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1.
Lixin Mao 《代数通讯》2017,45(10):4196-4209
A right R-module M is called glat if any homomorphism from any finitely presented right R-module to M factors through a finitely presented Gorenstein projective right R-module. The concept of glat modules may be viewed as another Gorenstein analogue of flat modules. We first prove that the class of glat right R-modules is closed under direct sums, direct limits, pure quotients and pure submodules for arbitrary ring R. Then we obtain that a right R-module M is glat if and only if M is a direct limit of finitely presented Gorenstein projective right R-modules. In addition, we explore the relationships between glat modules and Gorenstein flat (Gorenstein projective) modules. Finally we investigate the existence of preenvelopes and precovers by glat and finitely presented Gorenstein projective modules.  相似文献   

2.
Xuding Zhu 《Discrete Mathematics》1998,190(1-3):215-222
Suppose G is a graph. The chromatic Ramsey number rc(G) of G is the least integer m such that there exists a graph F of chromatic number m for which the following is true: for any 2-colouring of the edges of F there is a monochromatic subgraph isomorphic to G. Let Mn = min[rc(G): χ(G) = n]. It was conjectured by Burr et al. (1976) that Mn = (n − 1)2 + 1. This conjecture has been confirmed previously for n 4. In this paper, we shall prove that the conjecture is true for n = 5. We shall also improve the upper bounds for M6 and M7.  相似文献   

3.
Among the various problems of celestial mechanics related to the n-body problem, a certain amount of interest attaches to the specific situation wherein a passive gravitational point mass M moves under the assumption that the relative disposition of the other active gravitational masses experiences no large changes.

If the attracting masses are regarded as points and if changes in the relative disposition of the attracting bodies are neglected, one arrives at the problem of the motion of the point M in a field produced by n-stationary attracting centers (the point M here represents the (n+l)-th body).

In addition to the problem of central motion (n = 1), soluble dynamics problems of this category include Euler's case [1] of two (n= 2) stationary Newtonian attracting centers.

This problem, which for a long time was of solely theoretical Interest as an example of an integrable Liouville system [2], has recently been attracting attention in connection with the mechanics of artificial satellites, particularly after it was shown that the potential of an oblate spheroid can be approximated by the potential of two specifically chosen stationary Newtonian attracting centers [3 and 4].

The solution of the problem for n-attracting centers for n ≥ 3 is unknown, except for a single special case of three centers pointed out by Lagrange and considered In greater detail by J.A. Serre [5].

We shall concern ourselves here with problems on the existence of periodic trajectories in the case of n-attracting centers. An arbitrary and not necessarily Newtonian gravitational law will be assumed.

Our analysis is based on the theory of quasiindices of singular force field points as set forth in [60].  相似文献   


4.
We are concerned with the behavior of the minimum (maximum) eigenvalue λ0(n) (λn(n)) of an (n + 1) × (n + 1) Hermitian Toeplitz matrix Tn(ƒ) where ƒ is an integrable real-valued function. Kac, Murdoch, and Szegö, Widom, Parter, and R. H. Chan obtained that λ0(n) — min ƒ = O(1/n2k) in the case where ƒ C2k, at least locally, and ƒ — inf ƒ has a zero of order 2k. We obtain the same result under the second hypothesis alone. Moreover we develop a new tool in order to estimate the extreme eigenvalues of the mentioned matrices, proving that the rate of convergence of λ0(n) to inf ƒ depends only on the order ρ (not necessarily even or integer or finite) of the zero of ƒ — inf ƒ. With the help of this tool, we derive an absolute lower bound for the minimal eigenvalues of Toeplitz matrices generated by nonnegative L1 functions and also an upper bound for the associated Euclidean condition numbers. Finally, these results are extended to the case of Hermitian block Toeplitz matrices with Toeplitz blocks generated by a bivariate integrable function ƒ.  相似文献   

5.
The Koszul-like property for any finitely generated graded modules over a Koszul-like algebra is investigated and the notion of weakly Koszul-like module is introduced. We show that a finitely generated graded module M is a weakly Koszul-like module if and only if it can be approximated by Koszul-like graded submodules, which is equivalent to the fact that G(M) is a Koszul-like module, where G(M) denotes the associated graded module of M. As applications, the relationships between minimal graded projective resolutions of M and G(M), and Koszul-like submodules are established. Moreover, the Koszul dual of a weakly Koszul-like module is proved to be generated in degree 0 as a graded E(A)-module.  相似文献   

6.
Gould et al. (Combinatorics, Graph Theory and Algorithms, Vol. 1, 1999, pp. 387–400) considered a variation of the classical Turán-type extremal problems as follows: For a given graph H, determine the smallest even integer σ(H,n) such that every n-term graphic sequence π=(d1,d2,…,dn) with term sum σ(π)=d1+d2++dnσ(H,n) has a realization G containing H as a subgraph. In this paper, for given integers k and ℓ, ℓ7 and 3kℓ, we completely determine the smallest even integer σ(kC,n) such that each n-term graphic sequence π=(d1,d2,…,dn) with term sum σ(π)=d1+d2++dnσ(kC,n) has a realization G containing a cycle of length r for each r, krℓ.  相似文献   

