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In this paper we shall consider the assymptotic growth of |Pn(z)| 1/kn where Pn(z) is a sequence of entire functions of genus zero. Our results extend a result of J. Muller and A. Yavrian. We shall prove that if the sequence of entire functions has a geometric growth at each point in a set E being non-thin at ∞ then it has a geometric growth in C / also.(More)
We consider the problem of finding the initial temperature u(x, 0), from a countable set of measured values {u(x j , 1)}. The problem is severely ill-posed and a regularization is in order. Using the Hermite polynomials and coefficients of truncated Lagrange polynomials, we shall change the problem into an analytic interpolation problem and give explicitly(More)
Word segmentation is one of the most important tasks in NLP. This task, within Vietnamese language and its own features, faces some challenges, especially in words boundary determination. To tackle the task of Vietnamese word segmentation, in this paper, we propose the WS4VN system that uses a new approach based on Maximum matching algorithm combining with(More)
  • Tran Ngoc Lien, Duc Dang, Trong, Alain Pham, Ngoc Dinh
  • 2008
We consider the problem of finding a function defined on (0, ∞) from a countable set of values of its Laplace transform. The problem is severely ill-posed. We shall use the expansion of the function in a series of Laguerre polynomials to convert the problem in an analytic interpolation problem. Then, using the coefficients of Lagrange polynomials we shall(More)
We consider the problem of determining a pair of functions (u, f) satisfying the heat equation u t − ∆u = ϕ(t)f (x, y), where (x, y) ∈ Ω = (0, 1) × (0, 1) and the function ϕ is given. The problem is ill-posed. Under a slight condition on ϕ, we show that the solution is determined uniquely from some boundary data and the initial temperature. Using the(More)
We consider the problem of determining a pair of functions (u, f) satisfying the two-dimensional backward heat equation u t − ∆u = φ(t)f (x, y), t ∈ (0, T), (x, y) ∈ (0, 1) × (0, 1), u(x, y, T) = g(x, y) with a homogeneous Cauchy boundary condition, where φ and g are given approximately. The problem is severely ill-posed. Using an interpolation method and(More)
In this paper, we regularize the nonlinear inverse time heat problem in the unbounded region by Fourier method. Some new convergence rates are obtained. Meanwhile, some quite sharp error estimates between the approximate solution and exact solution are provided. Especially, the optimal convergence of the approximate solution at t = 0 is also proved.
Let Ω represent a two−dimensional isotropic elastic body. We consider the problem of determining the body force F whose form ϕ(t)(f 1 (x), f 2 (x)) with ϕ be given inexactly. The problem is nonlinear and ill-posed. Using the Fourier transform, the methods of Tikhonov's regularization and truncated integration, we construct a regu-larized solution from the(More)