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1.
Xiaoyong Xi  Qingyu He  Zhijun Lu 《Order》2016,33(2):289-298
Let CONT ? be the category of continuous domains and Scott continuous mappings that preserve the way-below relation on domains. Let ω-ALG ? be the full subcategory of CONT ? consisting of all countably based algebraic domains, and F I N be the category of finite posets and monotone mappings. The main result proved in this paper is that F I N is the largest Cartesian closed full subcategory of ω-ALG ?. On the other hand, it is shown that the algebraic L-domains form a Cartesian closed full subcategory of ALG ?.  相似文献   

2.
Ergodic homeomorphisms T and S of Polish probability spaces X and Y are evenly Kakutani equivalent if there is an orbit equivalence ?: X 0Y 0 between full measure subsets of X and Y such that, for some A ? X 0 of positive measure, ? restricts to a measurable isomorphism of the induced systems T A and S ?(A). The study of even Kakutani equivalence dates back to the seventies, and it is well known that any two zero-entropy loosely Bernoulli systems are evenly Kakutani equivalent. But even Kakutani equivalence is a purely measurable relation, while systems such as the Morse minimal system are both measurable and topological.Recently del Junco, Rudolph and Weiss studied a new relation, called nearly continuous Kakutani equivalence. A nearly continuous Kakutani equivalence is an even Kakutani equivalence where also X 0 and Y 0 are invariant G δ sets, A is within measure zero of both open and closed, and ? is a homeomorphism from X 0 to Y 0. It is known that nearly continuous Kakutani equivalence is strictly stronger than even Kakutani equivalence, and nearly continuous Kakutani equivalence is the natural strengthening of even Kakutani equivalence to the nearly continuous category—the category of maps that are continuous after sets of measure zero are removed. In this paper, we show that the Morse minimal substitution system is nearly continuously Kakutani equivalent to the binary odometer.  相似文献   

3.
For any positive integers n ≥ 1 and m ≥ 2, we give a constructive proof of the existence of linear n-dimensional Pfaff systems with m-dimensional time and with infinitely differentiable coefficient matrices such that the characteristic and lower characteristic sets of these systems are given sets that are the graphs of a concave continuous function and a convex continuous function, respectively, defined and monotone decreasing on simply connected closed bounded convex domains of the space ?m?1.  相似文献   

4.
We prove that the traction problem of homogeneous and isotropic elastostatics has a unique classical solution in bounded and exterior domains of class C2 for continuous boundary data.  相似文献   

5.
For semilinear elliptic equations ?Δu = λ|u| p?2 u?|u| q?2 u, boundary value problems in bounded and unbounded domains are considered. In the plane of exponents p × q, the so-called curves of critical exponents are defined that divide this plane into domains with qualitatively different properties of the boundary value problems and the corresponding parabolic equations. New solvability conditions for boundary value problems, conditions for the stability and instability of stationary solutions, and conditions for the existence of global solutions to parabolic equations are found.  相似文献   

6.
An exponential polynomial of order q is an entire function of the form
$$g(z) = {P_1}(z){e^{{Q_1}(z)}} + ...{P_k}(z){e^{{Q_k}(z)}},$$
where the coefficients Pj(z),Qj(z) are polynomials in z such that
$$\max \{ deg({Q_j})\} = q.$$
It is known that the majority of the zeros of a given exponential polynomial are in domains surrounding finitely many critical rays. The shape of these domains is refined by showing that in many cases the domains can approach the critical rays asymptotically. Further, it is known that the zeros of an exponential polynomial are always of bounded multiplicity. A new sufficient condition for the majority of zeros to be simple is found. Finally, a division result for a quotient of two exponential polynomials is proved, generalizing a 1929 result by Ritt in the case q = 1 with constant coefficients. Ritt’s result is closely related to Shapiro’s conjecture that has remained open since 1958.
  相似文献   

7.
Any (measurable) function K from Rn to R defines an operator K acting on random variables X by K(X) = K(X1,..., Xn), where the Xj are independent copies of X. The main result of this paper concerns continuous selectors H, continuous functions defined in Rn and such that H(x1, x2,..., xn) ∈ {x1, x2,..., xn}. For each such continuous selector H (except for projections onto a single coordinate) there is a unique point ωH in the interval (0, 1) so that, for any random variable X, the iterates H(N) acting on X converge in distribution as N → ∞ to the ωH-quantile of X.  相似文献   

