共查询到20条相似文献,搜索用时 15 毫秒
1.
B. FISHER K. TAS 《数学学报(英文版)》2006,22(6):1639-1644
Let f and g be distributions and let gn = (g * δn)(x), where δn (x) is a certain converging to the Dirac delta function. The non-commutative neutrix product fog of f and g to be the limit of the sequence {fgn }, provided its limit h exists in the sense that sequence is defined N-lim n-∞(f(x)g,, (x), φ(x)〉 = (h(x), φ(x)},for all functions p in 2. It is proved that (x^λ+1n^px+)0(x^μ+1n^qx+)=x+^λμ1n^p+qx+,(x^λ-1n^qx-)=x-^λ+μ1n^p+qx-,for λ+μ〈-1; λ,μ, λ+μ≠-1,-2…and p,q=0,1,2…… 相似文献
2.
For a fixed positive number γ, a real-valued function f defined on a convex subset D of a normed space X is said to be γ-convex if it satisfies the inequality
whenever x0, x1 ∈D and
. This paper presents some results on the boundedness and continuity of γ-convex functions. For instance, (a) if there is some x*∈D such that f is bounded below on D∩b̄(x*,γ), then so it is on each bounded subset of D; (b) if f is bounded on some closed ball b̄(x*,γ/2)⊂ D and D′ is a closed bounded subset of D, then f is bounded on D′ iff it is bounded above on the boundary of D′; (c) if dim X>1 and the interior of D contains a closed ball of radius γ, then f is either locally bounded or nowhere locally bounded in the interior of D; (d) if D contains some open ball B(x*,γ/2) in which f has at most countably many discontinuities, then the set of all points at which f is continuous is dense in D.The authors thank the referees for constructive remarks 相似文献
3.
The existence of multiple positive solutions is presented for the singular second-order boundary value problems
using the fixed point index, where f may be singular at x = 0 and x′ = 0.
The project is supported by the fund of natural science of Shandong Province. 相似文献
4.
Emin Özçag 《Proceedings Mathematical Sciences》1999,109(1):87-94
The distributionF(x
+, −r) Inx+ andF(x
−, −s) corresponding to the functionsx
+
−r lnx+ andx
−
−s respectively are defined by the equations
(1) and
(2) whereH(x) denotes the Heaviside function. In this paper, using the concept of the neutrix limit due to J G van der Corput [1], we evaluate
the non-commutative neutrix product of distributionsF(x
+, −r) lnx+ andF(x
−, −s). The formulae for the neutrix productsF(x
+, −r) lnx
+ ox
−
−s, x+
−r lnx+ ox
−
−s andx
−
−s o F(x+, −r) lnx+ are also given forr, s = 1, 2, ... 相似文献
5.
O. N. Litvin 《Ukrainian Mathematical Journal》1992,44(11):1378-1384
A general algorithm is proposed for constructing interlineation operators
, x=(x1, x2) with the properties
相似文献
6.
Let F be a subfield of a commutative field extending ℝ. Let
We say thatf :
preserves distanced ≥ 0 if for eachx,y ∈ ℝ ∣x- y∣= d implies ϕ2(f(x),f(y)) = d2
. We prove that each unit-distance preserving mappingf :
has a formI o (ρ,ρ), where
is a field homomorphism and
is an affine mapping with orthogonal linear part. 相似文献
7.
We count the number S(x) of quadruples \( {\left( {x_{1} ,x_{2} ,x_{3} ,x_{4} } \right)} \in \mathbb{Z}^{4} \) for which 相似文献
$ p = x^{2}_{1} + x^{2}_{2} + x^{2}_{3} + x^{2}_{4} \leqslant x $ 8.
J. B. Lasserre 《TOP》2012,20(1):119-129
We consider the semi-infinite optimization problem:
|