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Ricci Flow with Surgery on ThreeManifolds
"... This is a technical paper, which is a continuation of [I]. Here we verify most of the assertions, made in [I, §13]; the exceptions are (1) the statement that a 3manifold which collapses with local lower bound for sectional curvature is a graph manifold this is deferred to a separate paper, as the ..."
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Cited by 446 (2 self)
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, as the proof has nothing to do with the Ricci flow, and (2) the claim about the lower bound for the volumes of the maximal horns and the smoothness of the solution from some time on, which turned out to be unjustified, and, on the other hand, irrelevant for the other conclusions. The Ricci flow with surgery
A path independent integral and the approximate analysis of strain concentration by notches and cracks
, 1967
"... An integral is exhibited which has the same value for all paths surrounding a class of notches in twodimensional deformation fields of linear or nonlinear elastic materials. The integral may be evaluated almost by inspection for a few notch configurations. Also, for materials of the elasticplasti ..."
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Cited by 421 (11 self)
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. On the other hand, the integral may be expressed in terms of the concentrated deformation field in the vicinity of the notch tip. This implies that some information on strain concentrations is obtainable without recorse to detailed nonlinear analyses. Such an approach is exploited here. Applications are made
The Mondex Challenge: Machine Checked Proofs for an Electronic Purse
, 2006
"... The Mondex case study about the specification and refinement of an electronic purse as defined in [SCJ00] has recently been proposed as a challenge for formal systemsupported verification. This paper reports on the successful verification of the major part of the case study using the KIV specificat ..."
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Cited by 24 (9 self)
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specification and verification system. We demonstrate that even though the handmade proofs were elaborated to an enormous level of detail we still could find small errors in the underlying data refinement theory as well as the formal proofs of the case study. We also provide an alternative formalisation
Formal Proof of a Program: Find
, 2000
"... In 1971, C. A. R. Hoare gave the proof of correctness and termination of a rather complex algorithm, in a paper entitled Proof of a program: Find. It is a handmade proof, where the program is given together with its formal specification and where each step is fully justified by a mathematical reaso ..."
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Cited by 3 (2 self)
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In 1971, C. A. R. Hoare gave the proof of correctness and termination of a rather complex algorithm, in a paper entitled Proof of a program: Find. It is a handmade proof, where the program is given together with its formal specification and where each step is fully justified by a mathematical
Logic Programming in a Fragment of Intuitionistic Linear Logic
, 1994
"... When logic programming is based on the proof theory of intuitionistic logic, it is natural to allow implications in goals and in the bodies of clauses. Attempting to prove a goal of the form D ⊃ G from the context (set of formulas) Γ leads to an attempt to prove the goal G in the extended context Γ ..."
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Cited by 340 (44 self)
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∪{D}. Thus during the bottomup search for a cutfree proof contexts, represented as the lefthand side of intuitionistic sequents, grow as stacks. While such an intuitionistic notion of context provides for elegant specifications of many computations, contexts can be made more expressive and flexible
Specification and Verification of the ATMR Protocol using UNITY
 IN INTERNATIONAL WORKSHOP ON FORMAL METHODS FOR PARALLEL PROGRAMMING
, 1997
"... We propose a complete description and validation of the ATMR protocol within the UNITY formalism. An operational description using the UNITY programming notation is given as well as a specification of the main correctness properties in the UNITY temporal logic. This formal description helps to under ..."
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Cited by 4 (0 self)
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to understand precisely the mechanisms this protocol involves. In particular, we have noted the use of a incorrect detection algorithm to generate reset slots. Nevertheless, a handmade proof is given that shows the model satisfies the specification in spite of this spurious detection. Moreover, through
Proofs
"... “mcs ” — 2013/1/10 — 0:28 — page i — #1 Mathematics for Computer Science ..."
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Cited by 2 (0 self)
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“mcs ” — 2013/1/10 — 0:28 — page i — #1 Mathematics for Computer Science
PROOFS
"... Can we do something to improve the teaching of firstyear calculus? Michel Helfgott, SUNY Oswego After teaching mathematics for many years I have come to the conclusion that the above question has an affirmative answer. As is often mentioned, teaching is an art rather than a science, and I do not pr ..."
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without proof. 2. Convey the idea that sometimes there is more than one way to solve a problem. 3. Discuss significant applications in the classroom, not relegating them to the end as optional materials. 4. Place the subject in a historical perspective whenever possible.
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