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  • Bài báo/Newspaper

  • On the equilibrium prices of a regular locally Lipschitz exchange economy

    • Authors: Truong Xuan Duc (2024)

  • We extend classical results by Debreu and Dierker about equilibrium prices of a regular economy with continuously differentiable demand functions/excess demand function to a regular exchange economy with these functions being locally Lipschitz. Our concept of a regular economy is based on Clarke’s concept of regular value and we show that such a regular economy has a finite, odd number of equilibrium prices, the set of economies with infinite number of equilibrium prices has Lebesgue measure zero and there exist locally Lipschitz selections of equilibrium prices around a regular economy.
  • Bài báo/Newspaper

  • Uniqueness of meromorphic mappings partially shared hypersurfaces

    • Authors: Nguyen Van Thin (2024)

  • The purpose of this paper is to study uniqueness problem of meromorphic mapping from Cm into the complex space Pn(C) sharing partial fixed and moving hypersurfaces. Using the second main theorems due to S. D. Quang and D. P. An [12, 13], we obtain some uniqueness results. Our results are improved some before results in this trend. In our best knowledge, there are not any uniqueness results of meromorphic mapping partially shared hypersurfaces up to now.
  • Bài báo/Newspaper

  • A proximal point algorithm for solving a class of implicit equilibrium models

    • Authors: Dung Muu Le (2024)

  • We apply the proximal point algorithm to solve a class of implicit price equilibrium models including the Walras supply-demand and competitive equilibrium ones, where both supply and demand are given implicitly as the solution-sets of mathematical programs depending on the price. Such models are formulated as complementarity or variational inequality forms. We employ a monotonicity property of the cost operator to develop proximal point based algorithms to approximate an equilibrium point of the model. Convergence of the algorithm is proved and some computational results with many randomly generated data are reported to show that the proposed algorithms work well for this class of equilibrium models.
  • Bài báo/Newspaper

  • Uniqueness of L-functions sharing finite sets with meromorphic functions having Deficient Poles

    • Authors: Hoai An Vu (2024)

  • n this paper we investigate the uniqueness of L-functions sharing finite sets with meromorphic functions having deficient poles. Asa consequence, we have exhibited a extended version of a recent result of A. Banerjee and A. Kundu [1]. The results obtained in this paper improve and extend a recent result due to Khoai-An-Phuong [10] and a some result in [18].
  • Bài báo/Newspaper

  • Upper bound of multiplicity in Cohen-Macaulay rings of prime characteristic

    • Authors: Huong Duong (2024)

  • Let (R,m) be a local ring of prime characteristic p and of dimension d with the embedding dimension v, type s and the Frobenius test exponent for parameter ideals Fte(R). We will give an upper bound for the multiplicity of Cohen-Macaulay rings in prime characteristic in terms of Fte(R), d, v and s. Our result extends the main results for Gorenstein rings due to Huneke and Watanabe
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  • Degeneracy theorems for holomorphic mappings from a complex disc with finite growth index

    • Authors: Nguyen Thi Nhung (2024)

  • Abstract. In this paper, we prove degeneracy theorems for holomorphic mappings from a complex disc Δ(R) ⊂ C with finite growth index into Pn(C) sharing hyperplanes in general position. We further consider the case that intersecting points of the mappings and the hyperplanes with multiplicities more than a certain number do not need to be counted. These results generalize the previous degeneracy theorems for meromorphic mappings from Cm into Pn(C).
  • Bài báo/Newspaper

  • Secure direct message exchange based on simultaneous usage of two different degrees of freedom

    • Authors: Nguyen Ba An (2024)

  • In the era of information explosion supplied with a veryhigh level of technology as of today, the loss or leakage of information is one of the most severe problems. Security in communication has thus become more important than ever. In this paper, two protocols for quantum secure direct exchange of messages are proposed using hyperentangled photon pairs as resource for exchanging informative bits and single photons in hyperstates as resource for detecting eavesdroppers. In both the protocols the photons need to be transmitted only once from one to the other communicating party. However, the ways to transmit photons are different in the two proposed protocols. The first protocol employs block transmission of photons. Although its security is unconditional, it compulsorily requires qu...
  • Bài báo/Newspaper

  • New properties on the growth of ultrametric entire functions and applications

    • Authors: Alain Escassut (2024)

  • Let IK be a complete ultrametric algebraically closed field and let f be an entire function in IK whose order of growth is finite. We show that the type of growth is finite if and only if so is the cotype. We give bounds for the cotype of growth and also for the lower cotype of growth. We show that the type of growth of f is equal to its lower type if and only if its cotype is equal to its lower cotype and when these are realised, then the cotype is the product of the type by the order of growth and the order of growth (if > 0), is then equal to the lower order of growth. If an entire function h has an order of growth strictly inferior to the lower order of an entire function f, then h is a small function with respect to f. A similar comparison is made with the type of growth. Conve...