Search results for " proof"
showing 10 items of 118 documents
Amount of nonconstructivity in deterministic finite automata
2010
AbstractWhen D. Hilbert used nonconstructive methods in his famous paper on invariants (1888), P. Gordan tried to prevent the publication of this paper considering these methods as non-mathematical. L.E.J. Brouwer in the early twentieth century initiated intuitionist movement in mathematics. His slogan was “nonconstructive arguments have no value for mathematics”. However, P. Erdös got many exciting results in discrete mathematics by nonconstructive methods. It is widely believed that these results either cannot be proved by constructive methods or the proofs would have been prohibitively complicated. The author (Freivalds, 2008) [10] showed that nonconstructive methods in coding theory are…
Local Normal Forms for First-Order Logic with Applications to Games and Automata
1999
Building on work of Gaifman [Gai82] it is shown that every first-order formula is logically equivalent to a formula of the form ∃ x_1,...,x_l, \forall y, φ where φ is r-local around y, i.e. quantification in φ is restricted to elements of the universe of distance at most r from y. \par From this and related normal forms, variants of the Ehrenfeucht game for first-order and existential monadic second-order logic are developed that restrict the possible strategies for the spoiler, one of the two players. This makes proofs of the existence of a winning strategy for the duplicator, the other player, easier and can thus simplify inexpressibility proofs. \par As another application, automata mode…
Hegel e le prove dell'esistenza di Dio
2012
The essay examines Hegel’s treatment of the proofs of the existence of God, particular attention being paid to the peculiar physiognomy that they take on in the lectures on philosophy of religion. Reread as descriptions of the spiritual pathway of man’s elevation to God, the metaphysical tests, far from dissolving into empty exercise of the intellect, remain, in Hegel’s eyes, a question that is still topical, and all the more topical faced with an epoch now little inclined to favour the metaphysical ambitions of reason and especially the pretensions of a theology founded upon demonstrative bases.
Serrin-Type Overdetermined Problems: an Alternative Proof
2008
We prove the symmetry of solutions to overdetermined problems for a class of fully nonlinear equations, namely the Hessian equations. In the case of the Poisson equation, our proof is alternative to the proofs proposed by Serrin (moving planes) and by Weinberger. Moreover, our proof makes no direct use of the maximum principle while it sheds light on a relation between the Serrin problem and the isoperimetric inequality.
Mathematical properties of nested residues and their application to multi-loop scattering amplitudes
2021
Journal of high energy physics 02(2), 112 (2021). doi:10.1007/JHEP02(2021)112
Rebuttal to “Comment on “Evidence of electrical activity on Titan drawn from the Schumann resonances sent by Huygens probe” by J.A. Morente, J.A. Por…
2009
Abstract Hamelin et al. criticize some conclusions of our paper [Morente, J.A., Porti, J.A., Salinas, A., Navarro, E.A., 2008. Icarus 195, 802–811]. This rebuttal is our response to their criticism. In our view, their comments are contradictory and not based on scientific argument. Our paper presents a comprehensible methodology for extracting weak resonances from the late-time response of systems with high losses and our conclusions are derived from and supported by this methodology, which was first checked using an analytical function and later with the data from a numerical simulation of Titan’s atmosphere. Conversely, the Comment of Hamelin et al. does not contain any mathematical proof…
On some inequalities for the identric, logarithmic and related means
2015
We offer new proofs, refinements as well as new results related to classical means of two variables, including the identric and logarithmic means.
An Ehrenfeucht-Fraïssé Approach to Collapse Results for First-Order Queries over Embedded Databases
2001
We present a new proof technique for collapse results for first-order queries on databases which are embedded in N or R>o. Our proofs are by means of an explicitly constructed winning strategy for Duplicator in an Ehrenfeucht-FraissE game, and can deal with certain infinite databases where previous, highly involved methods fail. Our main result is that first-order logic has the natural-generic collapse over {N,≤ ,+} for arbitrary (i.e., possibly infinite) databases. Furthermore, a first application of this result shows the natural-generic collapse of first-order logic over {R>o,≤,+} for a certain kind of databases over R>o which consist of a possibly infinite number of regions.
Bicyclo[6.1.0]nonine
1988
MNDO-Rechnungen zeigen, das fur die drei konstitutionsisomeren cis-Bicyclo[6.1.0]nonine (1–3) jeweils zwei energiearme, zueinander diastereomere Konformere a und b existieren. Zur experimentellen Uberprufung werden die mit der Selenadiazol-Methode oder durch Dehydrobromierung hergestellten, hoch gespannten Bicyclen mit Hilfe von 1H- und 13C-NMR-Messungen auf die Population der Konformeren und auf deren wechselseitige Umwandlung durch Inversion der Achtringe untersucht. Bicyclo[6.1.0]nonine MNDO calculations reveal that two diastereomeric conformations a and b of low energy exist for each of the three isomeric cis-bicyclo[6.1.0]nonynes (1–3). For the experimental proof, the highly strained b…
The Duality of Entropy/Extropy, and Completion of the Kullback Information Complex
2018
The refinement axiom for entropy has been provocative in providing foundations of information theory, recognised as thoughtworthy in the writings of both Shannon and Jaynes. A resolution to their concerns has been provided recently by the discovery that the entropy measure of a probability distribution has a dual measure, a complementary companion designated as &ldquo