共查询到20条相似文献,搜索用时 31 毫秒
1.
Mitsuyasu Hashimoto 《代数通讯》2013,41(12):4569-4596
We discuss Matijevic–Roberts type theorem on strong F-regularity, F-purity, and Cohen–Macaulay F-injective (CMFI for short) property. Related to this problem, we also discuss the base change problem and the openness of loci of these properties. In particular, we define the notion of F-purity of homomorphisms using Radu–André homomorphisms and prove basic properties of it. We also discuss a strong version of strong F-regularity (very strong F-regularity), and compare these two versions of strong F-regularity. As a result, strong F-regularity and very strong F-regularity agree for local rings, F-finite rings, and essentially finite-type algebras over an excellent local rings. We prove the F-pure base change of strong F-regularity. 相似文献
2.
Mikhail Kovalyov 《纯数学与应用数学通讯》1987,40(5):589-607
In this paper we consider the initial value problem for the nonlinear wave equation □u = F(u, u′) in Friedman-Robertson-Walker space-time, □ being the D'Alambertian in local coordinates of space-time. We obtain decay estimates and show that the equation has global solutions for small initial data. We do it by reducing the problem to an initial value problem for the wave equation over hyperbolic space. As byproduct we derive decay and global existence for solutions of the wave equation over the hyperbolic space with small initial data. The same technique with some auxiliary lemmas similar to the ones proved in [6], [7] can be used to generalize the result to the case when F depends also on second derivatives of u in a certain way. 相似文献
3.
Arzu Erdem 《Mathematical Methods in the Applied Sciences》2015,38(7):1393-1404
In this paper, we consider an inverse source problem of identification of F(t) function in the linear parabolic equation ut = uxx + F(t) and u0(x) function as the initial condition from the measured final data and local boundary data. Based on the optimal control framework by Green's function, we construct Fréchet derivative of Tikhonov functional. The stability of the minimizer is established from the necessary condition. The CG algorithm based on the Fréchet derivative is applied to the inverse problem, and results are presented for a test example. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
4.
Simone Costa 《组合设计杂志》2020,28(5):366-383
Let F be a 2‐regular graph of order v. The Oberwolfach problem, OP(F), asks for a 2‐factorization of the complete graph on v vertices in which each 2‐factor is isomorphic to F. In this paper, we give a complete solution to the Oberwolfach problem over infinite complete graphs, proving the existence of solutions that are regular under the action of a given involution free group G. We will also consider the same problem in the more general context of graphs F that are spanning subgraphs of an infinite complete graph and we provide a solution when F is locally finite. Moreover, we characterize the infinite subgraphs L of F such that there exists a solution to OP(F) containing a solution to OP(L). 相似文献
5.
Najib Mahdou 《代数通讯》2013,41(10):3489-3496
In this article, we consider 2-von Neumann regular rings, that is, rings R with the property that, if F 2 → F 1 → F 0 → E → 0 is an exact sequence of R-modules with F 0, F 1, and F 2 finitely generated free modules, then the module E is projective. For each positive integer m, as well as for m = ∞, we exhibit a class of 2-von Neumann regular rings with Krull dimension m. For this purpose, we study trivial extensions of local rings by infinite-dimensional vector spaces over their residue fields. The article includes a brief discussion of the scope and precision of our results. 相似文献
6.
7.
《代数通讯》2013,41(4):1581-1586
Abstract In the paper by Furuya and Niitsuma [Furuya, M., Niitsuma, H. (2002a). On m -adic higher differentials and regularities of Noetherian complete local rings. J. Math. Kyoto Univ. 42(1):33–40], we gave a regularity criterion of complete Noetherian local rings in terms of the concept of m -adic higher differentials with some assumptions of separability on the residue fields of the local rings. The aim of this paper is to try to weaken “the separability assumptions” in a premise of the theorems in Furuya and Niitsuma (2002a). 相似文献
8.
Andreas Fischer 《Mathematical Programming》1997,76(3):513-532
The paper deals with complementarity problems CP(F), where the underlying functionF is assumed to be locally Lipschitzian. Based on a special equivalent reformulation of CP(F) as a system of equationsφ(x)=0 or as the problem of minimizing the merit functionΘ=1/2∥Φ∥
2
2
, we extend results which hold for sufficiently smooth functionsF to the nonsmooth case.
In particular, ifF is monotone in a neighbourhood ofx, it is proved that 0 εδθ(x) is necessary and sufficient forx to be a solution of CP(F). Moreover, for monotone functionsF, a simple derivative-free algorithm that reducesΘ is shown to possess global convergence properties. Finally, the local behaviour of a generalized Newton method is analyzed.
