共查询到20条相似文献,搜索用时 31 毫秒
1.
Pierre Maréchal 《Optimization Letters》2012,6(2):357-362
We generalize a well known convexity property of the multiplicative potential function. We prove that, given any convex function
g : \mathbbRm ? [0, ¥]{g : \mathbb{R}^m \rightarrow [{0}, {\infty}]}, the function ${({\rm \bf x},{\rm \bf y})\mapsto g({\rm \bf x})^{1+\alpha}{\bf y}^{-{\bf \beta}}, {\bf y}>{\bf 0}}${({\rm \bf x},{\rm \bf y})\mapsto g({\rm \bf x})^{1+\alpha}{\bf y}^{-{\bf \beta}}, {\bf y}>{\bf 0}}, is convex if β ≥ 0 and α ≥ β
1 + ··· + β
n
. We also provide further generalization to functions of the form (x,y1, . . . , yn)? g(x)1+af1(y1)-b1 ···fn(yn)-bn{({\rm \bf x},{\rm \bf y}_1, . . . , {y_n})\mapsto g({\rm \bf x})^{1+\alpha}f_1({\rm \bf y}_1)^{-\beta_1} \cdot \cdot \cdot f_n({\rm \bf y}_n)^{-\beta_n} } with the f
k
concave, positively homogeneous and nonnegative on their domains. 相似文献
2.
Igor V. Protasov 《Algebra Universalis》2009,62(4):339-343
Let ${\mathbb{A}}Let
\mathbbA{\mathbb{A}} be a universal algebra of signature Ω, and let I{\mathcal{I}} be an ideal in the Boolean algebra
P\mathbbA{\mathcal{P}_{\mathbb{A}}} of all subsets of
\mathbbA{\mathbb{A}} . We say that I{\mathcal{I}} is an Ω-ideal if I{\mathcal{I}} contains all finite subsets of
\mathbbA{\mathbb{A}} and f(An) ? I{f(A^{n}) \in \mathcal{I}} for every n-ary operation f ? W{f \in \Omega} and every A ? I{A \in \mathcal{I}} . We prove that there are 22à0{2^{2^{\aleph_0}}} Ω-ideals in
P\mathbbA{\mathcal{P}_{\mathbb{A}}} provided that
\mathbbA{\mathbb{A}} is countably infinite and Ω is countable. 相似文献
3.
In Finsler geometry, minimal surfaces with respect to the Busemann-Hausdorff measure and the Holmes-Thompson measure are called
BH-minimal and HT-minimal surfaces, respectively. In this paper, we give the explicit expressions of BH-minimal and HT-minimal
rotational hypersurfaces generated by plane curves rotating around the axis in the direction of
[(b)\tilde]\sharp{\tilde{\beta}^{\sharp}} in Minkowski (α, β)-space
(\mathbbVn+1,[(Fb)\tilde]){(\mathbb{V}^{n+1},\tilde{F_b})} , where
\mathbbVn+1{\mathbb{V}^{n+1}} is an (n+1)-dimensional real vector space, [(Fb)\tilde]=[(a)\tilde]f([(b)\tilde]/[(a)\tilde]), [(a)\tilde]{\tilde{F_b}=\tilde{\alpha}\phi(\tilde{\beta}/\tilde{\alpha}), \tilde{\alpha}} is the Euclidean metric, [(b)\tilde]{\tilde{\beta}} is a one form of constant length
b:=||[(b)\tilde]||[(a)\tilde], [(b)\tilde]\sharp{b:=\|\tilde{\beta}\|_{\tilde{\alpha}}, \tilde{\beta}^{\sharp}} is the dual vector of [(b)\tilde]{\tilde{\beta}} with respect to [(a)\tilde]{\tilde{\alpha}} . As an application, we first give the explicit expressions of the forward complete BH-minimal rotational surfaces generated
around the axis in the direction of
[(b)\tilde]\sharp{\tilde{\beta}^{\sharp}} in Minkowski Randers 3-space
(\mathbbV3,[(a)\tilde]+[(b)\tilde]){(\mathbb{V}^{3},\tilde{\alpha}+\tilde{\beta})} . 相似文献
4.
We consider the spectral decomposition of A, the generator of a polynomially bounded n-times integrated group whose spectrum set $\sigma(A)=\{i\lambda_{k};k\in\mathbb{\mathbb{Z}}^{*}\}We consider the spectral decomposition of A, the generator of a polynomially bounded n-times integrated group whose spectrum set
s(A)={ilk;k ? \mathbb\mathbbZ*}\sigma(A)=\{i\lambda_{k};k\in\mathbb{\mathbb{Z}}^{*}\}
is discrete and satisfies
?\frac1|lk|ldkn < ¥\sum \frac{1}{|\lambda_{k}|^{\ell}\delta_{k}^{n}}<\infty
, where ℓ is a nonnegative integer and
dk=min(\frac|lk+1-lk|2,\frac|lk-1-lk|2)\delta _{k}=\min(\frac{|\lambda_{k+1}-\lambda _{k}|}{2},\frac{|\lambda _{k-1}-\lambda _{k}|}{2})
. In this case, Theorem 3, we show by using Gelfand’s Theorem that there exists a family of projectors
(Pk)k ? \mathbb\mathbbZ*(P_{k})_{k\in\mathbb{\mathbb{Z}}^{*}}
such that, for any x∈D(A
n+ℓ
), the decomposition ∑P
k
x=x holds. 相似文献
5.
