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The Mathematical Precision of the Bible
, 2014
"... The Bible is the word of God; an account of the creation of the universe, of the relationship God has established with man and of His redemptive plan through a pattern man, Jesus Christ. As a discipline, mathematics plays an interpretive role of explaining, revealing the hidden beauty of numbers and ..."
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The Bible is the word of God; an account of the creation of the universe, of the relationship God has established with man and of His redemptive plan through a pattern man, Jesus Christ. As a discipline, mathematics plays an interpretive role of explaining, revealing the hidden beauty of numbers
Mathematical Control Theory: Deterministic Finite Dimensional Systems
 of Texts in Applied Mathematics
, 1990
"... The title of this book gives a very good description of its contents and style, although I might have added “Introduction to ” at the beginning. The style is mathematical: precise, clear statements (i.e., theorems) are asserted, then carefully proved. The book covers many of the key topics in contro ..."
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Cited by 485 (121 self)
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The title of this book gives a very good description of its contents and style, although I might have added “Introduction to ” at the beginning. The style is mathematical: precise, clear statements (i.e., theorems) are asserted, then carefully proved. The book covers many of the key topics
Homological Algebra of Mirror Symmetry
 in Proceedings of the International Congress of Mathematicians
, 1994
"... Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual Ca ..."
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Cited by 523 (3 self)
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Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual
An Introduction to the Kalman Filter
 UNIVERSITY OF NORTH CAROLINA AT CHAPEL HILL
, 1995
"... In 1960, R.E. Kalman published his famous paper describing a recursive solution to the discretedata linear filtering problem. Since that time, due in large part to advances in digital computing, the Kalman filter has been the subject of extensive research and application, particularly in the area o ..."
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Cited by 1146 (13 self)
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of autonomous or assisted navigation.
The Kalman filter is a set of mathematical equations that provides an efficient computational (recursive) means to estimate the state of a process, in a way that minimizes the mean of the squared error. The filter is very powerful in several aspects: it supports
Quantum complexity theory
 in Proc. 25th Annual ACM Symposium on Theory of Computing, ACM
, 1993
"... Abstract. In this paper we study quantum computation from a complexity theoretic viewpoint. Our first result is the existence of an efficient universal quantum Turing machine in Deutsch’s model of a quantum Turing machine (QTM) [Proc. Roy. Soc. London Ser. A, 400 (1985), pp. 97–117]. This constructi ..."
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Cited by 574 (5 self)
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be implemented and introduce some new, purely quantum mechanical primitives, such as changing the computational basis and carrying out an arbitrary unitary transformation of polynomially bounded dimension. We also consider the precision to which the transition amplitudes of a quantum Turing machine need
A computational approach to edge detection
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1986
"... This paper describes a computational approach to edge detection. The success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points. These goals must be precise enough to delimit the desired behavior of the detector while making minimal assumpti ..."
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Cited by 4675 (0 self)
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This paper describes a computational approach to edge detection. The success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points. These goals must be precise enough to delimit the desired behavior of the detector while making minimal
The DLV System for Knowledge Representation and Reasoning
 ACM Transactions on Computational Logic
, 2002
"... Disjunctive Logic Programming (DLP) is an advanced formalism for knowledge representation and reasoning, which is very expressive in a precise mathematical sense: it allows to express every property of finite structures that is decidable in the complexity class ΣP 2 (NPNP). Thus, under widely believ ..."
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Cited by 456 (102 self)
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Disjunctive Logic Programming (DLP) is an advanced formalism for knowledge representation and reasoning, which is very expressive in a precise mathematical sense: it allows to express every property of finite structures that is decidable in the complexity class ΣP 2 (NPNP). Thus, under widely
Through a New Looking Glass*: Mathematically Precise Visualization
"... Alice gazes through her looking glass at a perplexing world that confuses her [3], as vividly depicted in the recently released 3D movie Alice in Wonderland. Scientists, peering through their new looking glass of scientific visualization, derive illuminating insights from otherwise impenetrable peta ..."
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Cited by 1 (1 self)
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results. Issues of complexity and precision abound. In contrast to Alice’s world, scientific visualization should produce imagery that illuminates computational experiments. Much as 3D stereovision enriches the movieviewing experience, mathematically precise visualization will enrich scientific discovery
The synchronous approach to reactive and realtime systems
 Proceedings of the IEEE
, 1991
"... This special issue is devoted to the synchronous approach to reactive and realtime programming. This introductory paper presents and discusses the application fields and the principles of synchronous programming. The major concern of the synchronous approach is to base synchronous programming langu ..."
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Cited by 436 (15 self)
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languages on mathematical models. This makes it possible to handle compilation, logical correctness proofs, and verifications of realtime programs in a formal way, leading to a clean and precise methodology for design and programming. 1. INTRODUCTION: REALTIME AND REACTIVE SYSTEMS It is commonly accepted
A Mathematically Precise TwoLevel Formal Hardware Verification Methodology
, 1992
"... Theoremproving and symbolic trajectory evaluation are both described as methods for the formal verification of hardware. They are both used to achieve a common goalcorrectly designed hardwareand both are intended to be an alternative to conventional methods based on nonexhaustive simulati ..."
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Cited by 4 (1 self)
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high degree of automation and accurate models of circuit behavior and timing. From interactive theoremproving we gain access to powerful mathematical tools such as induction and abstraction. The interface between the HOL and Voss is, however, more than just an ad hoc translation of verification
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