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36
Completeness of the LELS Inference Rule in Automated Theorem Proving
"... The Extended Linking Strategy (ELS) is a hyperstyle strategy whose underlying principle is to control and perform (extend) a series of standard resolution on clauses. However it may be treated as a unique inference rule that serially links several resolution steps into one. We define links and clau ..."
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and clause chains, and introduce the ideas of ELS with left merging (LELS). We also presented the soundness and completeness proofs for ground LELS and use a fundamental theorem of logic (Herbrand’s theorem) and facts about the unification algorithm to show that LELS is, in fact, complete for first
NORMALISATION FOR THE FUNDAMENTAL CROSSED COMPLEX OF A SIMPLICIAL SET
, 2007
"... Crossed complexes are shown to have an algebra sufficiently rich to model the geometric inductive definition of simplices, and so to give a purely algebraic proof of the Homotopy Addition Lemma (HAL) for the boundary of a simplex. This leads to the fundamental crossed complex of a simplicial set. Th ..."
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Cited by 4 (3 self)
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. The main result is a normalisation theorem for this fundamental crossed complex, analogous to the usual theorem for simplicial abelian groups, but more complicated to set up and prove, because of the complications of the HAL and of the notion of homotopies for crossed complexes. We start with some
Solving the IndexNumber Problem in a Historical Perspective
, 2009
"... "The fundamental and wellknown theorem for the existence of a price index that is invariant under change in level of living is that each dollar of income be spent in the same way by rich or poor, with all income elasticities exactly unity (the homothetic case). Otherwise, a price change in lux ..."
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"The fundamental and wellknown theorem for the existence of a price index that is invariant under change in level of living is that each dollar of income be spent in the same way by rich or poor, with all income elasticities exactly unity (the homothetic case). Otherwise, a price change
unknown title
"... It is interesting to note that as practical limitations were removed, several fundamental or principal limitations were established. For instance, Carnot showed that there was a fundamental limit to how much energy could be extracted from a heat engine. Later this result was generalized to the sec ..."
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It is interesting to note that as practical limitations were removed, several fundamental or principal limitations were established. For instance, Carnot showed that there was a fundamental limit to how much energy could be extracted from a heat engine. Later this result was generalized
www.elsevier.com/locate/cam Connection coe!cients and zeros of orthogonal polynomials
, 1999
"... We discuss an old theorem of Obrechko1 and some of its applications. Some curious historical facts around this theorem are presented. We make an attempt to look at some known results on connection coe!cients, zeros and Wronskians of orthogonal polynomials from the perspective of Obrechko1’s theorem. ..."
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We discuss an old theorem of Obrechko1 and some of its applications. Some curious historical facts around this theorem are presented. We make an attempt to look at some known results on connection coe!cients, zeros and Wronskians of orthogonal polynomials from the perspective of Obrechko1’s theorem
OKLAHOMA'S STATUTORY CONSTITUTION MICHAEL K. A
"... The Oklahoma Constitution retains its original and historic character as a combination of constitutional and statutory provisions. This article traces the Constitution's evolution through the use of the initiative and referendum processes and sets that evolution in the context of the state&apos ..."
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of political forces that prefer an accessible constitution and fragmented governmental authority to the efficiencies that might result from a streamlined constitutional order. From the early Progressives to modern conservatives, Oklahomans have distrusted government and their Constitution reflects that fact
THE ROLE OF APPLIED MATHEMATICS
"... This is a very touching moment for my dear wife and me. The honorous doctorate of the BabeşBolyai University is a very great honour for me and I want to express my sincere gratitude to my dear colleagues, in particular to Professor Micula thank you so much to Professor Rus and to Professor Ţâm ..."
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profession. Mathematics is one of the oldest cultural achievements of mankind, as early as literature, art and music. ”Mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, intelligible only in a social context ” [1]. In fact, mathematics has
Real Analysis in Paraconsistent Logic
"... This paper begins an analysis of the real line using an inconsistencytolerant (paraconsistent) logic. We show that basic field and compactness properties hold, by way of novel proofs that make no use of consistencyreliant inferences; some techniques from constructive analysis are used instead. Whi ..."
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’ of analysis enables a fuller understanding of the fine structure of proofs. The strategy is to reverse engineer classical results (cf. [19, sec.16.1]), eventually deriving a paraconsistent basis for analysis, and this paper is a step in that direction. A fundamental result is the HeineBorel theorem
1SubNyquist Sampling: Bridging Theory and Practice
"... [ A review of past and recent strategies for subNyquist sampling] Signal processing methods have changed substantially over the last several decades. In modern applications, an increasing number of functions is being pushed forward to sophisticated software algorithms, leaving only delicate finely ..."
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tuned tasks for the circuit level. Sampling theory, the gate to the digital world, is the key enabling this revolution, encompassing all aspects related to the conversion of continuoustime signals to discrete streams of numbers. The famous ShannonNyquist theorem has become a landmark: a mathematical
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