The aim of the present paper is to state an asymptotic property Ρ of Shannon’s sampling theorem type, based on normalized cardinal sines, and keeping constant the sampling frequency of a not necessarilly band...The aim of the present paper is to state an asymptotic property Ρ of Shannon’s sampling theorem type, based on normalized cardinal sines, and keeping constant the sampling frequency of a not necessarilly band- limited signal. It generalizes in the limit the results stated by Marvasti et al. [7] and Agud et al. [1]. We show that Ρ is fulfilled for any constant signal working for every given sampling frequency. Moreover, we conjecture that Gaussian maps of the form e-Λt2 ,Λ∈R+, hold Ρ. We support this conjecture by proving the equality given by for the three first coefficients of the power series representation of e-Λt2 .展开更多
In computer networks, toughness is an important parameter which is used to measure the vulnerability of the network. Zhou et al. obtains a toughness condition for a graph to be fractional(k, m)-deleted and presents an...In computer networks, toughness is an important parameter which is used to measure the vulnerability of the network. Zhou et al. obtains a toughness condition for a graph to be fractional(k, m)-deleted and presents an example to show the sharpness of the toughness bound. In this paper, we remark that the previous example does not work and inspired by this fact, we present a new toughness condition for fractional(k, m)-deleted graphs improving the existing one. Finally, we state an open problem.展开更多
In Gao’s previous work, the authors determined several degree conditions of a graph which admits fractional factor in particular settings. It was revealed that these degree conditions are tight if b = f(x) = g(x) = a...In Gao’s previous work, the authors determined several degree conditions of a graph which admits fractional factor in particular settings. It was revealed that these degree conditions are tight if b = f(x) = g(x) = a for all vertices x in G. In this paper, we continue to discuss these degree conditions for admitting fractional factor in the setting that several vertices and edges are removed and there is a difference Δ between g(x) and f(x) for every vertex x in G. These obtained new degree conditions reformulate Gao’s previous conclusions, and show how Δ acts in the results. Furthermore,counterexamples are structured to reveal the sharpness of degree conditions in the setting f(x) =g(x) + Δ.展开更多
基金partially supported by MCI(Ministerio de Ciencia e Innovacion)and FEDER(Fondo Europeo Desarrollo Regional),grant number MTM2008--03679/MTMFundacion Seneca de la Region de Murcia,grant number 08667/PI/08JCCM(Junta de Comunidades de Castilla-La Mancha),grant number PEII09-0220-0222.
文摘The aim of the present paper is to state an asymptotic property Ρ of Shannon’s sampling theorem type, based on normalized cardinal sines, and keeping constant the sampling frequency of a not necessarilly band- limited signal. It generalizes in the limit the results stated by Marvasti et al. [7] and Agud et al. [1]. We show that Ρ is fulfilled for any constant signal working for every given sampling frequency. Moreover, we conjecture that Gaussian maps of the form e-Λt2 ,Λ∈R+, hold Ρ. We support this conjecture by proving the equality given by for the three first coefficients of the power series representation of e-Λt2 .
基金partially supported by MINECO(Grant No.MTM2014–51891–P and Fundación Séneca de la Región de Murcia 19219/PI/14)National Science Foundation of China(Grant No.11401519)
文摘In computer networks, toughness is an important parameter which is used to measure the vulnerability of the network. Zhou et al. obtains a toughness condition for a graph to be fractional(k, m)-deleted and presents an example to show the sharpness of the toughness bound. In this paper, we remark that the previous example does not work and inspired by this fact, we present a new toughness condition for fractional(k, m)-deleted graphs improving the existing one. Finally, we state an open problem.
基金Supported by NSFC(Grant Nos.11761083,11771402 and 11671053)Fundacion Seneca(Spain)(Grant No.20783/PI/18)Ministry of Science,Innovation and Universities(Spain)(Grant No.PGC2018-097198-B-100)。
文摘In Gao’s previous work, the authors determined several degree conditions of a graph which admits fractional factor in particular settings. It was revealed that these degree conditions are tight if b = f(x) = g(x) = a for all vertices x in G. In this paper, we continue to discuss these degree conditions for admitting fractional factor in the setting that several vertices and edges are removed and there is a difference Δ between g(x) and f(x) for every vertex x in G. These obtained new degree conditions reformulate Gao’s previous conclusions, and show how Δ acts in the results. Furthermore,counterexamples are structured to reveal the sharpness of degree conditions in the setting f(x) =g(x) + Δ.
