Acta Mathematica Vietnamica最新文献

A right R-module M is said to be dual-ADS if for every decomposition (M=Aoplus B) then A and B are mutually projective. The class of ADS*-modules contains the class of dual-ADS modules. In this article, we study several properties of these modules. It is shown that a module M is dual-ADS if and only if for any direct summand S and (T^prime le M) with (T^prime +S) a direct summand of M, then (T^prime ) contains a direct complement of S in (T^prime +S). A generalization of dual-ADS modules is considered, namely, ADS(^#)-modules. It is shown that a module M is ADS(^#) if and only if for any direct summand S of M, and any weak supplement (T^prime ) of S in (T^prime +S) such that (T^prime +S) is a direct summand of M, then (T^prime ) contains a direct complement of S in (T^prime +S).

In this paper, we are concerned with the characterization of the blow-up and global solutions for free boundary parabolic equation with competing nonlocal nonlinearity and absorption

where (q, alpha ge 1), (p=0) or (pge 1) and (gamma > 0) are given constants. This study is motivated from the works [Abdelhedi and Zaag: J. Differential Equations 272, 1–45, (2021); Souplet: SIAM J. Math. Anal. 29, 1301–1334, (1998); Zhou and Lin: J. Funct. Anal. 262, 3409–3429, (2012)] arisen from the investigation of many physical and biological phenomena such as population dynamics, combustion theory, phase separation in binary mixtures, theory of nuclear reactor dynamics... We first prove the local existence, uniqueness and stability of solution thanks to the “extension trick" introduced in [Du et al.: Math. Ann. 386(3-4), 2061–2106, (2023); Wang and Du: Discrete Contin. Dyn. Syst. Ser. B 26(4), 2201–2238, (2021)]. Second, by improving the comparison principle used in [Souplet: SIAM J. Math. Anal. 29, 1301–1334, (1998); Zhou and Lin: J. Funct. Anal. 262, 3409–3429, (2012)], we find a sharp criterion characterizing the blow-up and global solutions of (1) in term of power coefficients and initial data. We further show that there exists a threshold for the initial data that determines whether blow-up, global fast, or global slow solutions occur and find an upper bound for the existence time of blow-up solutions in two different cases (alpha >1) and (alpha =1). Our proofs are mainly based on the comparison principle by improving several techniques in previous works, combined new idea to handle differential inequalities and unified local existence theory for nonlocal semilinear parabolic equations.

In this article, we study monomial ideals associated with a simple graph, namely edge ideals of weighted oriented graphs. Let D be a weighted oriented graph. Assuming that all the vertices of D have weights greater than 1, we completely characterize weighted oriented graphs D for which I(D) is integrally closed, and show that this is equivalent to I(D) being normal. We also give an equivalent condition for (overline{I(D)}=I(D)) when the underlying simple graph of D is a complete graph. Finally, we give a necessary and sufficient condition when the edge ideal of a uniform whiskered graph is integrally closed.

By introducing the notion of distributive constant for a family of closed subschemes, we establish a general form of the second main theorem for algebraic non-degenerate meromorphic mappings from a generalized p-Parabolic manifold into a projective variety with arbitrary families of closed subschemes. As its consequence, we give a second main theorem for such meromorphic mappings intersecting arbitrary hypersurfaces with an explicitly truncation level for the counting functions.

This paper focuses on the study of a generalized semi-infinite programming, where the objective and the constraint functions are all real polynomials. We present a method for finding its global minimizers and global minimum using a hierarchy of semidefinite programming relaxations and prove the convergence result for the method. Numerical experiments are presented to show the efficiency of the proposed algorithm.

A differential 1-form (alpha ) on a manifold of odd dimension (2n+1), which satisfies the contact condition (alpha wedge (dalpha )^n ne 0) almost everywhere, but which vanishes at a point O, i.e., (alpha (O) = 0), is called a singular contact form at O. The aim of this paper is to study local normal forms (formal, analytic and smooth) of such singular contact forms. Our study leads naturally to the study of normal forms of singular primitive 1-forms of a symplectic form (omega ) in dimension 2n, i.e., differential 1-forms (gamma ) which vanish at a point and such that (dgamma = omega ), and their corresponding conformal vector fields. Our results are an extension and improvement of previous results obtained by other authors, in particular Lychagin (1975), Webster (Amer. J. Math. 109, 807–832 (1987)) and Zhitomirskii (1986, 1992). Besides the classical normalization techniques, such as the step-by step normalization methods based on the cohomological equations and the Moser path method, we also use the toric approach to the normalization problem for dynamical systems (Jiang et al. 2019; Zung, Ann. Math. 161, 141–156 2005; Zung 2016; Zung, Arch. Rational Mech. Anal. 229, 789–833 (2018)).

Let (varOmega ) be an open bounded subset of ({mathbb {R}}), (s in (frac{1}{2},1)) and (epsilon > 0). We investigate the problem

where (varphi , psi in C^infty ({mathbb {R}})) and (u_0 in {mathcal {M}}^+(varOmega )) satisfy certain assumptions. Here ((-Delta )^s) denotes the spectral Dirichlet Laplacian and ({mathcal {M}}^+(varOmega )) is the set of positive Radon measures on (varOmega ). We show that ((P_epsilon )) has a unique weak solution.

In this paper, we investigate the existence, uniqueness and stability of asymptotically almost periodic and almost automorphic solutions to the non-autonomous Oseen-Navier-Stokes Equations (ONSE) in an unbounded domain (varOmega subset mathbb {R}^{3}) exterior to a rigid body D, i.e., (varOmega =mathbb {R}^{3}backslash D), with the data belonging to L(^{p})-spaces and with the asymptotically almost periodic or almost automorphic external forces, respectively. Our method is based on the L(^{p}-L^{q}) smoothness of the evolution family corresponding to linearized equations in combination with interpolation functors and fixed-point arguments.

In this paper, we provide an upper bound for the conjunction probability of smooth stationary two-dimensional Gaussian fields. The key ingredient is the record method, which is generalized from the problem of estimating the distribution of the maximum. The given upper bound is also a good asymptotic formula.