To this end, the result by Mifflin that the composition of semismooth functions is again semismooth is extended top-order semismooth functions. Under a suitable regularity condition and ifF isp-order semismooth the generalized Newton method is shown to be locally well defined and superlinearly convergent with the
order of 1+p. 相似文献
9.
In this paper, we continue to study the properties of the global attractor for some p-Laplacian equations with a Lyapunov function F in a Banach space when the origin is no longer a local minimum point but a saddle point of F. By using the abstract result established in our previous work, we prove the existence of multiple equilibrium points in the global attractor for some p-Laplacian equations under some suitable assumptions in the case that the origin is an unstable equilibrium point. 相似文献
10.
Ronen Peretz 《Israel Journal of Mathematics》1998,105(1):1-59
The aim of this paper is to develop a theory for the asymptotic behavior of polynomials and of polynomial maps overR and overC and to apply it to the Jacobian conjecture. This theory gives a unified frame for some results on polynomial maps that were
not related before.
A well known theorem of J. Hadamard gives a necessary and sufficient condition on a local diffeomorphismf: R
n
→R
n
to be a global diffeomorphism. In order to show thatf is a global diffeomorphism it suffices to exclude the existence of asymptotic values forf.
The real Jacobian conjecture was shown to be false by S. Pinchuk. Our first application is to understand his construction
within the general theory of asymptotic values of polynomial maps and prove that there is no such counterexample for the Jacobian
conjecture overC. In a second application we reprove a theorem of Jeffrey Lang which gives an equivalent formulation of the Jacobian conjecture
in terms of Newton polygons. This generalizes a result of Abhyankar. A third application is another equivalent formulation
of the Jacobian conjecture in terms of finiteness of certain polynomial rings withinC[U, V].
The theory has a geometrical aspect: we define and develop the theory of etale exotic surfaces. The simplest such surface
corresponds to Pinchuk's construction in the real case. In fact, we prove one more equivalent formulation of the Jacobian
conjecture using etale exotic surfaces. We consider polynomial vector fields on etale exotic surfaces and explore their properties
in relation to the Jacobian conjecture.
In another application we give the structure of the real variety of the asymptotic values of a polynomial mapf: R
2
→R
2
. 相似文献
11.
Abstract In this paper we consider the problem of global analytic and Gevrey hypoellipticity and solvability for a class of partial
differential operators on a torus. We prove that global analytic and Gevrey hypoellipticity and solvability on the torus is
equivalent to certain Diophantine approximation properties.
Keywords: Global hypoellipticity, Global solvability, Gevrey classes, Diophantine approximation property
Mathematics Subject Classification (2000): 35D05, 46E10, 46F05, 58J99 相似文献
12.
A. A. Gerko 《Journal of Mathematical Sciences》2007,142(4):2205-2232
For finite modules over a local ring and complexes with finitely generated homology, we consider several homological invariants
sharing some basic properties with projective dimension.
In the second section, we introduce the notion of a semidualizing complex, which is a generalization of both a dualizing complex and a suitable module. Our goal is to establish some common properties of such complexes and the homological dimension with respect to them.
Basic properties are investigated in Sec. 2.1. In Sec. 2.2, we study the structure of the set of semidualizing complexes over
a local ring, which is closely related to the conjecture of Avramov-Foxby on the transitivity of the G-dimension. In particular,
we prove that, for a pair of semidualizing complexes X
1 and X
2 such that G
X2, we have X
2 ≃ X
1 ⊗
R
L
RHom
R
(X
1, X
2). Specializing to the case of semidualizing modules over Artinian rings, we obtain a number of quantitative results for the
rings possessing a configuration of semidualizing modules of special form. For the rings with m
3=0, this condition reduces to the existence of a nontrivial semidualizing module, and we prove a number of structural results
in this case.
In the third section, we consider the class of modules that contains the modules of finite CI-dimension and enjoys some nice
additional properties, in particular, good behavior in short exact sequences.
In the fourth section, we introduce a new homological invariant, CM-dimension, which provides a characterization for Cohen-Macaulay
rings in precisely the same way as projective dimension does for regular rings, CI-dimension for locally complete intersections,
and G-dimension for Gorenstein rings.
__________
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 30, Algebra,
2005. 相似文献
13.
