The concept of double conditional expectation is introduced. A series of properties for the double conditional expectation are obtained several convergence theorems and Jensen inequality are proved. Finally we discuss...The concept of double conditional expectation is introduced. A series of properties for the double conditional expectation are obtained several convergence theorems and Jensen inequality are proved. Finally we discuss the special cases and application for double conditional expectation. Key words double conditional expectation - covergence theorem - Jensen inequality - branching chain in random environment CLC number O 211.6 Foundation item: Supported by the National Science Foundation of China (10371092) and the Foundation of Wuhan UniversityBiography: HU Di-he (1935-), male, Professor, research direction: stochastic processes and random fractals.展开更多
We apply the newly proposed double absorbing boundary condition（DABC）（Hagstrom et al., 2014） to solve the boundary reflection problem in seismic finite-difference（FD） modeling. In the DABC scheme, the local high...We apply the newly proposed double absorbing boundary condition（DABC）（Hagstrom et al., 2014） to solve the boundary reflection problem in seismic finite-difference（FD） modeling. In the DABC scheme, the local high-order absorbing boundary condition is used on two parallel artificial boundaries, and thus double absorption is achieved. Using the general 2D acoustic wave propagation equations as an example, we use the DABC in seismic FD modeling, and discuss the derivation and implementation steps in detail. Compared with the perfectly matched layer（PML）, the complexity decreases, and the stability and fl exibility improve. A homogeneous model and the SEG salt model are selected for numerical experiments. The results show that absorption using the DABC is considerably improved relative to the Clayton–Engquist boundary condition and nearly the same as that in the PML.展开更多
Let X be a metric space and u a finite Borel measure on X. Let P^- u^q,t and P u^q,t be the packing premeasure and the packing measure on X, respectively, defined by the gauge （uB（x, r））^q（2r）^t, where q, t ∈...Let X be a metric space and u a finite Borel measure on X. Let P^- u^q,t and P u^q,t be the packing premeasure and the packing measure on X, respectively, defined by the gauge （uB（x, r））^q（2r）^t, where q, t ∈ R. For any compact set E of finite packing premeasure the authors prove： （1） if q ≤ 0 then P^- u^q,t（E） =P u^q,t （E）; （2） if q 〉 0 and u is doubling on E then P^- u^q,t （E） and P u^q,t （E） are both zero or neither.展开更多
We discuss the problem of higher-dimensional multifractal spectrum of local entropy for arbitrary invariant measures. By utilizing characteristics of a dynamical system, namely, higher-dimensional entropy capacities a...We discuss the problem of higher-dimensional multifractal spectrum of local entropy for arbitrary invariant measures. By utilizing characteristics of a dynamical system, namely, higher-dimensional entropy capacities and higher-dimensional correlation entropies, we obtain three upper estimates on the hlgher-dimensional multifractal spectrum of local entropies. We also study the domain of higher-dimensional multifractai spetrum of entropies.展开更多
In this paper, the Almgren＇s frequency function of the following sub-elliptic equation with singular potential on the Heisenberg group：-Cu＋V（z,t）u=Xi（aij（z,t）Xju）＋V（z,t）u=0 is introduced. The monotonicity ...In this paper, the Almgren＇s frequency function of the following sub-elliptic equation with singular potential on the Heisenberg group：-Cu＋V（z,t）u=Xi（aij（z,t）Xju）＋V（z,t）u=0 is introduced. The monotonicity property of the frequency is established and a doubling condition is obtained. Consequently, a quantitative proof of the strong unique continuation property for such equation is given.展开更多
文摘The concept of double conditional expectation is introduced. A series of properties for the double conditional expectation are obtained several convergence theorems and Jensen inequality are proved. Finally we discuss the special cases and application for double conditional expectation. Key words double conditional expectation - covergence theorem - Jensen inequality - branching chain in random environment CLC number O 211.6 Foundation item: Supported by the National Science Foundation of China (10371092) and the Foundation of Wuhan UniversityBiography: HU Di-he (1935-), male, Professor, research direction: stochastic processes and random fractals.
基金supported by the National Nature Science Foundation of China(Grant No.U1262208)the Important National Science & Technology Specific Projects(Grant No.2011ZX05019-008)
文摘We apply the newly proposed double absorbing boundary condition（DABC）（Hagstrom et al., 2014） to solve the boundary reflection problem in seismic finite-difference（FD） modeling. In the DABC scheme, the local high-order absorbing boundary condition is used on two parallel artificial boundaries, and thus double absorption is achieved. Using the general 2D acoustic wave propagation equations as an example, we use the DABC in seismic FD modeling, and discuss the derivation and implementation steps in detail. Compared with the perfectly matched layer（PML）, the complexity decreases, and the stability and fl exibility improve. A homogeneous model and the SEG salt model are selected for numerical experiments. The results show that absorption using the DABC is considerably improved relative to the Clayton–Engquist boundary condition and nearly the same as that in the PML.
基金Supported by Natural Science Foundation of China (10571063)
文摘Let X be a metric space and u a finite Borel measure on X. Let P^- u^q,t and P u^q,t be the packing premeasure and the packing measure on X, respectively, defined by the gauge （uB（x, r））^q（2r）^t, where q, t ∈ R. For any compact set E of finite packing premeasure the authors prove： （1） if q ≤ 0 then P^- u^q,t（E） =P u^q,t （E）; （2） if q 〉 0 and u is doubling on E then P^- u^q,t （E） and P u^q,t （E） are both zero or neither.
基金The NSF (10271057 and 10571086) of ChinaQing-lan Project in Nanjing Universityof Posts and Telecommunications (NY206053)
文摘We discuss the problem of higher-dimensional multifractal spectrum of local entropy for arbitrary invariant measures. By utilizing characteristics of a dynamical system, namely, higher-dimensional entropy capacities and higher-dimensional correlation entropies, we obtain three upper estimates on the hlgher-dimensional multifractal spectrum of local entropies. We also study the domain of higher-dimensional multifractai spetrum of entropies.
基金Project supported by the National Natural Science Foundation of China (Nos. 11071119, 11101132)
文摘In this paper, the Almgren＇s frequency function of the following sub-elliptic equation with singular potential on the Heisenberg group：-Cu＋V（z,t）u=Xi（aij（z,t）Xju）＋V（z,t）u=0 is introduced. The monotonicity property of the frequency is established and a doubling condition is obtained. Consequently, a quantitative proof of the strong unique continuation property for such equation is given.
