共查询到20条相似文献,搜索用时 15 毫秒
1.
Let X be a compact convex set and let ext X stand for the set of extreme points of X. We show that if $$f:X\rightarrow {\mathbb {R}}$$ is an affine function with the point of continuity property such that $$f\le 0$$ on $${\text {ext}}\,X$$, then $$f\le 0$$ on X. As a corollary of this minimum principle, we obtain a generalization of a theorem by C.H. Chu and H.B. Cohen by proving the following result. Let X, Y be compact convex sets such that every extreme point of X and Y is a weak peak point and let $$T:\mathfrak {A}^c(X)\rightarrow \mathfrak {A}^c(Y)$$ be an isomorphism such that $$\left\| T\right\| \cdot \left\| T^{-1}\right\| <2$$. Then $${\text {ext}}\,X$$ is homeomorphic to $${\text {ext}}\,Y$$. 相似文献
2.
In this paper, we mainly study a family of unbounded non-hyperbolic domains in $$\mathbb {C}^{n+m}$$, called Fock–Bargmann–Hartogs domains $$D_{n,m}(\mu )$$ ($$\mu >0$$) which are defined as a Hartogs type domains with the fiber over each $$z\in \mathbb {C}^{n}$$ being a ball of radius $$e^{-\frac{\mu }{2} {\Vert z\Vert }^{2}}$$. The purpose of this paper is twofold. Firstly, we obtain necessary and sufficient conditions for Rawnsley’s $$\varepsilon $$-function $$\varepsilon _{(\alpha ,g)}(\widetilde{w})$$ of $$\big (D_{n,m}(\mu ), g(\mu ;\nu )\big )$$ to be a polynomial in $$\Vert \widetilde{w}\Vert ^2$$, where $$g(\mu ;\nu )$$ is a Kähler metric associated with the Kähler potential $$\nu \mu {\Vert z\Vert }^{2} -\ln (e^{-\mu {\Vert z\Vert }^{2}}-\Vert w\Vert ^2)$$. Secondly, using above results, we study the Berezin quantization on $$D_{n,m}(\mu )$$ with the metric $$\beta g(\mu ;\nu )$$$$(\beta >0)$$. 相似文献
3.
Yasushi Nagata 《Annals of the Institute of Statistical Mathematics》1983,35(1):193-199
Summary LetX be a random variable from the one-parameter exponential family with the probability element β(θ) exp (θx)dm(x) for which an ambiguous prior information is available to the effect that θ is likely to be larger than or equal to a known
constant. The information is represented by a fuzzy set with the membership function χ(θ). Then it is shown that
is an admissible estimator for E
0
(X) under the quadratic loss function. 相似文献
4.
Piotr Migus 《Archiv der Mathematik》2019,112(4):395-405
Let
$$f,g:({\mathbb {R}}^n,0)\rightarrow ({\mathbb {R}}^m,0)$$
be
$$C^{r+1}$$
mappings and let
$$Z=\{x\in \mathbf {\mathbb {R}}^n:\nu (df (x))=0\}$$
,
$$0\in Z$$
,
$$m\le n$$
. We will show that if there exist a neighbourhood U of
$$0\in {\mathbb {R}}^n$$
and constants
$$C,C'>0$$
and
$$k>1$$
such that for
$$x\in U$$
$$\begin{aligned}&\nu (df(x))\ge C{\text {dist}}(x,Z)^{k-1}, \\&\left| \partial ^{s} (f_i-g_i)(x) \right| \le C'\nu (df(x))^{r+k-|s|}, \end{aligned}$$
for any
$$i\in \{1,\dots , m\}$$
and for any
$$s \in \mathbf {\mathbb {N}}^n_0$$
such that
$$|s|\le r$$
, then there exists a
$$C^r$$
diffeomorphism
$$\varphi :({\mathbb {R}}^n,0)\rightarrow ({\mathbb {R}}^n,0)$$
such that
$$f=g\circ \varphi $$
in a neighbourhood of
$$0\in {\mathbb {R}}^n$$
. By
$$\nu (df)$$
we denote the Rabier function. 相似文献
5.
Saharon Shelah 《Israel Journal of Mathematics》1988,62(3):355-380
Aroused by Todorcevic’s breakthrough we prove here some complementary consistency results, mainly
. We also get some generalization of his theorem to, e.g.,λ↛
forλ regular notω-Mahlo.
The author thanks the NSF and N.S.E.R.C. for partially supporting the research. Preliminary versions of §3 and §2 were circulated
in November ’84 and February ’85, respectively. 相似文献
6.
Let $$W(z_1, \ldots , z_n): ({\mathbb {C}}^*)^n \rightarrow {\mathbb {C}}$$ be a Laurent polynomial in n variables, and let $${\mathcal {H}}$$ be a generic smooth fiber of W. Ruddat et al. (Geom Topol 18:1343–1395, 2014) give a combinatorial recipe for a skeleton for $${\mathcal {H}}$$. In this paper, we show that for a suitable exact symplectic structure on $${\mathcal {H}}$$, the RSTZ-skeleton can be realized as the Liouville Lagrangian skeleton. 相似文献
7.
