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Point-plane incidences and some applications in positive characteristic
[article]
2018
arXiv
pre-print
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These are the problem of the minimum number of distinct nonzero values of a non-degenerate bilinear form on a point set in d=2, the analogue of the Erdős distinct distance problem in d=2,3 and additive ...
The point-plane incidence theorem states that the number of incidences between n points and m≥ n planes in the projective three-space over a field F, is O(m√(n)+ m k), where k is the maximum number of ...
This accounts for the role of the parameter k in Theorem 1 versus Theorem 2. ...
arXiv:1806.03534v1
fatcat:2lkpl6rdw5e47iq2okkvumu4my
Some Fundamental Theorems in Mathematics
[article]
2022
arXiv
pre-print
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An expository hitchhikers guide to some theorems in mathematics. ...
Liouville: every prime p=4k+1 is the sum of two squares. ...
Let π(x) be the prime-counting function which gives the number of primes smaller or equal to x. ...
arXiv:1807.08416v4
fatcat:lw7lbsxyznfrnaozilxapihmdy
The discrete yet ubiquitous theorems of Carathéodory, Helly, Sperner, Tucker, and Tverberg
[article]
2018
arXiv
pre-print
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We discuss five discrete results: the lemmas of Sperner and Tucker from combinatorial topology and the theorems of Carath\'eodory, Helly, and Tverberg from combinatorial geometry. ...
We explore their connections and emphasize their broad impact in application areas such as game theory, graph theory, mathematical optimization, computational geometry, etc. ...
He is grateful to the labex BEZOUT and the CERMICS research center atÉcole National des Ponts et Chaussées for the support received, and the enjoyable and welcoming environment in which the topics in this ...
arXiv:1706.05975v3
fatcat:rtwl6jd77zbtbklqco4wxym5ly
The discrete yet ubiquitous theorems of Carathéodory, Helly, Sperner, Tucker, and Tverberg
2019
Bulletin of the American Mathematical Society
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of dimension i in |K|; for example, the rank of H 0 (K, Z 2 ) counts the number of connected components of |K|. ...
In particular, if K is a single vertex, then all its homology groups are trivial except the 0th one. ...
Acknowledgments The authors are truly grateful to the two anonymous referees who provided a very large and very detailed set of comments, insights, and corrections. ...
doi:10.1090/bull/1653
fatcat:vby5jazp2zd6lc2ev3qqgxm2cq
Relevance of accurate Monte Carlo modeling in nuclear medical imaging
1999
Medical Physics (Lancaster)
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Current and future trends in the field are also discussed. ...
Factors which have contributed to the wider use include improved models of radiation transport processes, the practicality of application with the development of acceleration schemes and the improved speed ...
Von Neumann, Ulam and Fermi applied the method towards neutron diffusion problems in the Manhattan Project at Los Alamos during World War II. ...
doi:10.1118/1.598559
pmid:10227362
fatcat:ea6pbismqbccpn2qdnbatigg2e
Cycle Expansions for Intermittent Maps
2003
Progress of Theoretical Physics Supplement
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In a generic dynamical system chaos and regular motion coexist side by side, in different parts of the phase space. ...
Marginality leads to long-time dynamical correlations, in contrast to the exponentially fast decorrelations of purely chaotic dynamics. ...
A. was partially supported by the PRIN-2000 project "Chaos and localization in classical and quantum systems", by INFM PA "Weak chaos: theory and applications", and by EU contract QTRANS Network ("Quantum ...
doi:10.1143/ptps.150.1
fatcat:zjevxui46ncannqivc34eifchy
Quantization of classical maps with tunable Ruelle-Pollicott resonances
2003
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
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We investigate the correspondence between the decay of correlation in classical system, governed by Ruelle--Pollicott resonances, and the properties of the corresponding quantum system. ...
As an application of such tailormade resonances we reveal the role of Ruelle--Pollicott resonances for the localization properties of quantum energy eigenstates. ...
In both cases ⌬ϭ1/8. side, where ͐d⍀ Q kk Ј ϭ0. ͑The prime will be dropped in the following.͒ For nϭ0 the integral on the left-hand side of Eq. ͑27͒ gives the dimension N. ...
doi:10.1103/physreve.68.056201
pmid:14682865
fatcat:lyegfz7lyjbodefmy4j7uj7trm
Brain–Computer Interfaces for Human Augmentation
2019
Brain Sciences
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The field of brain–computer interfaces (BCIs) has grown rapidly in the last few decades, allowing the development of ever faster and more reliable assistive technologies for converting brain activity into ...
are listed in reference [71]. ...
