Search results for "arithmetic"
showing 10 items of 271 documents
Refutation systems for a system of nonsense-logic
2013
In the paper rejection systems for a system of nonsense-logic are investigated. The first rejection system consists of four rejected axioms and only one rejection rule the rule of rejection by detachment. The second one consists of one rejected axiom and two rejection rules: the rule of rejection by detachment and the rule of rejection by substitution. The aim of the paper is to present also a proof of Ł-decidability for the considered systems.
Numerical integration of subtraction terms
2016
Numerical approaches to higher-order calculations often employ subtraction terms, both for the real emission and the virtual corrections. These subtraction terms have to be added back. In this paper we show that at NLO the real subtraction terms, the virtual subtraction terms, the integral representations of the field renormalisation constants and -- in the case of initial-state partons -- the integral representation for the collinear counterterm can be grouped together to give finite integrals, which can be evaluated numerically. This is useful for an extension towards NNLO.
On the Rigorous Calculation of All Ohmic Losses in Rectangular Waveguide Multi-Port Junctions
2005
In this paper, all ohmic losses effects present in rectangular waveguide multi-port junctions are rigorous and efficiently computed. For this purpose, a new formulation based on the theory of cavities, which provides generalized admittance matrix representations for such junctions, is proposed. To validate this theory, we have successfully compared our results with numerical data of a lossy E-plane T-junction and of a hollow waveguide, as well as with experimental measurements of a real H-plane T-junction.
The H-graph with equal masses in terms of multiple polylogarithms
2021
The initial phase of the inspiral process of a binary system producing gravitational waves can be described by perturbation theory. At the third post-Minkowskian order a two-loop double box graph, known as H-graph contributes. We consider the case where the two objects making up the binary system have equal masses. We express all master integrals related to the equal-mass H-graph up to weight four in terms of multiple polylogarithms. We provide a numerical program which evaluates all master integrals up to weight four in the physical regions with arbitrary precision.
Theory of Computation, Fuzziness and a physics of the immaterial
2013
In this paper we advance three clear-cut proposals as a contribution to the discussion on the role of notions of Computation and Fuzziness as a bridge between Hard and Soft Sciences. We suggest that an important difference between the two great fami- lies of science lies in their subject or research having a grounding in nature or not, and that Theory of Computation is a glaring exception to this classifi- cation, being a textbook hard science but dealing with the immaterial. We further advance that such unicity is strongly connected with Church-Turing thesis, and discuss about the role of Computation and Fuzziness as pillars of immaterial sciences
Temporal evolution of neoclassical tearing modes in the frequently interrupted regime
2010
A phenomenological method for description of temporal evolution of neoclassical tearing modes in the frequently interrupted regime (FIR) is proposed. The method makes it possible to predict the beginning and the end of the FIR regime as well as the frequency of the FIR drops. A few experimental parameters which are used in the model are commonly measured quantities. Several specific ASDEX Upgrade (http://en.wikipedia.org/wiki/ASDEX_Upgrade) FIR discharges with different heating and different FIR behavior are analyzed in detail.
Why does placing the question before an arithmetic word problem improve performance. A situation model account.
2007
The aim of this paper is to investigate the controversial issue of the nature of the representation constructed by individuals to solve arithmetic word problems. More precisely, we consider the relevance of two different theories: the situation or mental model theory (Johnson-Laird, 1983; Reusser, 1989) and the schema theory (Kintsch & Greeno, 1985; Riley, Greeno, & Heller, 1983). Fourth-graders who differed in their mathematical skills were presented with problems that varied in difficulty and with the question either before or after the text. We obtained the classic effect of the position of the question, with better performance when the question was presented prior to the text. …
Recent results on syntactic groups of prefix codes
2012
International audience; We give a simplified presentation of groups in transformation monoids. We use this presentation to describe two recent results on syntactic groups of prefix codes. The first one uses Sturmian words to build finite bifix codes with a given permutation group as syntactic group. The second one describes a class of prefix codes such that all their syntactic groups are cyclic.
Suffix Automata and Standard Sturmian Words
2007
Blumer et al. showed (cf. [3,2]) that the suffix automaton of a word w must have at least |w|+1 states and at most 2|w|-1 states. In this paper we characterize the language L of all binary words w whose minimal suffix automaton S(w) has exactly |w| + 1 states; they are precisely all prefixes of standard Sturmian words. In particular, we give an explicit construction of suffix automaton of words that are palindromic prefixes of standard words. Moreover, we establish a necessary and sufficient condition on S(w) which ensures that if w ∈ L and a ∈ {0, 1} then wa ∈ L. By using such a condition, we show how to construct the automaton S(wa) from S(w). More generally, we provide a simple construct…
Achievement emotions and arithmetic fluency : Development and parallel processes during the early school years
2023
This study investigated the developmental trajectories and interrelationships of mathematics-related achieve-ment emotions and arithmetic fluency from first to third grade, and the effects of these on third grade mathe-matics performance. Participants were 232 Norwegian students. Students' emotions and arithmetic fluency were measured four times and mathematics performance once. Applying latent growth curve modeling, developmental patterns of decreasing enjoyment and increasing boredom were observed over time. The mean level of enjoyment remained fairly high, and of both boredom and anxiety quite low. Individual differences were observed in both the initial levels and development of all emo…