共查询到20条相似文献,搜索用时 281 毫秒
1.
Nader Masmoudi 《偏微分方程通讯》2015,40(8):1408-1440
In a recent paper [19], the authors obtained a sharp version of the Trudinger-Moser inequality in the whole space ?2, giving necessary and sufficient conditions for the boundedness and the compactness of general nonlinear functionals in W 1, 2(?2). We complete this study showing that an analogue of the result in [19] holds in arbitrary dimensions N ≥2. We also provide an application to the study of the existence of ground state solutions for quasilinear elliptic equations in ? N . 相似文献
2.
Jiaqun Wei 《代数通讯》2013,41(7):2456-2465
Let R be an exchange ring. In this article, we show that the following conditions are equivalent: (1) R has stable range not more than n; (2) whenever x ∈ R n is regular, there exists some unimodular regular w ∈ n R such that x = xwx; (3) whenever x ∈ R n is regular, there exist some idempotent e ∈ R and some unimodular regular w ∈ R n such that x = ew; (4) whenever x ∈ R n is regular, there exist some idempotent e ∈ M n (R) and some unimodular regular w ∈ R n such that x = we; (5) whenever a( n R) + bR = dR with a ∈ R n and b,d ∈ R, there exist some z ∈ R n and some unimodular regular w ∈ R n such that a + bz = dw; (6) whenever x = xyx with x ∈ R n and y ∈ n R, there exist some u ∈ R n and v ∈ n R such that vxyu = yx and uv = 1. These, by replacing unimodularity with unimodular regularity, generalize the corresponding results of Canfell (1995, Theorem 2.9), Chen (Chen 2000, Theorem 4.2 and Proposition 4.6, Chen 2001, Theorem 10), and Wu and Xu (1997, Theorem 9), etc. 相似文献
3.
Huanyin Chen 《代数通讯》2013,41(4):1352-1362
An element of a ring is called strongly J-clean provided that it can be written as the sum of an idempotent and an element in its Jacobson radical that commute. We investigate, in this article, a single strongly J-clean 2 × 2 matrix over a noncommutative local ring. The criteria on strong J-cleanness of 2 × 2 matrices in terms of a quadratic equation are given. These extend the corresponding results in [8, Theorems 2.7 and 3.2], [9, Theorem 2.6], and [11, Theorem 7]. 相似文献
4.
The article considers linear elliptic equations with regular Borel measures as inhomogeneity. Such equations frequently appear in state-constrained optimal control problems. By a counter example of Serrin [18], it is known that, in the presence of non-smooth data, a standard weak formulation does not ensure uniqueness for such equations. Therefore several notions of solution have been developed that guarantee uniqueness. In this note, we compare different definitions of solutions, namely the ones of Stampacchia [19] and Boccardo-Galouët [4] and the two notions of solutions of [2, 7], and show that they are equivalent. As side results, we reformulate the solution in the sense of [19], and prove the existence of solutions in the sense of [2, 4, 7] in case of mixed boundary conditions. 相似文献
5.
Iustin Coandă 《代数通讯》2013,41(12):4668-4672
Using the method of Coand? and Trautmann [4], we give a simple proof of a theorem due, in the smooth case, to Tyurin [9]: if a vector bundle E on a c-codimensional locally Cohen–Macaulay closed subscheme X of ? n extends to a vector bundle F on a similar closed subscheme Y of ? N , for every N > n, then E is the restriction to X of a direct sum of line bundles on ? n . Using the same method, we also provide a proof of the Babylonian tower theorem for locally complete intersection subschemes of projective spaces. 相似文献
6.
We show that the symplectic groups PSp6(q) are Hurwitz for all q = p m ≥ 5, with p an odd prime. The result cannot be improved since, for q even and q = 3, it is known that PSp6(q) is not Hurwitz. In particular, n = 6 turns out to be the smallest degree for which a family of classical simple groups of degree n, over 𝔽 p m , contains Hurwitz groups for infinitely many values of m. This fact, for a given (possibly large) p, also follows from [9] and [10]. 相似文献
7.
