tech system. Modern engineering sciences, to include naval engineering, call for more sophisticated mathematical...
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Hermann Weyl is quoted with saying in Philosophie der Mathematik und Naturwissenschaft 1927, p. 36: As a matter of fact, it is by no means impossible to build up a consistent “non-Archimedean” theory of magnitude...
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This volume features chapters that present contemporary research focus and results in the theory of Evolution Equations and its applications in the physical and natural sciences, in a unique combination of mat...
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A series of multidimensional integral identities is developed based on a novel substitution approach that involves at least two nested integrals, each with integration limits from 0 to ∞. The identities are expre...
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This chapter presents the two most relevant approaches to mathematical modeling: the long standing and by now classic Archimedean model, based on the Archimedean Principle, named by Otto Stolz after the ancien...
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