We consider an eigenvalue problem for a system on [0, 1]:
$$\left\{ {\begin{array}{*{20}l} {\left[ {\left( {\begin{array}{*{20}c} 0 & 1 \\ 1 & 0 \\ \end{array} } \right)\frac{{\text{d}}}
{{{\text{d}}x}} + \left( {\begin{array}{*{20}c} {p_{11} (x)} & {p_{12} (x)} \\ {p_{21} (x)} & {p_{22} (x)} \\ \end{array}
} \right)} \right]\left( {\begin{array}{*{20}c} {\varphi ^{(1)} (x)} \\ {\varphi ^{(2)} (x)} \\ \end{array} } \right) =
\lambda \left( {\begin{array}{*{20}c} {\varphi ^{(1)} (x)} \\ {\varphi ^{(1)} (x)} \\ \end{array} } \right)} \\ {\varphi
^{(2)} (0)\cosh \mu - \varphi ^{(1)} (0)\sinh \mu = \varphi ^{(2)} (1)\cosh \nu + \varphi ^{(1)} (1)\sinh \nu = 0} \\ \end{array}
} \right.$$ with constants
$$\mu ,\nu \in \mathbb{C}.$$ Under the assumption that p21, p22 are known, we prove a uniqueness theorem and provide a reconstruction formula for p11 and p12 from the spectral characteristics consisting of one spectrum and the associated norming constants. 相似文献
8.
Andrew Lorent 《Mathematische Annalen》2007,338(2):451-474
Given and any centrally symmetric convex polytope , define we prove that if a Radon measure μ has the property then s is an integer. For the case Θ is the Euclidean ball, this result was first proved by Marstrand in 1955 for Hausdorff measure
in the plane (Marstrand in Proc Lond Math Soc 3(4):257–302, 1954) and later for general Radon measures in (Marstrand in Trans Am Math Soc 205:369–392, 1964). 相似文献
9.
Given arbitrary integers d and r with
$$d \ge 4$$
and
$$1 \le r \le d + 1$$
, a reflexive polytope
$${\mathscr {P}}\subset {\mathbb R}^d$$
of dimension d with
$$\mathrm{depth}\,K[{\mathscr {P}}] = r$$
for which its dual polytope
$${\mathscr {P}}^\vee $$
is normal will be constructed, where
$$K[{\mathscr {P}}]$$
is the toric ring of
$${\mathscr {P}}$$
. 相似文献
10.
11.
Andreas Rosenschon 《K-Theory》2008,38(2):235-241
We give examples of smooth projective complex varieties of dimension d ≥ 4 and primes ℓ such that the morphic cohomology group is infinite, and is not finitely generated as a rational vector space. In particular, for these examples the semi-topological K-group has infinite dimension. 相似文献
12.
Francesca Crispo 《Acta Appl Math》2014,130(1):237-250
In this paper we study the nonlinear Klein-Gordon-Maxwell system $$\left \{\begin{array}{l@{\quad}l} -\Delta u+V(x)u-(2\omega+\phi)\phi u=f(x,u),&x\in{\mathbb{R}}^3,\\ \Delta \phi=(\omega+\phi)u^2,&x\in{\mathbb{R}}^3. \end{array} \right . $$ By means of a variant fountain theorem and the symmetric mountain pass theorem, we obtain the existence of infinitely many large energy solutions. 相似文献
13.
Bernd Greuel 《Results in Mathematics》1997,32(1-2):80-86
Generalizing two results of Rieger [8] and Selberg [10] we give asymptotic formulas for sums of type $${\matrix {\sum \limits_{n\leq x}\cr n\equiv l({\rm mod}k)\cr f_{\kappa}(n)\equiv s_{\kappa}({\rm mod}p_{\kappa})\cr (\kappa=1,\dots,r)\cr}}\qquad \chi(n)\qquad {\rm and} {\matrix {\sum \limits_{n\leq x}\cr n\equiv l({\rm mod}k)\cr f_{\kappa}(n)\equiv s_{\kappa}({\rm mod}p_{\kappa})\cr (\kappa=1,\dots,r)\cr}}\qquad \chi(n),$$ where χ is a suitable multiplicative function, f1,…, f r are “small” additive, prime-independent arithmetical functions and k, l are coprime. The proofs are based on an analytic method which consists of considering the Dirichlet series generated by $ \chi(n)z_{1}^{f_{1}(n)}\cdot... \cdot z_{r}^{f_{r}(n)},z_{1}\dots z_{r} $ complex. 相似文献
14.
