共查询到20条相似文献,搜索用时 683 毫秒
1.
Examples of factorial threefolds complete intersection in $${\mathbb{P}^5}$$ with many singularities
Pietro Sabatino 《Ricerche di matematica》2009,58(2):285-297
Denote by ν
m
(d) the maximal integer for which there exists for d >> 0{d \gg 0} a threefold
X ì \mathbbP5{X\subset \mathbb{P}^5} complete intersection of hypersurfaces of degree respectively d and d − 1 such that X has only ordinary singularities of order m and |Sing(X)| = ν
m
(d). We prove that, nm(d) 3 j(d){\nu_m(d)\ge \varphi(d)} where j(d) ~ d5{\varphi(d)\sim d^5} asymptotically. This result extends (Di Gennaro and Franco in Commun Contemp Math 10(5):745–764, 2008, Corollary 2.10). 相似文献
2.
Let M{\mathcal M} be a σ-finite von Neumann algebra and
\mathfrak A{\mathfrak A} a maximal subdiagonal algebra of M{\mathcal M} with respect to a faithful normal conditional expectation F{\Phi} . Based on Haagerup’s noncommutative L
p
space Lp(M){L^p(\mathcal M)} associated with M{\mathcal M} , we give a noncommutative version of H
p
space relative to
\mathfrak A{\mathfrak A} . If h
0 is the image of a faithful normal state j{\varphi} in L1(M){L^1(\mathcal M)} such that j°F = j{\varphi\circ \Phi=\varphi} , then it is shown that the closure of
{\mathfrak Ah0\frac1p}{\{\mathfrak Ah_0^{\frac1p}\}} in Lp(M){L^p(\mathcal M)} for 1 ≤ p < ∞ is independent of the choice of the state preserving F{\Phi} . Moreover, several characterizations for a subalgebra of the von Neumann algebra M{\mathcal M} to be a maximal subdiagonal algebra are given. 相似文献
3.
On the iterates of Euler's function 总被引:1,自引:0,他引:1
R. Warlimont 《Archiv der Mathematik》2001,76(5):345-349
Asymptotic representations are given for the three sums ?n £ x j(n)/j(j(n))\textstyle\sum\limits \limits _{n\le x} \varphi (n)/\varphi \bigl (\varphi (n)\bigr ), ?n £ x j(n)/j(j(n))\textstyle\sum\limits \limits _{n\le x} \varphi (n)/\varphi \bigl (\varphi (n)\bigr ), ?n £ x log j(n)/j(j(n)) ; j\textstyle\sum\limits \limits _{n\le x}\ \log \, \varphi (n)/\varphi \bigl (\varphi (n)\bigr )\ ; \ \varphi is Euler's function. 相似文献
4.
Misha Verbitsky 《Mathematische Zeitschrift》2010,264(4):939-957
Let (M, ω) be a Kähler manifold. An integrable function ${\varphi}Let (M, ω) be a K?hler manifold. An integrable function j{\varphi} on M is called ω
q
-plurisubharmonic if the current ddcjùwq-1{dd^c\varphi\wedge \omega^{q-1}} is positive. We prove that j{\varphi} is ω
q
-plurisubharmonic if and only if j{\varphi} is subharmonic on all q-dimensional complex subvarieties. We prove that a ω
q
-plurisubharmonic function is q-convex, and admits a local approximation by smooth, ω
q
-plurisubharmonic functions. For any closed subvariety Z ì M{Z\subset M} ,
dim\mathbbC Z £ q-1{\dim_\mathbb{C} Z\leq q-1} , there exists a strictly ω
q
-plurisubharmonic function in a neighbourhood of Z (this result is known for q-convex functions). This theorem is used to give a new proof of Sibony’s lemma on integrability of positive closed (p, p)-forms which are integrable outside of a complex subvariety of codimension ≥ p + 1. 相似文献
5.
Jean B. Lasserre 《Optimization Letters》2011,5(4):549-556
We consider the convex optimization problem P:minx {f(x) : x ? K}{{\rm {\bf P}}:{\rm min}_{\rm {\bf x}} \{f({\rm {\bf x}})\,:\,{\rm {\bf x}}\in{\rm {\bf K}}\}} where f is convex continuously differentiable, and
K ì \mathbb Rn{{\rm {\bf K}}\subset{\mathbb R}^n} is a compact convex set with representation
{x ? \mathbb Rn : gj(x) 3 0, j = 1,?,m}{\{{\rm {\bf x}}\in{\mathbb R}^n\,:\,g_j({\rm {\bf x}})\geq0, j = 1,\ldots,m\}} for some continuously differentiable functions (g
j
). We discuss the case where the g
j
’s are not all concave (in contrast with convex programming where they all are). In particular, even if the g
j
are not concave, we consider the log-barrier function fm{\phi_\mu} with parameter μ, associated with P, usually defined for concave functions (g
j
). We then show that any limit point of any sequence (xm) ì K{({\rm {\bf x}}_\mu)\subset{\rm {\bf K}}} of stationary points of fm, m? 0{\phi_\mu, \mu \to 0} , is a Karush–Kuhn–Tucker point of problem P and a global minimizer of f on K. 相似文献
6.
We establish conditions for the existence of an invariant set of the system of differential equations
\fracdj dt = a( j ), \fracdxdt = P( j )x + F( j, x ), \frac{{d{\rm{\varphi}} }}{{dt}} = a\left( {\rm{\varphi}} \right),\quad \frac{{dx}}{{dt}} = P\left( {\rm{\varphi}} \right)x + F\left( {{\rm{\varphi}}, x} \right), 相似文献
7.
V. A. Galaktionov 《NoDEA : Nonlinear Differential Equations and Applications》2009,16(5):597-655
The classic problem of regularity of boundary points for higher-order partial differential equations (PDEs) is concerned.
For second-order elliptic and parabolic equations, this study was completed by Wiener’s (J. Math. Phys. Mass. Inst. Tech.
3:127–146, 1924) and Petrovskii’s (Math. Ann. 109:424–444, 1934) criteria, and was extended to more general equations including
quasilinear ones. Since the 1960–1970s, the main success was achieved for 2mth-order elliptic PDEs; e.g., by Kondrat’ev and Maz’ya. However, the higher-order parabolic ones, with infinitely oscillatory
kernels, were not studied in such details. As a basic model, explaining typical difficulties of regularity issues, the 1D
bi-harmonic equation in a domain shrinking to the origin (0, 0) is concentrated upon:
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