广义Dedekind函数误差项的加权平方积分均值

研究了和式∑↑n≤x（n/ψ（n））^r的渐近公式中的误差项E（x;r）的加权平方积分均值。其中，r是正整数，ψ(n)是Dedekind函数。     

An integral formula for the total mean curvature matrix

The notion of total mean curvature matrix of a submanifold in ${\mathbb{R}}^n$ is defined. A kinematic integral formula for the total mean curvature matrix is proved.     

A footnote to mean square value of DirichletL-series

Following appropriate use of approximate functional equation for Hurwitz Zeta function, we obtain upper bounds for } Here fors = σ + it, L(s,x) denotes DirichletL-series for character x(modq). In particular, we obtain S(1/2 +it) ≪q logqt + t^5/8 q^−1/8, which is an improvement in the range q |t| < q^11/7, on hitherto best known result. This incidentally gives S(1/2+ it)≪ q log3q for |t|q^9/5.     

An integral representation for the weighted geometric mean and its applications

By virtue of Cauchy’s integral formula in the theory of complex functions,the authors establish an integral representation for the weighted geometric mean,apply this newly established integral representation to show that the weighted geometric mean is a complete Bernstein function,and find a new proof of the well-known weighted arithmetic-geometric mean inequality.     

Some results related to the integral mean value theorem

In this paper, some new results related to the integral mean value theorem are proven.     

On the mean square of Lerch zeta-functions

Using the approximate functional equation for L(l,a, s) = ?_n=0^￥ [(e(ln))/((n+a)^s)] L(\lambda,\alpha, s) = \sum\limits_{n=0}^{\infty} {e(\lambda n)\over (n+\alpha)^s} , we prove for fixed parameters $ 0<\lambda,\alpha\leq 1 $ 0<\lambda,\alpha\leq 1 asymptotic formulas for the mean square of L(l,a,s) L(\lambda,\alpha,s) inside the critical strip. This improves earlier results of D. Klusch and of A. Laurin)ikas.     

On the mean square of standard L-functions attached to Ikeda lifts

By using estimates on the frequency of large values of the Riemann zeta-function and modular L-functions attached to the full modular group SL(2, ℤ), we prove sharp upper and lower estimates of the mean square of standard L-functions attached to Siegel cusp forms which are Ikeda lifts, on boundaries and the central line of the critical strip. The mean square of spinor L-functions attached to Saito-Kurokawa lifts is also studied.     

On the integral mean value theorem

Novosibirsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 34, No. 6, pp. 150–152, November–December, 1993.     

An integral transform method for estimating the central mean and central subspaces

The central mean and central subspaces of generalized multiple index model are the main inference targets of sufficient dimension reduction in regression. In this article, we propose an integral transform (ITM) method for estimating these two subspaces. Applying the ITM method, estimates are derived, separately, for two scenarios: (i) No distributional assumptions are imposed on the predictors, and (ii) the predictors are assumed to follow an elliptically contoured distribution. These estimates are shown to be asymptotically normal with the usual root-n convergence rate. The ITM method is different from other existing methods in that it avoids estimation of the unknown link function between the response and the predictors and it does not rely on distributional assumptions of the predictors under scenario (i) mentioned above.     

Stochastic integral with respect to set-valued square integrable martingales

In this paper, we shall firstly illustrate why we should consider integral of a stochastic process with respect to a set-valued square integrable martingale. Secondly, we shall prove the representation theorem of set-valued square integrable martingale. Thirdly, we shall give the definition of stochastic integral of a stochastic process with respect to a set-valued square integrable martingale and the representation theorem of this kind of integrals. Finally, we shall prove that the stochastic integral is a set-valued sub-martingale.     

An Operatorial approach to singular integral equations of a modified type

In this article,the authors discuss a kind of modified singular integral equations on a disjoint union of closed contours or a disjoint union of open arcs.The authors introduce some singular integral operators associated with this kind of singular integral equations,and obtain some useful properties for them.An operatorial approach is also given together with some illustrated examples.     

An algorithm based on the regularization and integral mean value methods for the Fredholm integral equations of the first kind

In this paper, an algorithm based on the regularization and integral mean value methods, to handle the ill-posed multi-dimensional Fredholm equations, is introduced. The application of this algorithm is based on the transforming the first kind equation to a second kind equation by the regularization method. Then, by converting the first kind to a second kind, the integral mean value method is employed to handle the resulting Fredholm integral equations of the second kind. The efficiency of the approach will be shown by applying the procedure on some examples.