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1.
Let 𝒜 be an abelian category. A subcategory 𝒳 of 𝒜 is called coresolving if 𝒳 is closed under extensions and cokernels of monomorphisms and contains all injective objects of 𝒜. In this paper, we introduce and study Gorenstein coresolving categories, which unify the following notions: Gorenstein injective modules [8], Gorenstein FP-injective modules [20], Gorenstein AC-injective modules [3], and so on. Then we define a resolution dimension relative to the Gorenstein coresolving category 𝒢?𝒳(𝒜). We investigate the properties of the homological dimension and unify some important properties possessed by some known homological dimensions. In addition, we study stability of the Gorenstein coresolving category 𝒢?𝒳(𝒜) and apply the obtained properties to special subcategories and in particular to module categories. 相似文献
2.
GRADINGS OF SIMPLE JORDAN ALGEBRAS AND THEIR RELATION TO THE GRADINGS OF SIMPLE ASSOCIATIVE ALGEBRAS
《代数通讯》2013,41(9):4095-4102
In this paper we describe all group gradings of the simple Jordan algebra of a non-degenerate symmetric form on a vector space over a field of characteristic different from 2. If we use the notion of the Clifford algebra, then we are able to recover some of the gradings on matrix algebras obtained in an entirely different way in [BSZ]. 相似文献
3.
《代数通讯》2013,41(6):2481-2487
In 1989 Nichols and Zoeller [NZ] showed that finite dimensional k-Hopf algebras are free over Hopf subalgebras. An analog result for Yetter Drinfeld Hopf algebras was not known. In this paper the existence of such a basis will be proved. Moreover the existence of a basis in a certain categorial sense cannot be expected. 相似文献
4.
《代数通讯》2013,41(9):3773-3779
In [1], the author gave a positive solution to the problem in the survey of Jarden [2] on the closedness of the class of profinite groups that are isomorphic to absolute Galois groups of fields with respect to finite free products. In [3], O. V. Mel'nikov solved this problem for separable profinite groups ([3] was done earlier than [1]). In the same case, a more exact result on the absolute Galois groups of fields of fixed characteristic was obtained there. The proof proposed in 4-5 is simpler than that in [1] and, in addition, provides the results of Mel'nikov. On February, 2000, the author (knowing nothing about 4-5) found one more proof of these results. In the author opinion, this proof is the simplest and the construction used in the proof, as well as its properties (cf. Propositio n 1) can have other applications. 相似文献
5.
A model of intermittency based on superposition of Lévy driven Ornstein–Uhlenbeck processes is studied in [6]. In particular, as shown in Theorem 5.1 in that paper, finite superpositions obey a (sample path) central limit theorem under suitable hypotheses. In this paper we prove large (and moderate) deviation results associated with this central limit theorem. 相似文献
6.
《代数通讯》2013,41(6):2731-2744
In [5] we used functors which are compositions of localization functors to construct sheaves over an arbitrary ring R. These functors share some properties with localization, and questions like when is the composition of localizations a localization functor? arise naturally. In this note we answer this question and some related ones using the key concept of semi-compatibility. 相似文献
7.
《代数通讯》2013,41(8):3327-3339
Concerning the inversion of a polynomial map F: K 2 ? K 2 over an arbitrary field K, it is natural to consider the following questions: (1) Can we find a necessary and sufficient criterion in terms of resultants for F to be invertible with polynomial ((2) resp. rational) inverse such that, this criterion gives an explicit formula to compute the inverse of F in this case? MacKay and Wang [5] gave a partial answer to question (1), by giving an explicit expression of the inverse of F, when F is invertible without constant terms. On the other hand, Adjamagbo and van den Essen [3] have fully answered question (2) and have furnished a necessary and sufficient criterion which relies on the existence of some constants λ1, λ2 in K *. We improve this result by giving an explicit relation between λ1, λ2 and constants of the Theorem of MacKay and Wang [5]. Concerning question (2), Adjamagbo and Boury [2] give a criterion for rational maps which relies on the existence of two polynomials λ1, λ2. We also improve this result, by expliciting the relations between these λ1, λ2 and the coefficients of F. This improvement enables us, first to give an explicit proof of the corresponding Theorem of Abhyankhar [1], and secondly, to give a counter example where these λ1, λ2 are not in K *, contrary to claim of Yu [6]. 相似文献
8.
