On some solutions of a functional equation related to the partial sums of the Riemann zeta function

In this paper, we prove that infinite-dimensional vector spaces of α-dense curves are generated by means of the functional equations f(x)+f(2x)+⋯+f(nx)=0, with n≥2, which are related to the partial sums of the Riemann zeta function. These curves α-densify a large class of compact sets of the plane for arbitrary small α, extending the known result that this holds for the cases n=2,3. Finally, we prove the existence of a family of solutions of such functional equation which has the property of quadrature in the compact that densifies, that is, the product of the length of the curve by the nth power of the density approaches the Jordan content of the compact set which the curve densifies.

A note on the real projection of the zeros of partial sums of Riemann zeta function

This paper proves that the real projection of each simple zero of any partial sum of the Riemann zeta function ζn(s):=∑nk=11ks,n>2 , is an accumulation point of the set {Res : ζ n (s) = 0}.

Computing the zeros of the partial sums of the Riemann zeta function

In this paper, we introduce a formula for the exact number of zeros of every partial sum of the Riemann zeta function inside infinitely many rectangles of the critical strips where they are situated.

The Zeros of Riemann Zeta Partial Sums Yield Solutions to f(x) + f(2x) + · · · + f(nx) = 0

This paper proves that every zero of any n th , n ≥ 2, partial sum of the Riemann zeta function provides a vector space of basic solutions of the functional equation f(x)+f(2x)+⋯+f(nx)=0,x∈R . The continuity of the solutions depends on the sign of the real part of each zero.

Measuring color differences in automotive samples with lightness flop: a test of the AUDI2000 color-difference formula

From a set of gonioapparent automotive samples from different manufacturers we selected 28 low-chroma color pairs with relatively small color differences predominantly in lightness. These color pairs were visually assessed with a gray scale at six different viewing angles by a panel of 10 observers. Using the Standardized Residual Sum of Squares (STRESS) index, the results of our visual experiment were tested against predictions made by 12 modern color-difference formulas. From a weighted STRESS index accounting for the uncertainty in visual assessments, the best prediction of our whole experiment was achieved using AUDI2000, CAM02-SCD, CAM02-UCS and OSA-GP-Euclidean color-difference formulas, which were no statistically significant different among them. A two-step optimization of the original AUDI2000 color-difference formula resulted in a modified AUDI2000 formula which performed both, significantly better than the original formula and below the experimental inter-observer variability. Nevertheless the proposal of a new revised AUDI2000 color-difference formula requires additional experimental data.

The Critical Strips of the Sums 1 + 2z + ... + nz

We give a partition of the critical strip, associated with each partial sum 1 + 2z + ... + nz of the Riemann zeta function for Re z < −1, formed by infinitely many rectangles for which a formula allows us to count the number of its zeros inside each of them with an error, at most, of two zeros. A generalization of this formula is also given to a large class of almost-periodic functions with bounded spectrum.

Use of subpixel techniques in pocket cameras to measure vibrations and displacements

Presentación oral SPIE Photonics Europe, Brussels, 16-19 April 2012.

Internalization of quality management in service organizations

Purpose – The purpose of this paper is to analyze the internalization of quality management (QM) on the basis of quality certifiable standards – also referred to as meta-standards – in service organizations. More specifically, the paper analyzes the case of the internalization of a quality standard in the Spanish hotel industry. Design/methodology/approach – The paper examines the relationships between the measures of internalization, benefit, QM tools and motivation, using partial least squares in the framework of the structural equation modeling technique. Findings – The results show that the hotels that have internalized the standard to a greater extent are more likely to be driven by internal motivation, develop more QM tools and achieve greater benefits than the hotels with a lower degree of internalization. Originality/value – As previous studies have examined these issues in relation to the internalization of ISO standards, the present study adds to this important stream of research and contributes by advancing the understanding of these issues through the case of a specific standard for the hotel industry.

The effects of quality and environmental management on competitive advantage: A mixed methods study in the hotel industry

This paper reports results derived from a mixed methods study where 13 hotel managers were initially interviewed, followed by a quantitative study of 355 additional managers. Data were analysed using partial least squares path modelling. The research question related to the relationship between quality and environmental management and the competitive advantage sought by hotels. The results indicate that quality management and environmental management permit the improvement of competitive advantage in terms of both costs and differentiation. Moreover, hotels implementing quality programmes find fewer obstacles in implementing environmental management.