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STRUCTURAL THEOREMS FOR SYMBOLIC SUMMATION

by Carsten Schneider
"... Starting with Karr’s structural theorem for summation —the discrete version of Liouville’s structural theorem for integration — we work out crucial properties of the underlying difference fields. This leads to new and constructive structural theorems for symbolic summation. E.g., these results can b ..."
Abstract - Cited by 9 (7 self) - Add to MetaCart
Starting with Karr’s structural theorem for summation —the discrete version of Liouville’s structural theorem for integration — we work out crucial properties of the underlying difference fields. This leads to new and constructive structural theorems for symbolic summation. E.g., these results can

OBB-Tree: A hierarchical structure for rapid interference detection

by S. Gottschalk, M. C. Lint, D. Manocha - PROC. ACM SIGGRAPH, 171–180 , 1996
"... We present a data structure and an algorithm for efficient and exact interference detection amongst complex models undergoing rigid motion. The algorithm is applicable to all general polygonal and curved models. It pre-computes a hierarchical representation of models using tight-fitting oriented bo ..."
Abstract - Cited by 845 (53 self) - Add to MetaCart
bounding box trees. At runtime, the algorithm traverses the tree and tests for overlaps between oriented bounding boxes based on a new separating axis theorem, which takes less than 200 operations in practice. It has been implemented and we compare its performance with other hierarchical data structures

New structure theorem for subresultants

by Henri Lombardi, Marie-Françoise Roy, Mohab Safey El Din , 2001
"... We give a new structure theorem for subresultants precising their gap structure and derive from it a new algorithm for computing them. If d is a bound on the degrees and τ a bound on the bitsize of the minors extracted from Sylvester matrix, our algorithm has O(d²) arithmetic operations and size of ..."
Abstract - Cited by 10 (0 self) - Add to MetaCart
We give a new structure theorem for subresultants precising their gap structure and derive from it a new algorithm for computing them. If d is a bound on the degrees and τ a bound on the bitsize of the minors extracted from Sylvester matrix, our algorithm has O(d²) arithmetic operations and size

Structure theorems for AP rings

by David W. Lewis, Stefan A. G, De Wannemacker , 2007
"... In “New Proofs of the structure theorems for Witt Rings”, the first author shows how the standard ring-theoretic results on the Witt ring can be deduced in a quick and elementary way from the fact that the Witt ring of a field is integral and from the specific nature of the explicit annihilating pol ..."
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In “New Proofs of the structure theorems for Witt Rings”, the first author shows how the standard ring-theoretic results on the Witt ring can be deduced in a quick and elementary way from the fact that the Witt ring of a field is integral and from the specific nature of the explicit annihilating

A theory of type polymorphism in programming

by Robin Milner - Journal of Computer and System Sciences , 1978
"... The aim of this work is largely a practical one. A widely employed style of programming, particularly in structure-processing languages which impose no discipline of types, entails defining procedures which work well on objects of a wide variety. We present a formal type discipline for such polymorp ..."
Abstract - Cited by 1076 (1 self) - Add to MetaCart
The aim of this work is largely a practical one. A widely employed style of programming, particularly in structure-processing languages which impose no discipline of types, entails defining procedures which work well on objects of a wide variety. We present a formal type discipline

Singularity Detection And Processing With Wavelets

by Stephane Mallat, Wen Liang Hwang - IEEE Transactions on Information Theory , 1992
"... Most of a signal information is often found in irregular structures and transient phenomena. We review the mathematical characterization of singularities with Lipschitz exponents. The main theorems that estimate local Lipschitz exponents of functions, from the evolution across scales of their wavele ..."
Abstract - Cited by 595 (13 self) - Add to MetaCart
Most of a signal information is often found in irregular structures and transient phenomena. We review the mathematical characterization of singularities with Lipschitz exponents. The main theorems that estimate local Lipschitz exponents of functions, from the evolution across scales

A New Method for Solving Hard Satisfiability Problems

by Bart Selman, Hector Levesque, David Mitchell - AAAI , 1992
"... We introduce a greedy local search procedure called GSAT for solving propositional satisfiability problems. Our experiments show that this procedure can be used to solve hard, randomly generated problems that are an order of magnitude larger than those that can be handled by more traditional approac ..."
Abstract - Cited by 730 (21 self) - Add to MetaCart
approaches such as the Davis-Putnam procedure or resolution. We also show that GSAT can solve structured satisfiability problems quickly. In particular, we solve encodings of graph coloring problems, N-queens, and Boolean induction. General application strategies and limitations of the approach are also

AgentSpeak(L): BDI Agents speak out in a logical computable language

by Anand S. Rao , 1996
"... Belief-Desire-Intention (BDI) agents have been investigated by many researchers from both a theoretical specification perspective and a practical design perspective. However, there still remains a large gap between theory and practice. The main reason for this has been the complexity of theorem-prov ..."
Abstract - Cited by 514 (2 self) - Add to MetaCart
Belief-Desire-Intention (BDI) agents have been investigated by many researchers from both a theoretical specification perspective and a practical design perspective. However, there still remains a large gap between theory and practice. The main reason for this has been the complexity of theorem

Fast probabilistic algorithms for verification of polynomial identities

by J. T. Schwartz - J. ACM , 1980
"... ABSTRACT The starthng success of the Rabm-Strassen-Solovay pnmahty algorithm, together with the intriguing foundattonal posstbthty that axtoms of randomness may constttute a useful fundamental source of mathemaucal truth independent of the standard axmmaUc structure of mathemaUcs, suggests a wgorous ..."
Abstract - Cited by 520 (1 self) - Add to MetaCart
ABSTRACT The starthng success of the Rabm-Strassen-Solovay pnmahty algorithm, together with the intriguing foundattonal posstbthty that axtoms of randomness may constttute a useful fundamental source of mathemaucal truth independent of the standard axmmaUc structure of mathemaUcs, suggests a

A STRUCTURE THEOREM FOR COMPLETE INTERSECTIONS

by Eun Jeong Choi, Oh-jin Kang, Hyoung J. Ko , 2009
"... Buchsbaum and Eisenbud proved a structure theorem for Gorenstein ideals of grade 3. In this paper we derive a class of the perfect ideals from a class of the complete matrices. From this we give a structure theorem for complete intersections of grade g > 3. ..."
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Buchsbaum and Eisenbud proved a structure theorem for Gorenstein ideals of grade 3. In this paper we derive a class of the perfect ideals from a class of the complete matrices. From this we give a structure theorem for complete intersections of grade g > 3.
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