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961.
Let K be an algebraic number field and f a complex-valued function on the ideal class group of K. Then, f extends in a natural way to the set of all non-zero ideals of the ring of integers of K and we can consider the Dirichlet series \({L(s,f) =\sum_{{\mathfrak a}} f({\mathfrak a}){\bf N}({\mathfrak a})^{-s}}\) which converges for \({{\mathfrak R}(s) >1 }\). After extending this function to \({{\mathfrak R}(s)=1}\), and in the case that f does not contain the trivial character, we study the special value L(1, f) when f is algebraic valued and K is an imaginary quadratic field. Applying Kronecker’s limit formula and Baker’s theory of linear forms in logarithms, we derive a variety of results related to the transcendence of this special value. 相似文献
962.
Let f:X→Y be an algebraic fiber space with general fiber F. If Y is of maximal Albanese dimension, we show that κ(X)≥κ(Y)+κ(F). 相似文献
963.
Dimitrios Bagkavos 《Annals of the Institute of Statistical Mathematics》2011,63(5):1019-1046
A new kernel based local linear estimate of the hazard rate, under the random right censorship model is proposed in this article.
We study its finite sample and asymptotic properties and prove its asymptotic normality. Then we bring in three popular methods
for bandwidth selection to the hazard setting as potential bandwidth choice rules for the estimate. We discuss their practical
implementation and through Monte Carlo simulations we use four distributions with different hazard rate shapes to compare
their performance over various sample sizes and levels of censoring. 相似文献
964.
In this paper, we show the following result: Let K
i
be a knot in a closed orientable 3-manifold M
i
such that (M
i
,K
i
) is not homeomorphic to (S
2 ×S
1, x
0 ×S
1), i = 1, 2. Suppose that the Euler Characteristic of any meridional essential surface in each knot complement E(K
i
) is less than the difference of one and twice of the tunnel number of K
i
. Then the tunnel number of their connected sum will not go down. If in addition that the distance of any minimal Heegaard
splitting of each knot complement is strictly more than 2, then the tunnel number of their connected sum is super additive. 相似文献
965.
Danilo Bazzanella 《Archiv der Mathematik》2011,97(5):453-458
Let d(n) denote the number of positive divisors of the natural number n. The aim of this paper is to investigate the validity of the asymptotic formulafor \({x \to + \infty,}\) assuming a hypothetical estimate on the meanwhich is a weakened form of a conjecture of M. Jutila.
相似文献
$\begin{array}{lll}\sum \limits_{x < n \leq x+h(x)}d(n)\sim h(x)\log x\end{array}$
$\begin{array}{lll} \int \limits_X^{X+Y}(\Delta(x+h(x))-\Delta (x))^2\,{d}x, \end{array}$
966.
Sylvie Ruette 《Israel Journal of Mathematics》2011,184(1):275-299
For a continuous map on a topological graph containing a unique loop S it is possible to define the degree and, for a map of degree 1, rotation numbers. It is known that the set of rotation numbers
of points in S is a compact interval and for every rational r in this interval there exists a periodic point of rotation number r. The whole rotation set (i.e., the set of all rotation numbers) may not be connected and it is not known in general whether
it is closed. 相似文献
967.
We consider steady compressible Navier-Stokes-Fourier system in a bounded two-dimensional domain. We show the existence of
a weak solution for arbitrarily large data for the pressure law p(ϱ, ϑ) ∼ ϱ
γ
+ ϱϑ if γ > 1 and p(ϱ, ϑ) ∼ ϱ ln
α
(1 + ϱ) + ϱϑ if γ = 1, α > 0, depending on the model for the heat flux. 相似文献
968.
A heuristic framework for turbine layout optimization in a wind farm is proposed that combines ad-hoc heuristics and mixed-integer linear programming. In our framework, large-scale mixed-integer programming models are used to iteratively refine the current best solution according to the recently-proposed proximity search paradigm. Computational results on very large scale instances involving up to 20,000 potential turbine sites prove the practical viability of the overall approach. 相似文献
969.
Yong-Zhuo Chen 《Positivity》2016,20(1):115-130
In this paper, the stability of a class of nonautonomous nonlinear difference equations that are determined by functions which satisfy certain contractive type condition is studied in metric spaces, and its variant problem in ordered Banach spaces is also investigated. Several examples are given to illustrate their applications. 相似文献
970.
We study the algebra \({{\mathrm{{\mathcal {MD}}}}}\) of generating functions for multiple divisor sums and its connections to multiple zeta values. The generating functions for multiple divisor sums are formal power series in q with coefficients in \({\mathbb {Q}}\) arising from the calculation of the Fourier expansion of multiple Eisenstein series. We show that the algebra \({{\mathrm{{\mathcal {MD}}}}}\) is a filtered algebra equipped with a derivation and use this derivation to prove linear relations in \({{\mathrm{{\mathcal {MD}}}}}\). The (quasi-)modular forms for the full modular group \({{\mathrm{SL}}}_2({\mathbb {Z}})\) constitute a subalgebra of \({{\mathrm{{\mathcal {MD}}}}}\), and this also yields linear relations in \({{\mathrm{{\mathcal {MD}}}}}\). Generating functions of multiple divisor sums can be seen as a q-analogue of multiple zeta values. Studying a certain map from this algebra into the real numbers we will derive a new explanation for relations between multiple zeta values, including those of length 2, coming from modular forms. 相似文献