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PageRank as a Weak Tournament Solution
2007We observe that ranking systems--a theoretical framework for web page ranking and collaborative filtering introduced by Altman and Tennenholtz--and tournament solutions--a well-studied area of social choice theory--are strongly related. This relationship permits a mutual transfer of axioms and solution concepts.
Felix Brandt 0001, Felix A. Fischer
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Journal of Chemical Education, 1986
The cubic equations that arise when accurately calculating the concentrations of the various species of a monobasic acid or base in solution have recently attracted some attention in this journal.
Ian J. McNaught, Gavin D. Peckham
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The cubic equations that arise when accurately calculating the concentrations of the various species of a monobasic acid or base in solution have recently attracted some attention in this journal.
Ian J. McNaught, Gavin D. Peckham
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2015
So far, we have focussed on solutions of SDEs where we are simply given a filtration, and with it the Brownian motion W and the random measure μ. We then construct the solution to our equation ( 17.2). In essence, we have used no properties of the filtration except the fact that W and μ are adapted.
Samuel N. Cohen, Robert J. Elliott
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So far, we have focussed on solutions of SDEs where we are simply given a filtration, and with it the Brownian motion W and the random measure μ. We then construct the solution to our equation ( 17.2). In essence, we have used no properties of the filtration except the fact that W and μ are adapted.
Samuel N. Cohen, Robert J. Elliott
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1993
Let u be a weak solution of equations of the type of (1.1) of Chap. II in Ω T We will establish local and global bounds for u in. Ω T . Global bounds depend on the data prescribed on the parabolic boundary of Ω T . Local bounds are given in terms of local integral norms of u. Consider the cubes K ρ ⊂ K 2ρ .
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Let u be a weak solution of equations of the type of (1.1) of Chap. II in Ω T We will establish local and global bounds for u in. Ω T . Global bounds depend on the data prescribed on the parabolic boundary of Ω T . Local bounds are given in terms of local integral norms of u. Consider the cubes K ρ ⊂ K 2ρ .
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1997
Let 0 < T < +∞, A and B be c.n.o. in H. In the previous chapter, we have answered the following question: what must be A and B for each bounded weak solution of equation (1) on [0,T) to have a limit in H as t → T?
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Let 0 < T < +∞, A and B be c.n.o. in H. In the previous chapter, we have answered the following question: what must be A and B for each bounded weak solution of equation (1) on [0,T) to have a limit in H as t → T?
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1998
It is shown that under appropriate ellipticity assumptions, weak solutions of partial differential equations (PDEs) are smooth. This applies in particular to the Laplace equation for harmonic functions, thereby justifying Dirichlet’s principle introduced in the previous paragraph.
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It is shown that under appropriate ellipticity assumptions, weak solutions of partial differential equations (PDEs) are smooth. This applies in particular to the Laplace equation for harmonic functions, thereby justifying Dirichlet’s principle introduced in the previous paragraph.
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On \(\gamma\)-weak solutions of elliptic equations
1995Summary: We build on the `alternative' approach to the Dirichlet problem in weighted Sobolev spaces to formulate sufficient conditions for interior regularity of \(\gamma\)-weak solutions of the Dirichlet problem for second order elliptic PDEs with Lipschitz coefficients. Next, we prove a maximum principle (for \(\gamma\)-weak subsolutions).
DRAGOMIR, Sorin, BARLETTA, Elisabetta
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