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1.
It is shown that if dim Y < ∞ and if f(X) = Y is a mapping between compact metric spaces such that 1 ? m ? dim f-1(y)?n for all y ? Y, then there exists a closed set K ? X such that dim K ? n ? m and dim f(K) = dim Y. This answers a question posed by J. Keesling and D. Wilson.  相似文献   

2.
We study the birational geometry of varieties of maximal Albanese dimension in this article. Given a non-birational, generically finite, and surjective morphism f: XY between varieties of maximal Albanese dimension, we show that the plurigenera P m (X) and P m (Y) for some m?≥ 2 could be equal only in very restrictive situations. We also prove that the 5-th pluricanonical map of a variety of maximal Albanese dimension always induces the Iitaka model.  相似文献   

3.
Let f(x) be an indefinite quadratic form with real coefficients in n variables with nonzero determinant d. The collection of all values of v(f) = |d|?1ninf |f(x)|, where infimum is taken over xZn such that f(x) ≠ 0 (x ≠ 0) is called the spectrum of nonzero minima (spectrum of minima) of such forms. The spectrum is said to be discrete if for every δ > 0, there are only finitely many values of v(f) > δ. It is proved that for rational quadratic forms in n ≥ 3 variables and real quadratic forms in n ≥ 21 variables the spectra of nonzero minima are discrete. Also the spectra of minima of indefinite ternary and quaternary rational quadratic forms are discrete.  相似文献   

4.
Let X be a set of k×k matrices in which each element is nonnegative. For a positive integer n, let P(n) be an arbitrary product of n matrices from X, with any ordering and with repetitions permitted. Define X to be a primitive set if there is a positive integer n such that every P(n) is positive [i.e., every element of every P(n) is positive]. For any primitive set X of matrices, define the index g(X) to be the least positive n such that every P(n) is positive. We show that if X is a primitive set, then g(X)?2k?2. Moreover, there exists a primitive set Y such that g(Y) = 2k?2.  相似文献   

5.
We show that the O(K · n4) algorithm of Hamacher (1982) for finding the K best cut-sets fails because it may produce cuts rather than cut-sets. With the convention that two cuts (X, X) and (Y, Y) are different whenever XY the K best cut problem can be solved in O(K · n4).  相似文献   

6.
It is shown that every Euclidean manifold M has the following property for any m?1: If f:XY is a perfect surjection between finite-dimensional metric spaces, then the mapping space C(X,M) with the source limitation topology contains a dense Gδ-subset of maps g such that dimBm(g)?mdimf+dimY−(m−1)dimM. Here, Bm(g)={(y,z)∈Y×M||f−1(y)∩g−1(z)|?m}. The existence of residual sets of finite-to-one maps into product of manifolds and spaces having disjoint disks properties is also obtained.  相似文献   

7.
For a compact Hausdorff space X, C(X) denotes the algebra of all complex-valued continuous functions on X. For a positive integer n, we say that C(X) is n-th root closed if, for each fC(X), there exists gC(X) such that f=gn. It is shown that, for each integer m?2, there exists a compact Hausdorff space Xm such that C(Xm) is m-th root closed, but not n-th root closed for each integer n relatively prime to m. This answers a question posed by Countryman Jr. [R.S. Countryman Jr., On the characterization of compact Hausdorff X for which C(X) is algebraically closed, Pacific J. Math. 20 (1967) 433-438] et al.  相似文献   

8.
Let X be a linear space over a commutative field K. We characterize a general solution f,g,h,k:XK of the pexiderized Go?a?b-Schinzel equation f(x+g(x)y)=h(x)k(y), as well as real continuous solutions of the equation.  相似文献   

9.
. We develop the theory of canonical and pluricanonical adjoints, of global canonical and pluricanonical adjoints, and of adjoints and global adjoints to an irreducible, algebraic hypersurface V?? n , under certain hypotheses on the singularities of V. We subsequently apply the results of the theory to construct a non-singular threefold of general type X, desingularization of a hypersurface V of degree six in ?4, having the birational invariants q 1=q 2=p g =0, P 2=P 3=5. We demonstrate that the bicanonical map ? |2KX| is birational and finally, as a consequence of the Riemann–Roch theorem and vanishing theorems, we prove that any non-singular model Y, birationally equivalent to X, has the canonical divisors K Y that do not (simultaneously) satisfy the two properties: (K Y 3)>0 and K Y numerically effective.  相似文献   

10.
The (isotone) map f: XX is an increasing (decreasing) operator on the poset X if f(x) ? f2(x) (f2(x) ? f(x), resp.) holds for each xX. Properties of increasing (decreasing) operators on complete lattices are studied and shown to extend and clarify those of closure (resp. anticlosure) operators. The notion of the decreasing closure, f, (the increasing anticlosure, f,) of the map f: XX is introduced extending that of the transitive closure, f?, of f. ff, and f are all shown to have the same set of fixed points. Our results enable us to solve some problems raised by H. Crapo. In particular, the order structure of H(X), the set of retraction operators on X is analyzed. For X a complete lattice H(X) is shown to be a complete lattice in the pointwise partial order. We conclude by claiming that it is the increasing-decreasing character of the identity maps which yields the peculiar properties of Galois connections. This is done by defining a u-v connection between the posets X and Y, where u: XX (v: YY) is an increasing (resp. decreasing) operator to be a pair f, g of maps f; XY, g: YX such that gf ? u, fg ? v. It is shown that the whole theory of Galois connections can be carried over to u-v connections.  相似文献   

