Addendum to the paper “on a theorem of Miranda”

An existence theorem is proved for closed convex surfaces whose principal radii of curvature regarded as functions of the unit normal vectorn satisfy the equation

Correction to the paper “on the curvature of a generalization of a contact metric manifolds”

We considered in Example 3.1 of the paper [1] an S-structure on R^2n+s . We concluded that when s > 1 this manifold cannot be of constant φ-sectional curvature. Unfortunately this result is wrong. In fact, essentially due to a sign mistake in defining the φ-structure and a consequent transposition of the elements of the φ-basis (3.2), some of the Christoffel’s symbols were incorrect. In the present rectification, using a more slendler tecnique, we prove that our manifold is of constant φ-sectional curvature −3s and then it is η-Einstein.     

The effective application of a new approach to the generalized orienteering problem

The Orienteering Problem (OP) is an important problem in network optimization in which each city in a network is assigned a score and a maximum-score path from a designated start city to a designated end city is sought that is shorter than a pre-specified length limit. The Generalized Orienteering Problem (GOP) is a generalized version of the OP in which each city is assigned a number of scores for different attributes and the overall function to optimize is a function of these attribute scores. In this paper, the function used was a non-linear combination of attribute scores, making the problem difficult to solve. The GOP has a number of applications, largely in the field of routing. We designed a two-parameter iterative algorithm for the GOP, and computational experiments suggest that this algorithm performs as well as or better than other heuristics for the GOP in terms of solution quality while running faster. Further computational experiments suggest that our algorithm also outperforms the leading algorithm for solving the OP in terms of solution quality while maintaining a comparable solution speed.     

How to estimate the sum of a series?

<正>Now we’ll learn how to estimate the sum of a series?We have been able to use the integral test to show that a series ∞∑(n=1)a_n is convergent or divergent.But we also don’t know the best way to find the sum of the series.It is difficult to compute the sum of any series.Here is the best way to find an approximation to the sum of the series.You know     

An operator-theoretic approach to theorems of the Pick-Nevanlinna and Carathéodory types

In this paper we deal with singularities of the linear systems of plane curves passing through S, where S is a zerodimensional closed subscheme of degree n of P ²=P _k ² ,k an algebraically closed field of any characteristic. We determine the least degree of a nonsingular curve passing through S, when S is in uniform position. This paper was written while the author was member of C.N.R., Sez. 3 of G.N.S.A.G.A. and was supported by M.P.I. funds     

Erratum to the paper “Quadratic descent of hermitian forms”

There exists a mistake in the proof of Theorem 4.2. We present a new proof of this theorem, which shows that the main results of the paper are still true.     

Corrigendum to “Note on zeros of the derivative of the Selberg zeta-function”

We correct constants in asymptotic formulas of our paper “Note on zeros of the derivative of the Selberg zeta-function”, Arch. Math. 91 (2008), 238–246. The online version of the original article can be found under doi:.     

Identifying the limiting distribution by a general approach of Stein’s method

A general exchange pair approach is developed to identify the limiting distribution for any sequence of random variables, by calculating the conditional mean and the conditional second moments. The error of approximation is also studied. In particular, a Berry-Esseen type bound of O(n~(-3/4)) is obtained for the Curie-Weiss model at the critical temperature.     

The absolute generalized harmonic-Cesàro summability of a Fourier series

[8] . , , [2] , . - , , , . .     

On a general class of trigonometric functions and Fourier series†

We discuss a general class of trigonometric functions whose corresponding Fourier series can be used to calculate several interesting numerical series. Particular cases are presented.     

Necessary conditions for the weak generalized localization of Fourier series with “lacunary sequence of partial sums”

It has been established that, on the subsets $ \mathbb{T}^N = [ - \pi ,\pi ]^N $ describing a cross W composed of N-dimensional blocks, $ W_{x_s x_t } = \Omega _{x_s x_t } \times [ - \pi ,\pi ]^{N - 2} (\Omega _{x_s x_t } $ is an open subset of [?π, π]²) in the classes $ L_p (\mathbb{T}^N ),p > 1 $ , a weak generalized localization holds, for N ≥ 3, almost everywhere for multiple trigonometric Fourier series when to the rectangular partial sums $ S_n (x;f)(x \in \mathbb{T}^N ,f \in L_p ) $ of these series corresponds the number n = (n ₁,…, n _N ) ∈ ? ₊ ^N , some components n _j of which are elements of lacunary sequences. In the present paper, we prove a number of statements showing that the structural and geometric characteristics of such subsets are sharp in the sense of the numbers (generating W) of the N-dimensional blocks $ W_{x_s x_t } $ as well as of the structure and geometry of $ W_{x_s x_t } $ . In particular, it is proved that it is impossible to take an arbitrary measurable two-dimensional set or an open three-dimensional set as the base of the block.     

Comments on “a numerical approach to the infinite horizon problem of deterministic control theory”

In the paper cited above a proof about an estimate of the rate of convergence for a special discretization scheme for the Hamilton—Jacobi equation is given. The proof is essentially based on the identification between functions andv _h ^k . Here we give a simple example which shows that this identification is incorrect.