Sylvain Ervedoza 《偏微分方程通讯》2013,38(11):1996-2019
The goal of this article is to analyze control properties of parabolic equations with a singular potential ? μ/|x|2, where μ is a real number. When μ ≤ (N ? 2)2/4, it was proved in [19] that the equation can be controlled to zero with a distributed control which surrounds the singularity. In the present work, using Carleman estimates, we will prove that this assumption is not necessary, and that we can control the equation from any open subset as for the heat equation. Then we will study the case μ > (N ? 2)2/4, and prove that the situation changes completely: indeed, we will consider a sequence of regularized potentials μ/(|x|2 + ?2), and prove that we cannot stabilize the corresponding systems uniformly with respect to ? > 0, due to the presence of explosive modes which concentrate around the singularity. 相似文献
8.
Lingling Fan 《代数通讯》2013,41(3):799-806
Let R be an associative ring with identity. An element a ∈ R is called strongly clean if a = e + u with e 2 = e ∈ R, u a unit of R, and eu = ue. A ring R is called strongly clean if every element of R is strongly clean. Strongly clean rings were introduced by Nicholson [7]. It is unknown yet when a matrix ring over a strongly clean ring is strongly clean. Several articles discussed this topic when R is local or strongly π-regular. In this note, necessary conditions for the matrix ring 𝕄 n (R) (n > 1) over an arbitrary ring R to be strongly clean are given, and the strongly clean property of 𝕄2(RC 2) over the group ring RC 2 with R local is obtained. 相似文献
9.
Mamoru Furuya 《代数通讯》2013,41(8):3130-3146
Let A be an analytic algebra over a field k of characteristic p > 0. In this article, for an analytic k-algebra we introduce the concept of analytic pn-basis which generalizes the pn-basis defined in [1], and the concept of an pn-admissible field for an algebraic function field, we give regularity criteria and absolute regularity criteria for an analytic algebra A/k in terms of the higher differential algebra and analytic pn-basis. The results are partial extension of our previous results for affine algebras to the case of analytic algebras (cf. [1, 3]), and these are partial generalization of results of Orbanz in the analytic case (cf. [9]). 相似文献
10.
Marcelo Flores 《代数通讯》2013,41(8):3372-3381
This paper deals with the variety of commutative algebras satisfying the identity β{(yx 2)x ? ((yx)x)x} + γ{yx 3 ? ((yx)x)x} = 0, where β, γ are scalars. These algebras appeared as one of the four families of degree four identities in Carini, Hentzel, and Piacentini-Cattaneo [6]. We give a characterization of representations and irreducible modules on these algebras. Our results require that the characteristic of the ground field is different from 2, 3. 相似文献
11.
Alexander N. Grishkov 《代数通讯》2013,41(6):2242-2253
We use groups with triality to construct a series of nonassociative Moufang loops. Certain members of this series contain an abelian normal subloop with the corresponding quotient being a cyclic group. In particular, we give a new series of examples of finite abelian-by-cyclic Moufang loops. The previously known [10] loops of this type of odd order 3q 3, with prime q ≡ 1 (mod 3), are particular cases of our series. Some of the examples are shown to be embeddable into a Cayley algebra. 相似文献
12.
This article is a sequel of [4], where we defined supervaluations on a commutative semiring R and studied a dominance relation ? ≥ ψ between supervaluations ? and ψ on R, aiming at an enrichment of the algebraic tool box for use in tropical geometry. A supervaluation ?: R → U is a multiplicative map from R to a supertropical semiring U, cf. [4], [7], [8], [5], [9], with further properties, which mean that ? is a sort of refinement, or covering, of an m-valuation (= monoid valuation) v: R → M. In the most important case, that R is a ring, m-valuations constitute a mild generalization of valuations in the sense of Bourbaki [1], while ? ≥ ψ means that ψ: R → V is a sort of coarsening of the supervaluation ?. If ?(R) generates the semiring U, then ? ≥ ψ iff there exists a “transmission” α: U → V with ψ = α ○ ?. Transmissions are multiplicative maps with further properties, cf. [4, Section 5]. Every semiring homomorphism α: U → V is a transmission, but there are others which lack additivity, and this causes a major difficulty. In the main body of the article we study surjective transmissions via equivalence relations on supertropical semirings. We put special emphasis on homomorphic equivalence relations. Even those are often much more complicated than congruences by ideals in usual commutative algebra. 相似文献
13.
Jean-Yves Chemin 《偏微分方程通讯》2015,40(5):878-896
By applying Wiegner's method in [16], we first prove the large time decay estimate for the global solutions of a 2.5 dimensional Navier-Stokes system, which is a sort of singular perturbed 2-D Navier-Stokes system in three space dimension. As an application of this decay estimate, we give a simplified proof for the global wellposedness result in [6] for 3-D Navier-Stokes system with one slow variable. Let us also mention that compared with the assumptions for the initial data in [6], here the assumptions in Theorem 1.3 are weaker. 相似文献
14.