Let R be a commutative ring with 1 ≠ 0, G be a nontrivial finite group, and let Z(R) be the set of zero divisors of R. The zero-divisor graph of R is defined as the graph Γ(R) whose vertex set is Z(R)* = Z(R)?{0} and two distinct vertices a and b are adjacent if and only if ab = 0. In this paper, we investigate the interplay between the ring-theoretic properties of group rings RG and the graph-theoretic properties of Γ(RG). We characterize finite commutative group rings RG for which either diam(Γ(RG)) ≤2 or gr(Γ(RG)) ≥4. Also, we investigate the isomorphism problem for zero-divisor graphs of group rings. First, we show that the rank and the cardinality of a finite abelian p-group are determined by the zero-divisor graph of its modular group ring. With the notion of zero-divisor graphs extended to noncommutative rings, it is also shown that two finite semisimple group rings are isomorphic if and only if their zero-divisor graphs are isomorphic. Finally, we show that finite noncommutative reversible group rings are determined by their zero-divisor graphs. 相似文献
14.
Dirk Hachenberger 《Finite Fields and Their Applications》1999,5(4):3246
Given an extension E/F of Galois fields and an intermediate field K, we consider the problem whether the (E, K)-trace of a primitive F-normal element of E can be a prescribed F-normal element of K. An interesting application is the existence of trace-compatible sequences of primitive F-normal elements for certain towers of Galois fields. In this respect, particular emphasis is laid on extensions having prime power degree. 相似文献
15.
In this paper, we consider hypothesis testing problems in which the involved samples are drawn from generalized multivariate modified Bessel populations. This is a much more general distribution that includes both the multivariate normal and multivariate-t distributions as special cases. We derive the distribution of the Hotelling's T2-statistic for both the one- and two-sample problems, as well as the distribution of the Scheffe's T2-statistic for the Behrens–Fisher problem. In all cases, the non-null distribution of the corresponding F-statistic follows a new distribution which we introduce as the non-central F-Bessel distribution. Some statistical properties of this distribution are studied. Furthermore, this distribution was utilized to perform some power calculations for tests of means for different models which are special cases of the generalized multivariate modified Bessel distribution, and the results compared with those obtained under the multivariate normal case. Under the null hypothesis, however, the non-central F-Bessel distribution reduces to the central F-distribution obtained under the classical normal model. 相似文献
16.
In this paper, we consider the initial value problem for the Rosenau equation with damped term. The decay structure of the equation is of the regularity‐loss type, which causes the difficulty in high‐frequency region. Under small assumption on the initial value, we obtain the decay estimates of global solutions for n≥1. The proof also shows that the global solutions may be approximated by the solutions to the corresponding linear problem for n≥2. We prove that the global solutions may be approximated by the superposition of nonlinear diffusion wave for n = 1. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
17.
In this paper, we consider some well-known equilibrium problems and their duals in a topological Hausdorff vector space X for a bifunction F defined on K x K,where K is a convex subset of X. Some necessary conditions are investigated, proving different results depending on the behaviour of F on the diagonal set. The concept of proper quasimonotonicity for bifunctions is defined, and the relationship with generalized monotonicity is investigated. The main result proves that the condition of proper quasimonotonicity is sharp in order to solve the dual equilibrium problem on every convex set. 相似文献
18.
In this paper we consider the problem of decomposing tensor products of certain singular unitary representations of a semisimple
Lie group G. Using explicit models for these representations (constructed earlier by one of us) we show that the decomposition is controlled
by a reductive homogeneous space . Our procedure establishes a correspondence between certain unitary representations of G and those of . This extends the usual -correspondence for dual reductive pairs. As a special case we obtain a correspondence between certain representations of
real forms of E
7 and F
4. 相似文献
19.
We introduce a categorical framework for the study of representations
of G(F), where G is a reductive group, and F is a 2-dimensional
local field, i.e. F = K((t)), where K is a local field.
Our main result says that the space of functions on G(F), which is an
object of a suitable category of representations of G(F) with the respect to
the action of G on itself by left translations, becomes a representation of
a certain central extension of G(F), when we consider the action by right
translations. 相似文献
20.
《Optimization》2012,61(1):51-68
In this article, we consider a lower order penalty function and its ε-smoothing for an inequality constrained nonlinear programming problem. It is shown that any strict local minimum satisfying the second-order sufficiency condition for the original problem is a strict local minimum of the lower order penalty function with any positive penalty parameter. By using an ε-smoothing approximation to the lower order penalty function, we get a modified smooth global exact penalty function under mild assumptions. 相似文献