7.
Let πi :EiM, i=1,2, be oriented, smooth vector bundles of rank k over a closed, oriented n-manifold with zero sections si :MEi. Suppose that U is an open neighborhood of s1(M) in E1 and F :UE2 a smooth embedding so that π2Fs1 :MM is homotopic to a diffeomorphism f. We show that if k>[(n+1)/2]+1 then E1 and the induced bundle f*E2 are isomorphic as oriented bundles provided that f have degree +1; the same conclusion holds if f has degree −1 except in the case where k is even and one of the bundles does not have a nowhere-zero cross-section. For n≡0(4) and [(n+1)/2]+1<kn we give examples of nonisomorphic oriented bundles E1 and E2 of rank k over a homotopy n-sphere with total spaces diffeomorphic with orientation preserved, but such that E1 and f*E2 are not isomorphic oriented bundles. We obtain similar results and counterexamples in the more difficult limiting case where k=[(n+1)/2]+1 and M is a homotopy n-sphere.  相似文献   

8.
Let C be a planar region. Choose n points p1,,pnI.I.D. from the uniform distribution over C. Let MCn be the number of these points that are maximal. If C is convex it is known that either E(MCn)=Θ(√n)> or E(MCn)=O(log n). In this paper we will show that, for general C, there is very little that can be said, a-priori, about E(MCn). More specifically we will show that if g is a member of a large class of functions then there is always a region C such that E(MCn)=Θ(g(n)). This class contains, for example, all monotically increasing functions of the form g(n)= nlnβn, where 0<<1 and β0. This class also contains nondecreasing functions like g(n)=ln*n. The results in this paper remain valid in higher dimensions.  相似文献   

9.
The general form of a continuous mapping φ acting on the real vector space of all n × n complex Hermitian or real symmetric matrices, and preserving spectrum and commutativity, is derived. It turns out that φ is either linear or its image forms a commutative set.  相似文献   

10.
A target, whose initial position is unknown, is performing a random walk on the integers. A searcher, starting at the origin, wants to follow a search plan for which E[τk] is finite, where k ≥ 1 and τ is the time to capture. The searcher, who has a prior distribution over the target's initial position, can move only to adjacent positions, and cannot travel faster than the target. Necessary and sufficient conditions are given for the existence of search plans for which E[τk] is finite and a minimum.  相似文献   

11.
In this paper, we provide a solution of the quadrature sum problem of R. Askey for a class of Freud weights. Let r> 0, b (− ∞, 2]. We establish a full quadrature sum estimate
1 p < ∞, for every polynomial P of degree at most n + rn1/3, where W2 is a Freud weight such as exp(−¦x¦), > 1, λjn are the Christoffel numbers, xjn are the zeros of the orthonormal polynomials for the weight W2, and C is independent of n and P. We also prove a generalisation, and that such an estimate is not possible for polynomials P of degree M = m(n) if m(n) = n + ξnn1/3, where ξn → ∞ as n → ∞. Previous estimates could sum only over those xjn with ¦xjn¦ σx1n, some fixed 0 < σ < 1.  相似文献   

12.
We consider the following model Hr(n, p) of random r-uniform hypergraphs. The vertex set consists of two disjoint subsets V of size | V | = n and U of size | U | = (r − 1)n. Each r-subset of V × (r−1U) is chosen to be an edge of H ε Hr(n, p) with probability p = p(n), all choices being independent. It is shown that for every 0 < < 1 if P = (C ln n)/nr−1 with C = C() sufficiently large, then almost surely every subset V1 V of size | V1 | = (1 − )n is matchable, that is, there exists a matching M in H such that every vertex of V1 is contained in some edge of M.  相似文献   

13.
The scaled factorial moments Fq are studied for 28Si–AgBr collisions at 14.6 AGeV. These moments follow the generalized power law Fq(M)[g(M)]q. The values of q/2 obtained from the linear fits of ln Fq versus ln F2 graphs are found to obey the Brax–Peschanski formula with Levy index μ = 1.635 ± 0.012 for η space and μ = 1.801 ± 0.003 for space. These values lie within the Levy stable region 0  μ  2. An analytical continuation of the Brax–Peschanski formula has been used to obtain the multifractal spectra f(q) in negative q region.  相似文献   

14.
Let Mbe a monoid. A ring Ris called M-π-Armendariz if whenever α = a1g1+ a2g2+ · · · + angn, β = b1h1+ b2h2+ · · · + bmhmR[M] satisfy αβ ∈ nil(R[M]), then aibj ∈ nil(R) for all i, j. A ring R is called weakly 2-primal if the set of nilpotent elements in R coincides with its Levitzki radical. In this paper, we consider some extensions of M-π-Armendariz rings and further investigate their properties under the condition that R is weakly 2-primal. We prove that if R is an M-π-Armendariz ring then nil(R[M]) = nil(R)[M]. Moreover, we study the relationship between the weak zip-property (resp., weak APP-property, nilpotent p.p.-property, weak associated prime property) of a ring R and that of the monoid ring R[M] in case R is M-π-Armendariz.  相似文献   

