Acta Mathematica Vietnamica最新文献

We study the exploration of an Erdös-Rényi random graph by a respondent-driven sampling method, where discovered vertices reveal their neighbors. Some of them receive coupons to reveal in their turn their own neighborhood. This leads to the study of a Markov chain on the random graph that we study. For sparse Erdös-Rényi graphs of large sizes, this process correctly renormalized converges to the solution of a deterministic curve, solution of a system of ODEs absorbed on the abscissa axis. The associated fluctuation process is also studied, providing a functional central limit theorem, with a Gaussian limiting process. Simulations and numerical computation illustrate the study.

In this note, we give some results on maximal subextensions of plurisubharmonic functions on hyperconvex domains in (mathbb C^n) and introduce the notion about cone of maximal subextensions of plurisubharmonic functions. Furthermore, we establish the invariant of this cone through proper holomorphic surjections.

Motivated by the Jacobian problem, this article is concerned with the density of the image set (F( mathbb {Z}^n)) of polynomial maps (Fin mathbb {Z}[X_1,dots ,X_n]^n) with (det DFequiv 1). It is shown that if such a map F is not invertible, its image set (F( mathbb {Z}^n)) must be very thin in the lattice ( mathbb {Z}^n): (1) for almost all lines l in ( mathbb {Z}^n) the numbers (texttt {#}(F^{-1}(l) cap mathbb {Z}^n)) are uniformly bounded; (2) (texttt {#}{ zin F( mathbb {Z}^n): vert z_ivert le B} ll B^{n-1}) as (Brightarrow +infty ), where the implicit constants depend on F.

In this paper we prove the existence of initial data satisfying the constraint equations corresponding to the 1+3 formulation of asymptotically flat spherically symmetric Einstein-Vlasov-Maxwell system, when the charge of the particles is either low or large, the initial distribution function is compactly supported, the shift vector is non-zero and the isotropic metric ansatz is not diagonal. This result extends the work (Rein and Rendall, Commun. Math. Phys. 150(3), 561–583 1992) concerning the existence of solutions to the constraint equations for chargeless particles.

In this work, we propose a new method for solving a bilevel split variational inequality problem (BSVIP) in Hilbert spaces. The proposed method is inspired by the subgradient extragradient method for solving a monotone variational inequality problem. A strong convergence theorem for an algorithm for solving such a BSVIP is proved without knowing any information of the Lipschitz and strongly monotone constants of the mappings. Moreover, we do not require any prior information regarding the norm of the given bounded linear operator. Special cases are considered. Two numerical examples are given to illustrate the performance of our algorithm.

In this paper, we establish a decomposition theorem for strong martingale Hardy space (sH_p^sigma ), which is based on its atomic decomposition theorem. By using of this decomposition theorem, we investigate the real interpolation spaces between (sH_p^sigma ;(0<ple 1)) and (sL_2). Furthermore, with the help of the decomposition theorem and the real interpolation method, a sufficient condition to ensure the boundedness of a sublinear operator defined on strong martingale Hardy-Lorentz spaces is given.

We study the behavior of various properties of commutative Noetherian rings under Segre products, with a special focus on properties in positive prime characteristic defined using the Frobenius endomorphism. Specifically, we construct normal graded rings of finite Frobenius representation type that are not Cohen-Macaulay.

We-24pt study the nonlinear stochastic time-fractional diffusion equation in the spatial domain (mathbb {R}) driven by a locally Lipschitz source satisfying

where (xin mathbb {R},alpha in (0,1],gamma ge 1-alpha ), the source term is defined (F(t,x,u) = f(t,x,u(t,x))) ( + rho (t,x,u(t,x))dot{W}(t,x)) and W is the multiplicative space-time white noise. We investigate the existence, uniqueness of a maximal random field solution. Moreover, we prove the stability of the solution with respect to perturbed fractional orders (alpha , gamma ) and the initial condition.

We propose a globally convergent numerical method to compute solutions to a general class of quasi-linear PDEs with both Neumann and Dirichlet boundary conditions. Combining the quasi-reversibility method and a suitable Carleman weight function, we define a map of which fixed point is the solution to the PDE under consideration. To find this fixed point, we define a recursive sequence with an arbitrary initial term using the same manner as in the proof of the contraction principle. Applying a Carleman estimate, we show that the sequence above converges to the desired solution. On the other hand, we also show that our method delivers reliable solutions even when the given data are noisy. Numerical examples are presented.

Let (X,ω) be an n-dimensional compact Kähler manifold and fix an integer m such that 1 ≤ m ≤ n. Let μ be a finite Borel measure on X satisfying the conditions ({mathscr{H}}_{m}(delta , A,omega )). We study degenerate complex Hessian equations of the form (ω + dd^cφ)^m ∧ ω^n−m = F(φ,.)dμ. Under some natural conditions on F, we prove that if (0<delta <frac {m}{n-m}), then this equation has a unique continuous solution.