《代数通讯》2013,41(11):5085-5094
Let R be a commutative Noetherian ring and let M be a finite (that is, finitely generated) R-module. The notion grade of M, grade M, has been introduced by Rees as the least integer t ≥ 0 such that Ext t R (M,R) ≠ 0, see [11]. The Gorenstein dimension of M, G-dim M, has been introduced by Auslander as the largest integer t ≥ 0 such that Ext t R (M, R) ≠ 0, see [3]. In this paper the R-module M is called G-perfect if grade M = G-dim M. It is a generalization of perfect module. We prove several results for the new concept similar to the classical results. 相似文献
9.
《随机分析与应用》2013,31(5):893-901
In this paper we discuss how to select the optimal policy from a set of possible policies for a model of forest succession, which can be characterized by a set of trees and the corresponding average life-span with each possible tree transition. The transition probabilities are estimated by counting the numbers of sapling trees of each species under a canopy tree. [1]. In our setting the transition matrix is defined by using the linguistic terms and as a consequence, the expected longevity of each tree is fuzzy. We use the Dempster–Shafer theory [8] ('76) together with techniques of Norton [7] ('88) and Smetz [9] ('76) to approximate the transition probabilities. 相似文献
10.
Hong Zhang 《随机分析与应用》2017,35(6):1084-1112
Continuing the study of stochastic motion that we started [11], we present in this article the kinematics of such a motion. We begin by defining the quadratic derivative of an S2-process, and show that this derivative of the Brownian motion captures the variance uncertainty. We show, under certain vanishing derivatives and independence conditions, the martingale properties of an S1-process. Starting with an S1-process, we derive the equation of motion, an Itô equation corresponding to a G-diffusion process. 相似文献
11.
12.
《Numerical Functional Analysis & Optimization》2013,34(7-8):941-952
We extend the results of Pollard [7] and give asymptotic estimates for the norm of the Fourier-Jacobi projection operator in the appropriate weighted Lp space. 相似文献
13.
Naoki Taniguchi 《代数通讯》2018,46(3):1165-1178
In this paper, we investigate the question of when the determinantal ring R over a field k is an almost Gorenstein local/graded ring in the sense of [14]. As a consequence of the main result, we see that if R is a non-Gorenstein almost Gorenstein local/graded ring, then the ring R has a minimal multiplicity. 相似文献
14.
Age-specific mortality rates are often disaggregated by different attributes, such as sex, state, and ethnicity. Forecasting age-specific mortality rates at the national and sub-national levels plays an important role in developing social policy. However, independent forecasts at the sub-national levels may not add up to the forecasts at the national level. To address this issue, we consider reconciling forecasts of age-specific mortality rates, extending the methods of Hyndman et al. in 2011 to functional time series, where age is considered as a continuum. The grouped functional time series methods are used to produce point forecasts of mortality rates that are aggregated appropriately across different disaggregation factors. For evaluating forecast uncertainty, we propose a bootstrap method for reconciling interval forecasts. Using the regional age-specific mortality rates in Japan, obtained from the Japanese Mortality Database, we investigate the one- to ten-step-ahead point and interval forecast accuracies between the independent and grouped functional time series forecasting methods. The proposed methods are shown to be useful for reconciling forecasts of age-specific mortality rates at the national and sub-national levels. They also enjoy improved forecast accuracy averaged over different disaggregation factors. Supplementary materials for the article are available online. 相似文献
15.