15.
Let R be an associative ring with 1. A left R module M is uniserial i f the lattice L(M) of its submodules is totally ordered under inclusion. We give an example of a uniserial module M with the property of having two submodules 0 < H < K < M such that M is isomorphic to K/H (we call a module M with this property shrinkable). Then we give an example of a uniserial module M isomorphic to all its nonzero quotients M/N, N<M, and with L(M) isomorphic to ω2+1; this solves a problem of Hirano and Mogami [7]. Finally we show that for uniserial modules the property of being shrinkable is connected to the problem of deciding whether a module, which is both a homomorphic image of a finite direct sum of uniserial modules and a submodule of a finite direct sum of uniserial modules, is a finite direct sum of uniserial modules  相似文献   

16.
The problem of constructing (m, n) cages suggests the following class of problems. For a graph parameter θ, determine the minimum or maximum value of p for which there exists a k-regular graph on p points having a given value of θ. The minimization problem is solved here when θ is the achromatic number, denoted by ψ. This result follows from the following main theorem. Let M(p, k) be the maximum value of ψ(G) over all k-regular graphs G with p points, let {x} be the least integer of size at least x, and let be given by ω(k) = {i(ik+1)+1:1i<∞}. Define the function ƒ(p, k) by . Then for fixed k2 we have M(p, K=ƒ(p, k) if pω(k) and M(p, k)=ƒ(p,k-1 if pε ω(k) for all p sufficiently large with respect to k.  相似文献   

17.
The parametric resource allocation problem asks to minimize the sum of separable single-variable convex functions containing a parameter λ, Σi = 1ni(xi + λgi(xi)), under simple constraints Σi = 1n xi = M, lixiui and xi: nonnegative integers for i = 1, 2, …, n, where M is a given positive integer, and li and ui are given lower and upper bounds on xi. This paper presents an efficient algorithm for computing the sequence of all optimal solutions when λ is continuously changed from 0 to ∞. The required time is O(GMlog2 n + n log n + n log(M/n)), where G = Σi = 1n ui − Σi = 1n li and an evaluation of ƒi(·) or gi(·) is assumed to be done in constant time.  相似文献   

18.
If are maximal nests on a finite-dimensional Hilbert space H, the dimension of the intersection of the corresponding nest algebras is at least dim H. On the other hand, there are three maximal nests whose nest algebras intersect in the scalar operators. The dimension of the intersection of two nest algebras (corresponding to maximal nests) can be of any integer value from n to n(n+1)/2, where n=dim H. For any two maximal nests there exists a basis {f1,f2,…,fn} of H and a permutation π such that and where Mi=  span{f1,f2,…,fi} and Ni= span{fπ(1),fπ(2),…,fπ(i)}. The intersection of the corresponding nest algebras has minimum dimension, namely dim H, precisely when π(j)=nj+1,1jn. Those algebras which are upper-triangular matrix incidence algebras, relative to some basis, can be characterised as intersections of certain nest algebras.  相似文献   

19.
The influence of surface roughness in the prediction of the mean flow and turbulent properties of a high-speed supersonic (M = 2.7, Re/m = 2 × 107) turbulent boundary layer flow over a flat plate is numerically investigated. In particular, the performance of the kω and stress–ω turbulence models is evaluated against the available experimental data. Even though the performance of these models have been proven satisfactory in the computation of incompressible boundary layer flow over rough surfaces, their validity for high-speed compressible has not been investigated yet. It is observed from this study that, for smooth surface, both kω and stress–ω models perform very well in predicting the mean flow and turbulence quantities in supersonic flow. For rough surfaces, both models matched the experimental data fairly well for lower roughness heights but performed unsatisfactorily for higher roughness conditions. Overall the performance of the kω model is better than the stress–ω model. The stress–ω model does not show any strong advantages to make up for the extra computational cost associated with it. The predictions indicate that the ω boundary conditions at the wall in both models, especially the stress–ω model, need to be refined and reconsidered to include the geometric factor for supersonic flow over surfaces with large roughness values.  相似文献   

20.
Let G be an infinite locally finite connected graph. We study the reconstructibility of G in relation to the structure of its end set . We prove that an infinite locally finite connected graph G is reconstructible if there exists a finite family i)0i (n2) of pairwise finitely separable subsets of such that, for all x,y,x′,yV(G) and every isomorphism f of G−{x,y} onto G−{x′,y′} there is a permutation π of {0,…,n−1} such that for 0i<n. From this theorem we deduce, as particular consequences, that G is reconstructible if it satisfies one of the following properties: (i) G contains no end-respecting subdivision of the dyadic tree and has at least two ends of maximal order; (ii) the set of thick ends or the one of thin ends of G is finite and of cardinality greater than one. We also prove that if almost all vertices of G are cutvertices, then G is reconstructible if it contains a free end or if it has at least a vertex which is not a cutvertex.  相似文献   

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