M. Chacron 《代数通讯》2013,41(11):4613-4631
Let D be a division ring with centre Z and with involution (*). Let V be a valuation of D with value group Γ, a linearly ordered additive group (non necessarily commutative) together with a symbol ∞ (positive infinity). We assume that for each nonzero symmetric element s = s* of D, which is algebraic over Z, we have for all nonzero elements x of D, V(xa ? ax) > V(ax). We define the residue characteristic exponent p of V to be the characteristic χ of the associated residue division ring written as D V , if χ ≠ 0, and p = 1, if χ = 0. We show here that if F is a finite dimensional commutative subalgebra of D over Z, which is *-closed (i.e., F* = F), and if (*) is of the first kind (i.e., each central element of D must be symmetric), then [F: Z] = 2 r p m where m is a nonnegative integer and r = 0 or 1 according as the restricted involution in F is trivial or not. The case of an involution (*) of the second kind (i.e., some central element of D is not symmetric) requires (for this author) a stronger type of valuation, namely, V is a *-valuation, that is to say, for all elements x of D, we have V(x*) = V(x), a condition which readily implies Γ must be Abelian. Here, we can show that for F as in the preceding, [F: Z] = p m , where m is again a nonnegative integer. The preceding results generalize a theorem of Gräter and improve in parts recent theorems of this author in [2]. In the special case p = 2 the results provide a modicum of answers to the questions opened informally in [2] (see concluding paragraph in [2] or here Question 3.2.1). More is to be said in the third and final section of this work. 相似文献
15.
16.
Álvaro Muñoz 《代数通讯》2018,46(9):3873-3888
In this paper we give a complete classification of pointed fusion categories over ? of global dimension 8. We first classify the equivalence classes of pointed fusion categories of dimension 8, and then we proceed to determine which of these equivalence classes have equivalent categories of modules following the procedure presented in [9, 11]. The results of this paper permit to recover the classification of twisted quantum doubles of groups of order 8 up to gauge equivalence of braided quasi-Hopf algebras that was previously done in [6] and [5]. 相似文献
17.
It is known that the semigroup Sing n of all singular self-maps of X n = {1,2,…, n} has rank n(n ? 1)/2. The idempotent rank, defined as the smallest number of idempotents generating Sing n , has the same value as the rank. (See Gomes and Howie, 1987.) Idempotents generating Sing n can be seen as special cases (with m = r = 2) of (m, r)-path-cycles, as defined in Ay\i k et al. (2005). The object of this article is to show that, for fixed m and r, the (m, r)-rank of Sing n , defined as the smallest number of (m, r)-path-cycles generating Sing n , is once again n(n ? 1)/2. 相似文献
18.
In this paper, we prove the global existence and uniqueness of solution to d-dimensional (for d = 2, 3) incompressible inhomogeneous Navier-Stokes equations with initial density being bounded from above and below by some positive constants, and with initial velocity u0 ∈ Hs( R 2) for s > 0 in 2-D, or u0 ∈ H1( R 3) satisfying ‖u0‖L2 ‖?u0‖L2 being sufficiently small in 3-D. This in particular improves the most recent well-posedness result in [10], which requires the initial velocity u0 ∈ H2( R d) for the local well-posedness result, and a smallness condition on the fluctuation of the initial density for the global well-posedness result. 相似文献
19.
Morton E. Harris 《代数通讯》2013,41(8):3668-3671
At some point, after publication, the author realized that the proof of [3, Theorem 5.2] is incorrect. This proof incorrectly adapts the proof of [1, Theorem 4.8] since [3, (5.5)] is incorrect. Using the same proof outline, we correct the proof of [3, Theorem 5.2]. 相似文献
20.
In 1967, Shioda [20] determined the ring of invariants of binary octavics and their syzygies using the symbolic method. We discover that the syzygies determined in [20] are incorrect. In this paper, we compute the correct equations among the invariants of the binary octavics and give necessary and sufficient conditions for two genus 3 hyperelliptic curves to be isomorphic over an algebraically closed field k, char k ≠ 2, 3, 5, 7. For the first time, an explicit equation of the hyperelliptic moduli for genus 3 is computed in terms of absolute invariants. 相似文献