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1
Content available remote

Two-parameter multipliers on hardy spaces

100%
Simon P.
Colloquium Mathematicum
|
1998
|
tom 77
|
nr 1
9-31
2
Content available remote

Hardy type inequalities for two-parameter Vilenkin-Fourier coefficients

63%
Simon P., Weisz F.
Studia Mathematica
|
1997
|
tom 125
|
nr 3
231-246
EN
Our main result is a Hardy type inequality with respect to the two-parameter Vilenkin system (*) $(∑_{k=1}^∞ ∑_{j=1}^∞ |f̂(k,j)|^{p}(kj)^{p-2})^{1/p} ≤ C_p∥f∥_{H^p_{**}}$ (1/2 < p≤2) where f belongs to the Hardy space $H_{**}^p (G_m × G_s)$ defined by means of a maximal function. This inequality is extended to p > 2 if the Vilenkin-Fourier coefficients of f form a monotone sequence. We show that the converse of (*) also holds for all p > 0 under the monotonicity assumption.
3
Content available remote

Monte Carlo simulation and analytic approximation of epidemic processes on large networks

63%
Nagy N., Simon P.
Open Mathematics
|
2013
|
tom 11
|
nr 4
800-815
EN
Low dimensional ODE approximations that capture the main characteristics of SIS-type epidemic propagation along a cycle graph are derived. Three different methods are shown that can accurately predict the expected number of infected nodes in the graph. The first method is based on the derivation of a master equation for the number of infected nodes. This uses the average number of SI edges for a given number of the infected nodes. The second approach is based on the observation that the epidemic spreads along the cycle graph as a front. We introduce a continuous time Markov chain describing the evolution of the front. The third method we apply is the subsystem approximation using the edges as subsystems. Finally, we compare the steady state value of the number of infected nodes obtained in different ways.
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