Hassan Issa 《Integral Equations and Operator Theory》2011,70(4):569-582
Let
W ì \mathbb Cd{\Omega \subset{\mathbb C}^{d}} be an irreducible bounded symmetric domain of type (r, a, b) in its Harish–Chandra realization. We study Toeplitz operators Tng{T^{\nu}_{g}} with symbol g acting on the standard weighted Bergman space Hn2{H_\nu^2} over Ω with weight ν. Under some conditions on the weights ν and ν
0 we show that there exists C(ν, ν
0) > 0, such that the Berezin transform [(g)\tilde]n0{\tilde{g}_{\nu_{0}}} of g with respect to H2n0{H^2_{\nu_0}} satisfies:
\labele0||[(g)\tilde]n0||¥ £ C(n,n0)||Tng||,\label{e0}\|\tilde{g}_{\nu_0}\|_\infty \leq C(\nu,\nu_0)\|T^\nu_g\|, 相似文献
6.
D. S. Romanov 《Computational Mathematics and Modeling》2012,23(1):72-78
The article studies diagnostic tests for local k -fold coalescences of variables in Boolean functions f( [(x)\tilde]n )( 1 £ k £ n, 1 £ t £ 22k ) f\left( {{{\tilde{x}}^n}} \right)\left( {1 \leq k \leq n,\;1 \leq t \leq {2^{{2^k}}}} \right) . Upper and lower bounds are proved for the Shannon function of the length of the diagnostic test for local k -fold coalescences generated by the system of functions Ftk \Phi_t^k . The Shannon function of the length of a complete diagnostic test for local k -fold coalescences behaves asymptotically as 2
k
(n − k + 1) for n → ∞, k → ∞. 相似文献
7.
A new generalized Radon transform R
α, β
on the plane for functions even in each variable is defined which has natural connections with the bivariate Hankel transform,
the generalized biaxially symmetric potential operator Δ
α, β
, and the Jacobi polynomials Pk(b, a)(t)P_{k}^{(\beta,\,\alpha)}(t). The transform R
α, β
and its dual Ra, b*R_{\alpha,\,\beta}^{\ast} are studied in a systematic way, and in particular, the generalized Fuglede formula and some inversion formulas for R
α, β
for functions in
La, bp(\mathbbR2+)L_{\alpha,\,\beta}^{p}(\mathbb{R}^{2}_{+}) are obtained in terms of the bivariate Hankel–Riesz potential. Moreover, the transform R
α, β
is used to represent the solutions of the partial differential equations Lu:=?j=1majDa, bju=fLu:=\sum_{j=1}^{m}a_{j}\Delta_{\alpha,\,\beta}^{j}u=f with constant coefficients a
j
and the Cauchy problem for the generalized wave equation associated with the operator Δ
α, β
. Another application is that, by an invariant property of R
α, β
, a new product formula for the Jacobi polynomials of the type Pk(b, a)(s)C2ka+b+1(t)=còòPk(b, a)P_{k}^{(\beta,\,\alpha)}(s)C_{2k}^{\alpha+\beta+1}(t)=c\int\!\!\int P_{k}^{(\beta,\,\alpha)} is obtained. 相似文献
8.
A class Uk1 (J){\mathcal{U}}_{\kappa 1} (J) of generalized J-inner mvf’s (matrix valued functions) W(λ) which appear as resolvent matrices for bitangential interpolation problems in the generalized Schur class of p ×q mvf¢s Skp ×qp \times q \, {\rm mvf's}\, {\mathcal{S}}_{\kappa}^{p \times q} and some associated reproducing kernel Pontryagin spaces are studied. These spaces are used to describe the range of the
linear fractional transformation TW based on W and applied to Sk2p ×q{\mathcal{S}}_{\kappa 2}^{p \times q}. Factorization formulas for mvf’s W in a subclass U°k1 (J) of Uk1(J){\mathcal{U}^{\circ}_{\kappa 1}} (J)\, {\rm of}\, {\mathcal{U}}_{\kappa 1}(J) found and then used to parametrize the set Sk1+k2p ×q ?TW [ Sk2p ×q ]{\mathcal{S}}_{{\kappa 1}+{\kappa 2}}^{p \times q} \cap T_{W} \left[ {\mathcal{S}}_{\kappa 2}^{p \times q} \right]. Applications to bitangential interpolation problems in the class Sk1+k2p ×q{\mathcal{S}}_{{\kappa 1}+{\kappa 2}}^{p \times q} will be presented elsewhere. 相似文献
9.
W?odzimierz B?k 《Potential Analysis》2010,32(1):17-27
A modification of the Lyons-Sullivan discretization of positive harmonic functions on a Riemannian manifold M is proposed. This modification, depending on a choice of constants C = {C
n
:n = 1,2,..}, allows for constructing measures nxC, x ? M\nu_x^\mathbf{C},\ x\in M, supported on a discrete subset Γ of M such that for every positive harmonic function f on M
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