11.
We show that, for every orthogonally additive homogeneous polynomial P on a space of continuous functions C(K) with values in a Banach space Y, there exists a linear operator S:C(K)→Y such that P(f)=S(fn). This is the C(K) version of a related result of Sundaresam for polynomials on Lp spaces.  相似文献   

12.
Fix integers m, n such that 1 ≤ mn ? 3. Let X ? Pn be an integral non-degenerate m-dimensional variety. Assume either char(K) = 0 or char(K) > deg(X). Here we prove that all general 0-dimensional sections of X containing a tangent vector to a smooth point of X are protectively equivalent if and only if n ? m + 1 ≤ deg(X) ≤ n ? m + 2.  相似文献   

13.
We provide irreducibility criteria for multivariate polynomials with coefficients in an arbitrary field that extend a classical result of Pólya for polynomials with integer coefficients. In particular, we provide irreducibility conditions for polynomials of the form f(X)(Y ? f 1(X))…(Y ? f n (X)) + g(X), with f, f 1, ?, f n , g univariate polynomials over an arbitrary field.  相似文献   

14.
Let ν(n) denote the number of distinct prime factors of n. We show that the equation n + ν(n) = m + ν(m) has many solutions with nm. We also show that if ν is replaced by an arbitrary, integer-valued function f with certain properties assumed about its average order, then the equation n + f(n) = m + f(m) has infinitely many solutions with nm.  相似文献   

15.
Let K be a field with char K ≠ 3 and it two positive integers such that 1 ≤i <t/2,t ≠ 3i. The classification problem for maximal Cohen-Macaulay modules over K[[X,Y]]/(Xt+Y3 ) is complicated if t≥ 6, because there exist parameter families of non-isomorphic maximal Cohen-Macaulay modules [Sc], or [GK], [Yo, Ch.9] and [DG]). Here we describe parameter families of such modules N, such that N/YN is a direct sum of copies of K[[X]]/(X i)K[[X]]/(Xt-i ).  相似文献   

16.
Let (X, Y) have regression function m(x) = E(Y | X = x), and let X have a marginal density f1(x). We consider two nonparameteric estimates of m(x): the Watson estimate when f1 is known and the Yang estimate when f1 is known or unknown. For both estimates the asymptotic distribution of the maximal deviation from m(x) is proved, thus extending results of Bickel and Rosenblatt for the estimation of density functions.  相似文献   

17.
We study the problem of the Baire classification of integrals g (y) = (If)(y) = ∫ X f(x, y)dμ(x), where y is a parameter that belongs to a topological space Y and f are separately continuous functions or functions similar to them. For a given function g, we consider the inverse problem of constructing a function f such that g = If. In particular, for compact spaces X and Y and a finite Borel measure μ on X, we prove the following result: In order that there exist a separately continuous function f : X × Y → ℝ such that g = If, it is necessary and sufficient that all restrictions g| Y n of the function g: Y → ℝ be continuous for some closed covering { Y n : n ∈ ℕ} of the space Y.__________Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 11, pp. 1443–1457, November, 2004.  相似文献   

18.
For a natural number m?0, a map from a compactum X to a metric space Y is an m-dimensional Lelek map if the union of all non-trivial continua contained in the fibers of f is of dimension ?m. In [M. Levin, Certain finite-dimensional maps and their application to hyperspaces, Israel J. Math. 105 (1998) 257-262], Levin proved that in the space C(X,I) of all maps of an n-dimensional compactum X to the unit interval I=[0,1], almost all maps are (n−1)-dimensional Lelek maps. Moreover, he showed that in the space C(X,Ik) of all maps of an n-dimensional compactum X to the k-dimensional cube Ik (k?1), almost all maps are (nk)-dimensional Lelek maps. In this paper, we generalize Levin's result. For any (separable) metric space Y, we define the piecewise embedding dimension ped(Y) of Y and we prove that in the space C(X,Y) of all maps of an n-dimensional compactum X to a complete metric ANR Y, almost all maps are (nk)-dimensional Lelek maps, where k=ped(Y). As a corollary, we prove that in the space C(X,Y) of all maps of an n-dimensional compactum X to a Peano curve Y, almost all maps are (n−1)-dimensional Lelek maps and in the space C(X,M) of all maps of an n-dimensional compactum X to a k-dimensional Menger manifold M, almost all maps are (nk)-dimensional Lelek maps. It is known that k-dimensional Lelek maps are k-dimensional maps for k?0.  相似文献   

19.
Let X=V(f1,…,fnm)⊂Rn be a compact real algebraic set and g:XR2m be a continuous function. If the diagonal in X×X is isolated in the set of self-intersection points of g, we define the intersection number of g. In the case where X is a manifold and g is an immersion it is the intersection number defined by Whitney. In the case where g is a polynomial mapping, we present an effective formula for this number.  相似文献   

20.
Let FX,Y(x,y) be a bivariate distribution function and Pn(x), Qm(y), n, m = 0, 1, 2,…, the orthonormal polynomials of the two marginal distributions FX(x) and FY(y), respectively. Some necessary conditions are derived for the co-efficients cn, n = 0, 1, 2,…, if the conditional expectation E[Pn(X) ∥ Y] = cnQn(Y) holds for n = 0, 1, 2,…. Several examples are given to show the application of these necessary conditions.  相似文献   

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