Shen Yunfu 《数学学报(英文版)》1997,13(1):59-63
We define a new topology on the space of strong types on a subsetA of a model of a given theory and prove that either
. We also deduce an open map theorem. 相似文献
15.
Luiz Renato Fontes Roberto H. Schonmann 《Probability Theory and Related Fields》2008,141(3-4):513-541
We study the threshold θ ≥ 2 contact process on a homogeneous tree of degree κ = b + 1, with infection parameter λ ≥ 0 and started from a product measure with density p. The corresponding mean-field model displays a discontinuous transition at a critical point and for it survives iff , where this critical density satisfies , . For large b, we show that the process on has a qualitatively similar behavior when λ is small, including the behavior at and close to the critical point . In contrast, for large λ the behavior of the process on is qualitatively distinct from that of the mean-field model in that the critical density has . We also show that , where 1 < Φ2 < Φ3 < ..., , and .
The work of L.R.F. was partially supported by the Brazilian CNPq through grants 307978/2004-4 and 475833/2003-1, and by FAPESP
through grant 04/07276-2. The work of R.H.S. was partially supported by the American N.S.F. through grant DMS-0300672. 相似文献
16.
Alena Haddley Poj Lertchoosakul Radhakrishnan Nair 《Periodica Mathematica Hungarica》2017,74(1):128-136
Let \(\kappa \) be an infinite cardinal, and \(2^\kappa <\lambda \le 2^{\kappa ^+}\). We prove that if there is a weak diamond on \(\kappa ^+\) then every \(\{C_\alpha :\alpha <\lambda \}\subseteq \mathcal {D}_{\kappa ^+}\) satisfies Galvin’s property. On the other hand, Galvin’s property is consistent with the failure of the weak diamond (and even with Martin’s axiom in the case of \(\aleph _1\)). We derive some consequences about weakly inaccessible cardinals. We also prove that the negation of a similar property follows from the proper forcing axiom. 相似文献
17.
We prove that, under CH, any space with a regular \({G_{\delta}}\)-diagonal and caliber \({\omega_1}\) is separable; a corollary of this result answers, under CH, a question of Buzyakova. For any Urysohn space X, we establish the inequality \({|X|\leqq wL{(X)}^{s\Delta_2(X)\cdot{\dot(X)}}}\) which represents a generalization of a theorem of Basile, Bella, and Ridderbos. We also show that if X is a Hausdorff space, then \({|X| \leqq {(\pi\chi(X)\cdot d(X))}^{{\rm ot}(X)\cdot\psi_c(X)}}\); this result implies ?apirovski?’s inequality \({|X|\leqq \pi\chi{(X)}^{c(X)\cdot\psi(X)}}\) which only holds for regular spaces. It is also proved that \({|X|\leqq \pi\chi{(X)}^{{\rm ot}(X)\cdot\psi_c(X)\cdot aL_c(X)}}\) for any Hausdorff space X; this gives one more generalization of the famous Arhangel’skii’s inequality \({|X|\le 2^{\chi(X)\cdot L(X)}}\). 相似文献
18.
Notes on combinatorial set theory 总被引:1,自引:0,他引:1
Saharon Shelah 《Israel Journal of Mathematics》1973,14(3):262-277
We shall prove some unconnected theorems: (1) (G.C.H.) \omega _{\alpha + 1} \to \left( {\omega _\alpha + \xi } \right)_2^2 when ℵα is regular, │ξ│+<ωα. (2) There is a Jonsson algebra in ℵα+n, and \aleph _{a + n} \not \to \left[ {\aleph _{a + n} } \right]_{\aleph _{a + n} }^{n + 1} if 2^{\aleph _{ - - } } = \aleph
_{a + n} \cdot (3) If λ>ℵ0 is a strong limit cardinal, then among the graphs with ≦λ vertices each of valence <λ there is a universal one. (4)(G.C.H.) If f is a set mapping on \omega _{a + 1} (ℵα regular) │f(x)∩f(y│<ℵα, then there is a free subset of order-type ζ for every ζ<ωα+1. 相似文献
19.
Results in Mathematics - The link operator $${P_{\alpha}^\rho(f,x)=\sum_{k=1}^\infty s_{\alpha,k}(x)\int_0^\infty \theta_{\alpha,k}^\rho(t)f(t)dt+e^{-\alpha x}f(0)}$$ , $${\alpha, \rho >... 相似文献
20.
For an idealJ on an infinite setX with add(J)=κ, let
be the smallest size of any subfamilyY ofJ with the property that any member ofJ can be covered by less than κ members ofY. We study the value of
forA in
, where
denotes the smallest [δ]<θ ideal onP
κ(λ). We also discuss the problem of whether there exists a setA such that
, or even
.
Some of the material in this paper originally appeared as part of the author's doctoral dissertation completed at the Université
de Caen, 1998.
Partially supported by the Israel Science Foundation. Publication 813. 相似文献