8.
To an arbitrary involutive stereotype algebra A the continuous envelope operation assigns its nearest, in some sense, involutive stereotype algebra EnvCA so that homomorphisms to various C*-algebras separate the elements of EnvC A but do not distinguish between the properties of A and those of EnvCA.  相似文献   

9.
Each Platonic polyhedron P can be folded using a continuous folding process into a face of P so that the resulting shape is flat and multilayered, while two of the faces are rigid during the motion. In previous works, explicit formulas of continuous functions for such motions were given and the same result as above was shown to hold for any tetrahedron. In this paper, we show that a truncated regular tetrahedron can be folded continuously via explicit continuous folding mappings into a flat (folded) state, such that two of the hexagonal faces are rigid. Furthermore, given any general tetrahedron P and any truncated tetrahedron Q of P, we show that if Q contains the largest inscribed sphere of P and satisfies some condition, then Q can be folded continuously into a flat folded state such that two of the hexagonal faces of Q are rigid during the motion.  相似文献   

10.
We study the Wu metric for the non-convex domains of the form \( E_{2m} = \{ z \in \mathbb {C}^{n} : \vert {z_{1} \vert }^{2m} + \vert {z_{2}\vert }^{2} + {\cdots } + \vert {z_{n-1}\vert }^{2} + \vert {z_{n}\vert }^{2} <1 \}\), where 0 < m < 1/2. We give explicit expressions for the Kobayashi metric and the Wu metric on such pseudo-eggs E 2m . We verify that the Wu metric is a continuous Hermitian metric on E 2m , real analytic everywhere except along the complex hypersurface Z = {(0,z 2,…,z n ) ∈ E 2m }. We also show that the holomorphic curvature of the Wu metric for this non-compact family of pseudoconvex domains is bounded above in the sense of currents by a negative constant independent of m. This verifies a conjecture of S. Kobayashi and H. Wu for such E 2m .  相似文献   

11.
A new class of hybrid BDF-like methods is presented for solving systems of ordinary differential equations (ODEs) by using the second derivative of the solution in the stage equation of class 2 + 1hybrid BDF-like methods to improve the order and stability regions of these methods. An off-step point, together with two step points, has been used in the first derivative of the solution, and the stability domains of the new methods have been obtained by showing that these methods are A-stable for order p, p =?3,4,5,6,7and A(α)-stable for order p, 8 ≤ p ≤?14. The numerical results are also given for four test problems by using variable and fixed step-size implementations.  相似文献   

12.
New methods for obtaining representations of solutions of the Cauchy problem for linear evolution equations, i.e., equations of the form u t '(t, x) = Lu(t, x), where the operator L is linear and depends only on the spatial variable x and does not depend on time t, are proposed. A solution of the Cauchy problem, that is, the exponential of the operator tL, is found on the basis of constructions proposed by the author combined with Chernoff’s theorem on strongly continuous operator semigroups.  相似文献   

13.
We present necessary and sufficient conditions on planar compacta K and continuous functions f on K in order that f generate the algebras P(K), R(K), A(K) or C(K). We also unveil quite surprisingly simple examples of non-polynomial convex compacta K ? C and fP(K) with the property that fP(K) is a homeomorphism of K onto its image, but for which f ?1 ? P(f(K)). As a consequence, such functions do not admit injective holomorphic extensions to the interior of the polynomial convex hull \(\widehat K\). On the other hand, it is shown that the restriction f*|G of the Gelfand-transform f* of an injective function fP(K) is injective on every regular, bounded complementary component G of K. A necessary and sufficient condition in terms of the behaviour of f on the outer boundary of K is given in order that f admit a holomorphic injective extension to \(\widehat K\). We also include some results on the existence of continuous logarithms on punctured compacta containing the origin in their boundary.  相似文献   

14.
This paper is devoted to the study of evolution problems of the form \(-\frac {du}{dr}(t) \in A(t)u(t) + f(t, u(t))\) in a new setting, where, for each t, A(t) : D(A(t)) → 2 H is a maximal monotone operator in a Hilbert space H and the mapping t?A(t) has continuous bounded or Lipschitz variation on [0, T], in the sense of Vladimirov’s pseudo-distance. The measure dr gives an upper bound of that variation. The perturbation f is separately integrable on [0, T] and separately Lipschitz on H. Several versions and new applications are presented.  相似文献   