Mihajlo Cekić 《偏微分方程通讯》2017,42(11):1781-1836
In this paper, we consider the problem of identifying a connection ? on a vector bundle up to gauge equivalence from the Dirichlet-to-Neumann map of the connection Laplacian ?*? over conformally transversally anisotropic (CTA) manifolds. This was proved in [9] for line bundles in the case of the transversal manifold being simple—we generalize this result to the case where the transversal manifold only has an injective ray transform. Moreover, the construction of suitable Gaussian beam solutions on vector bundles is given for the case of the connection Laplacian and a potential, following the works of [11]. This in turn enables us to construct the Complex Geometrical Optics (CGO) solutions and prove our main uniqueness result. We also reduce the problem to a new non-abelian X-ray transform for the case of simple transversal manifolds and higher rank vector bundles. Finally, we prove the recovery of a flat connection in general from the DN map, up to gauge equivalence, using an argument relating the Cauchy data of the connection Laplacian and the holonomy. 相似文献
16.
Elisabeth Remm 《代数通讯》2017,45(7):2956-2966
The notion of breadth of a nilpotent Lie algebra was introduced and used to approach problems of classification up to isomorphism in [5]. In the present paper, we study this invariant in terms of characteristic sequence, another invariant, introduced by Goze and Ancochea in [1]. This permits to complete the determination of Lie algebras of breadth 2 studied in [5] and to begin the work for Lie algebras with breadth greater than 2. 相似文献
17.
Stochastic robustness of control systems under random excitation motivates challenging developments in geometric approach to robustness. The assumption of normality is rarely met when analyzing real data and thus the use of classic parametric methods with violated assumptions can result in the inaccurate computation of p-values, effect sizes, and confidence intervals. Therefore, quite naturally, research on robust testing for normality has become a new trend. Robust testing for normality can have counterintuitive behavior, some of the problems have been introduced in Stehlík et al. [Chemometrics and Intelligent Laboratory Systems 130 (2014): 98–108]. Here we concentrate on explanation of small-sample effects of normality testing and its robust properties, and embedding these questions into the more general question of testing for sphericity. We give geometric explanations for the critical tests. It turns out that the tests are robust against changes of the density generating function within the class of all continuous spherical sample distributions. 相似文献
18.
《偏微分方程通讯》2013,38(11-12):2081-2119
We obtain in the semi-classical setup of “black-box” long-range perturbations a representation for the derivative of spectral shift function ξ(λ) related to two self-adjoint operators L j (h), j = 1,2. We show that the derivative ξ′(λ) is estimated by the norms of the cut-off resolvents of the operators L j (h). Finally, we establish a Weyl type formula for the spectral shift function ξ(λ) generalizing the results of Robert [19] and Christiansen [5]. 相似文献
19.
Stéphane Launois 《代数通讯》2017,45(3):1294-1313
Cauchon [5] introduced the so-called deleting derivations algorithm. This algorithm was first used in noncommutative algebra to prove catenarity in generic quantum matrices, and then to show that torus-invariant primes in these algebras are generated by quantum minors. Since then this algorithm has been used in various contexts. In particular, the matrix version makes a bridge between torus-invariant primes in generic quantum matrices, torus orbits of symplectic leaves in matrix Poisson varieties and totally non-negative cells in totally non-negative matrix varieties [12]. This led to recent progress in the study of totally non-negative matrices such as new recognition tests [18]. The aim of this article is to develop a Poisson version of the deleting derivations algorithm to study the Poisson spectra of the members of a class 𝒫 of polynomial Poisson algebras. It has recently been shown that the Poisson Dixmier–Moeglin equivalence does not hold for all polynomial Poisson algebras [2]. Our algorithm allows us to prove this equivalence for a significant class of Poisson algebras, when the base field is of characteristic zero. Finally, using our deleting derivations algorithm, we compare topologically spectra of quantum matrices with Poisson spectra of matrix Poisson varieties. 相似文献
20.
《代数通讯》2013,41(10):4357-4376
Let k be a field and H a Hopf k-algebra with bijective antipode, R an H-module algebra over k and A = R#H the associated smash product. The fixed subring of R under H is denoted by S. Let P be an R#H-module. Thus P is an S-module. The aim of this paper is to study the projectivity of P as a module over S. We get a generalization of some results of J.J. Garcia and Angel Del Rio [4] of Ida Doraiswamy [8] and of ours [[7], section 5]. 相似文献