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81.
Christian Jansson 《Journal of Global Optimization》2004,28(1):121-137
In this paper, we consider the computation of a rigorous lower error bound for the optimal value of convex optimization problems. A discussion of large-scale problems, degenerate problems, and quadratic programming problems is included. It is allowed that parameters, whichdefine the convex constraints and the convex objective functions, may be uncertain and may vary between given lower and upper bounds. The error bound is verified for the family of convex optimization problems which correspond to these uncertainties. It can be used to perform a rigorous sensitivity analysis in convex programming, provided the width of the uncertainties is not too large. Branch and bound algorithms can be made reliable by using such rigorous lower bounds. 相似文献
82.
For each sN define the constant θs with the following properties: if an entire function g(z) of type t(g)<θs satisfies then g is a polynomial; conversely, for any δ>0 there exists an entire transcendental function g(z) satisfying the display conditin and t(g)<θs+δ. The result θ1=log2 is known due to Hardy and Pólya. We provide the upper bound θsπs/3 and improve earlier lower bounds due to Gelfond (1929) and Selberg (1941). 相似文献
83.
In general, the sup-min convolution has been used for fuzzy arithmetic to analyze fuzzy system reliability, where the reliability of each system component is represented by fuzzy numbers. It is well known that Tω-based addition preserves the shape of L-R type fuzzy numbers. In this paper, we show Tω-based multiplication also preserves the shape of L-R type fuzzy numbers. We then apply Tω-based arithmetic operations to fuzzy system reliability analysis. In fact, we show that we can simplify fuzzy arithmetic operations and even get the exact solutions for L-R type fuzzy system reliability, while others [Singer, Fuzzy Sets Syst. 34 (1990) 145; Cheng and Mon, Fuzzy Sets Syst. 56 (1993) 29; Chen, Fuzzy Sets Syst. 64 (1994) 31] have got the approximate solutions using sup-min convolution for evaluating fuzzy system reliability. 相似文献
84.
Mean-value theorems and extensions of the Elliott-Daboussi theorem on additive arithmetic semigroups
Wen-Bin Zhang 《The Ramanujan Journal》2008,15(1):47-75
We present more general forms of the mean-value theorems established before for multiplicative functions on additive arithmetic
semigroups and prove, on the basis of these new theorems, extensions of the Elliott-Daboussi theorem. Let
be an additive arithmetic semigroup with a generating set ℘ of primes p. Assume that the number G(m) of elements a in
with “degree” ∂(a)=m satisfies
with constants q>1, ρ
1<ρ
2<⋅⋅⋅<ρ
r
=ρ, ρ≥1, γ>1+ρ. For the main result, let α,τ,η be positive constants such that α>1,τ
ρ≥1, and τ
α
ρ≥1. Then for a multiplicative function f(a) on
the following two conditions (A) and (B) are equivalent. These are (A) All four series
converge and
and (B) The order τ
ρ mean-value
exists with m
f
≠0 and the limit
exists with M
v
(α)>0.
相似文献
85.
In Oman and Salminen [19], the authors introduce and study residually small rings, defined as follows: an infinite commutative ring R with identity is residually smallif for every r∈R?{0}, there exists an ideal Ir of R such that r?Ir and |R∕Ir|<|R|. The purpose of this note is to extend our study. In particular, we continue our investigation of residually small rings and then generalize this notion to modules. 相似文献
86.
87.
给出了Toader型平均T[A(a,b),G(a,b)]关于调和平均H(a,b)与算术平均A(a,b)组合的精确界.作为应用,发现了几个关于第二类完全椭圆积分的精确不等式. 相似文献
88.
《Mathematische Nachrichten》2017,290(17-18):3029-3037
In this note, we show that any projective subspace arrangement can be realized as a generalized star configuration variety. This type of interpolation result may be useful in designing linear codes with prescribed codewords of minimum weight, as well as in answering a couple of questions about the number of equations needed to define a generalized star configuration variety. 相似文献
89.
90.
J.A. Tenreiro Machado 《Optimization》2014,63(8):1167-1179