Acknowledgments: This research was supported by the European Fund for Regional Development (EFRD-or EFRE in German) under Grants GE-1-1-047 and IT-1-2-001. ...
doi:10.3390/brainsci9020022
pmid:30682766
pmcid:PMC6406539
fatcat:4kjekrytqrcd7h4egrqlxsdbpq
Computational universes
2005
Chaos, Solitons & Fractals
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Suspicions that the world might be some sort of a machine or algorithm existing "in the mind" of some symbolic number cruncher have lingered from antiquity. ...
Modern developments in physics and computer science have lent support to the thesis, but empirical evidence is needed before it can begin to replace our contemporary world view. ...
Tee from the University of Auckland has provided reference [4] , and Peter Mittelstaedt referred to the beautiful quotation of Kant. ...
doi:10.1016/j.chaos.2004.11.055
fatcat:cwzhp45zujeefavfv3kebucafq
Frontiers of chaotic advection
2017
Reviews of Modern Physics
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This work reviews the present position of and surveys future perspectives in the physics of chaotic advection: the field that emerged three decades ago at the intersection of fluid mechanics and nonlinear ...
We thank the Lorentz Center for its financial support and the Lorentz Center staff for making the workshop a great success. ...
We acknowledge the three who are no longer with us, Hassan Aref, John Blake, and Slava (Viatcheslav) Meleshko, with whom we planned and worked on the paper. ...
doi:10.1103/revmodphys.89.025007
fatcat:r4qm33uup5bobhnijyofvnq4ue
An Introduction to Cellular Automata
[chapter]
1999
Cellular Automata
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The c.a will have output 1, that is be in accepting state, at each prime time t. ...
Fischer uses a similar but less efficient method : he crosses out the multiples of every integer, (thereby loosing his time in vain for integers not prime), starting from their square, which is the first ...
An illustration for the square diagonal grouper is given in Figures 14 and 15. ...
doi:10.1007/978-94-015-9153-9_1
fatcat:vi4d6bwvrnhkdl6vg7oaey6fea
Analyzing the environment structure of higher-order languages using frame strings
2007
Theoretical Computer Science
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Reasoning about program behaviour in programming languages based on the λ calculus requires reasoning in a unified way about control, data and environment structure. ...
We state the critical theorems needed to establish correctness of the entire technology suite, with their proofs. ...
We developed the core of our frame-string model while visiting the University of Aarhus in the Fall of 2004. ...
doi:10.1016/j.tcs.2006.12.031
fatcat:ariqc6ukl5eprlfidptb3uhddi
Floating Bodies of Equilibrium in 2D, the Tire Track Problem and Electrons in a Parabolic Magnetic Field
[article]
2007
arXiv
pre-print
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Starting point is the differential equation given by the author in archive physics/0205059 and Studies in Appl. Math. 111 (2003) 167-183. ...
The curves are also trajectories of charges in a perpendicular magnetic field. ...
Introduction In this paper we consider a class of curves, which are solution to three problems: (i) the two-dimensional version of the floating body problem asked by Stanislaw Ulam in the Scottish Book ...
arXiv:physics/0701241v3
fatcat:tm5zbhyuc5f7rfg3eyt6kc6aly
Editors: Nils Anders Danielsson, Bengt Nordström
Aloïs Brunel; licensed under Creative Commons License BY-ND 18th International Workshop on Types for Proofs and Programs (TYPES 2011)
unpublished
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Borsuk-Ulam theorem. ...
The winding number around a point z ∈ C of a closed curve γ basically counts how many time γ turns counterclockwise around z. ...
proof of the prime number theorem. ...
fatcat:qwyvcyvuobei3fuir2wqll22pq
Heuristic Algorithm for Efficient Data Retrieval Scheduling in the Multichannel Wireless Broadcast Environments
2015
International Journal of Computer Applications Technology and Research
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In this paper, we investigate the multi-item data retrieval scheduling in the push-based multichannel broadcast environments. ...
When there is no replicated item in a broadcast cycle, we show that an optimal retrieval schedule can be obtained in polynomial time. 337 investigate the approximability of MCDR in push-based broadcast ...
along the corresponding ring segment. ...
doi:10.7753/ijcatr0405.1001
fatcat:7xpnnpep5vd7hcrmcjr4fvpnq4
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