15.
Let G be a non-compact group, K the compact subgroup fixed by a Cartan involution and assume G / K is an exceptional, symmetric space, one of Cartan type EF or G. We find the minimal integer, L(G),  such that any convolution product of L(G) continuous, K-bi-invariant measures on G is absolutely continuous with respect to Haar measure. Further, any product of L(G) double cosets has non-empty interior. The number L(G) is either 2 or 3, depending on the Cartan type, and in most cases is strictly less than the rank of G.  相似文献   

16.
We study the growth of the quantity ∫T|R′(z)|dm(z) for rational functions R of degree n which are bounded and univalent in the unit disk and prove that this quantity can grow like n γ , γ > 0, as n → ∞. Some applications of this result to problems of regularity of boundaries of Nevanlinna domains are considered. We also discuss a related result of Dolzhenko, which applies to general (non-univalent) rational functions.  相似文献   

17.
We prove that if R is a commutative, reduced, local ring, then R is Hopfian if and only if the ring R[x] is Hopfian. This answers a question of Varadarajan [16], in the case when R is a reduced local ring. We provide examples of non-Noetherian Hopfian commutative domains by proving that the finite dimensional domains are Hopfian. Also, we derive some general results related to Hopfian rings.  相似文献   

18.
In this paper, we are mainly concerned with semicontinuity of complete lattices and their distributive reflections, introduced by Rav in 1989. We prove that for a complete lattice L, the distributive reflection Ld is isomorphic to the lattice of all radicals determined by principal ideals of L in the set-inclusion order, obtaining a method to depict the distributive reflection of a given lattice. It is also proved that if a complete lattice L is semicontinuous and every semiprime element xL is the largest in d(x), then Ld is continuous whenever the distributive reflector d is Scott continuous. We construct counterexamples to confirm a conjecture and solve two open problems posed by Zhao in 1997.  相似文献   

19.
We study compact complex submanifolds S of quotient manifolds X = ?/Γ of irreducible bounded symmetric domains by torsion free discrete lattices of automorphisms, and we are interested in the characterization of the totally geodesic submanifolds among compact splitting complex submanifolds S ? X, i.e., under the assumption that the tangent sequence over S splits holomorphically. We prove results of two types. The first type of results concerns S ? X which are characteristic complex submanifolds, i.e., embedding ? as an open subset of its compact dual manifold M by means of the Borel embedding, the non-zero(1, 0)-vectors tangent to S lift under a local inverse of the universal covering map π : ? → X to minimal rational tangents of M.We prove that a compact characteristic complex submanifold S ? X is necessarily totally geodesic whenever S is a splitting complex submanifold. Our proof generalizes the case of the characterization of totally geodesic complex submanifolds of quotients of the complex unit ball Bnobtained by Mok(2005). The proof given here is however new and it is based on a monotonic property of curvatures of Hermitian holomorphic vector subbundles of Hermitian holomorphic vector bundles and on exploiting the splitting of the tangent sequence to identify the holomorphic tangent bundle TSas a quotient bundle rather than as a subbundle of the restriction of the holomorphic tangent bundle TXto S. The second type of results concerns characterization of total geodesic submanifolds among compact splitting complex submanifolds S ? X deduced from the results of Aubin(1978)and Yau(1978) which imply the existence of K¨ahler-Einstein metrics on S ? X. We prove that compact splitting complex submanifolds S ? X of sufficiently large dimension(depending on ?) are necessarily totally geodesic. The proof relies on the Hermitian-Einstein property of holomorphic vector bundles associated to TS,which implies that endomorphisms of such bundles are parallel, and the construction of endomorphisms of these vector bundles by means of the splitting of the tangent sequence on S. We conclude with conjectures on the sharp lower bound on dim(S) guaranteeing total geodesy of S ? X for the case of the type-I domains of rank2 and the case of type-IV domains, and examine a case which is critical for both conjectures, i.e., on compact complex surfaces of quotients of the 4-dimensional Lie ball, equivalently the 4-dimensional type-I domain dual to the Grassmannian of 2-planes in C~4.  相似文献   

20.
We give an example of an infinite metrizable space X such that the space Cp(X), of continuous real-valued functions on X endowed with the pointwise topology, is not homeomorphic to its own square Cp(X) × Cp(X). The space X is a zero-dimensional subspace of the real line. Our result answers a long-standing open question in the theory of function spaces posed by A. V. Arhangel’skii.  相似文献   

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