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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 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 On the real-analytic infinitesimal cr automorphism of hypersurfaces of infinite type Authors: Ninh Van Thu (2024) We consider a real smooth hypersurface M ⊂ C2, which is of D’Angelo infinite type at p 2 M. The purpose of this paper is to show that the real vector space of tangential holomorphic vector field germs at p vanishing at p is either trivial or of real dimension 1

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 ...

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 employ...

Bài báo/Newspaper Weighted sharing of sets in wider sense under the ambit of higher indexed polynomials Authors: Abhijit Banerjee (2024) In this article, with respect to the recently introduced definition of weighted sharing of sets in the wider sense [8], we have comprehensivelyextended and improved some well known results in the literature. As the definition involves the manipulations of two polynomials, we perceive that the characteristizations of the underlying polynomials become utmost important. This realization urges us to introduce the definition of the index of polynomial. Noting that, in case of weighted sharing of sets the polynomials so far chosen are of lower index, after defining and streamlining the index concept, we explore the influence of using polynomials with higher indices in the context of weight...