Learning Curves and p-charts for a preliminary estimation of asymptotic performances of a manufacturing process

This paper presents a method for a preliminary estimation of asymptotic performances of a manufacturing process based on the knowledge of its learning curve estimated during the setting up of p-chart. The main novelties of the method are the possibility of estimating the asymptotic variability of a process and providing a simple approach for evaluating the period of revision of process control limits. An application of the method to a real example taken from the literature is also provided

Validity of the zero-thermodynamic law in off-equilibrium coupled harmonic oscillators

In order to describe the thermodynamics of the glassy systems it has been recently introduced an extra parameter also called effective temperature which generalizes the fluctuation-dissipation theorem (FDT) to systems off-equilibrium and supposedly describes thermal fluctuations around the aging state. Here we investigate the applicability of a zero-th law for non-equilibrium glassy systems based on these effective temperatures by studying two coupled subsystems of harmonic oscillators with Monte Carlo dynamics. We analyze in detail two types of dynamics: 1) sequential dynamics where the coupling between the subsystems comes only from the Hamiltonian and 2) parallel dynamics where there is a further coupling between the subsystems arising from the dynamics. We show that the coupling described in the first case is not enough to make asymptotically the effective temperatures of two interacting subsystems coincide, the reason being the too small thermal conductivity between them in the aging state. This explains why different interacting degrees of freedom in structural glasses may stay at different effective temperatures without never mutually thermalizing.Comment: 23 pages, REVTeX, 4 eps figure

Almost all trees are almost graceful

The Graceful Tree Conjecture of Rosa from 1967 asserts that the vertices of each tree T of order n can be injectively labeled by using the numbers {1,2,…,n} in such a way that the absolute differences induced on the edges are pairwise distinct. We prove the following relaxation of the conjecture for each γ>0 and for all n>n 0(γ). Suppose that (i) the maximum degree of T is bounded by (Formula presented.)), and (ii) the vertex labels are chosen from the set {1,2,…,⌈(1+γ)n⌉}. Then there is an injective labeling of V(T) such that the absolute differences on the edges are pairwise distinct. In particular, asymptotically almost all trees on n vertices admit such a labeling. The proof proceeds by showing that a certain very natural randomized algorithm produces a desired labeling with high probability

An assessment of the strength of knots and splices used as eye terminations in a sailing environment

Research into knots, splices and other methods of forming an eye termination has been limited, despite the fact that they are essential and strongly affect the performance of a rope. The aim of this study was to carry out a comprehensive initial assessment of the breaking strength of eye terminations commonly used in a sailing environment, thereby providing direction for further work in the field. Supports for use in a regular tensile testing machine were specially developed to allow individual testing of each sample and a realistic spread of statistical data to be obtained. Over 180 break tests were carried out on four knots (the bowline, double bowline, figure-of-eight loop and perfection loop) and two splices (three-strand eye splice and braid-on-braid splice). The factors affecting their strength were investigated. A statistical approach to the analysis of the results was adopted. The type of knot was found to have a significant effect on the strength. This same effect was seen in both types of rope construction (three-strand and braid-on-braid). Conclusions were also drawn as to the effect of splice length, eye size, manufacturer and rope diameter on the breaking strength of splices. Areas of development and further investigation were identified

On some problems involving Hardy's function

Some problems involving the classical Hardy function $$Z(t) := \zeta(1/2+it)\bigl(\chi(1/2+it)\bigr)^{-1/2}, \quad \zeta(s) = \chi(s)\zeta(1-s)$$ are discussed. In particular we discuss the odd moments of $Z(t)$, the distribution of its positive and negative values and the primitive of $Z(t)$. Some analogous problems for the mean square of $|\zeta(1/2+it)|$ are also discussed.Comment: 15 page

Structure and phase-composition of Ti-doped gas atomized Raney-type Ni catalyst precursor alloys

Raney-type Ni precursor alloys containing 75 at.% Al and doped with 0, 0.75, 1.5 and 3.0 at.% Ti have been produced by a gas atomization process. The resulting powders have been classified by size fraction with subsequent investigation by powder XRD, SEM and EDX analysis. The undoped powders contain, as expected, the phases Ni2Al3, NiAl3 and an Al-eutectic. The Ti-doped powders contain an additional phase with the TiAl3 DO22 crystal structure. However, quantitative analysis of the XRD results indicate a far greater fraction of the TiAl3 phase is present than could be accounted for by a simple mass balance on Ti. This appears to be a (TixNi1-x)Al3 phase in which higher cooling rates favour small x (low Ti-site occupancy by Ti atoms). SEM and EDX analysis reveal that virtually all the available Ti is contained within the TiAl3 phase, with negligible Ti dissolved in either the Ni2Al3 or NiAl3 phases

Associations of Hair Dye and Relaxer Use with Breast Tumor Clinicopathologic Features: Findings from the Women’s Circle of Health Study

Background Building upon our earlier findings of significant associations between hair dye and relaxer use with increased breast cancer risk, we evaluated associations of select characteristics of use with breast tumor clinicopathology. Methods Using multivariable-adjusted models we examined the associations of interest in a case-only study of 2998 women with breast cancer, overall and stratified by race and estrogen receptor (ER) status, addressing multiple comparisons using Bonferroni correction. Results Compared to salon application of permanent hair dye, home kit and combination application (both salon and home kit application) were associated with increased odds of poorly differentiated tumors in the overall sample. This association was consistent among Black (home kit: OR 2.22, 95 % CI: 1.21–5.00; combination: OR 2.46, 95 % CI: 1.21–5.00), but not White women, and among ER+ (home kit: OR 1.47, 95 % CI: 0.82–2.63; combination: OR 2.98, 95 % CI: 1.62–5.49) but not ER-cases. Combination application of relaxers was associated with increased odds of tumors \u3e2.0 cm vs. \u3c1.0 cm (OR = 1.82, 95 % CI: 1.23–2.69). Longer duration and earlier use of relaxers and combination application of permanent hair dyes and relaxers were associated with breast tumor features including higher tumor grade and larger tumor size, which often denote more aggressive phenotypes, although the findings did not maintain significance with Bonferroni correction. Conclusions These novel data support reported associations between hair dye and relaxer use with breast cancer, showing for the first time, associations with breast tumor clinicopathologic features. Improved hair product exposure measurement is essential for fully understanding the impact of these environmental exposure with breast cancer and to guide risk reduction strategies in the future

Competition between Pauli and orbital effects in a charge-density wave system

We present angular dependent magneto-transport and magnetization measurements on alpha-(ET)2MHg(SCN)4 compounds at high magnetic fields and low temperatures. We find that the low temperature ground state undergoes two subsequent field-induced density-wave type phase transitions above a critical angle of the magnetic field with respect to the crystallographic axes. This new phase diagram may be qualitatively described assuming a charge density wave ground state which undergoes field-induced transitions due to the interplay of Pauli and orbital effects.Comment: 11 pages, 4 figures, shown at the APS march meeting 2000, appears in the Ph.D. thesis of J. S. Qualls (Florida State University, 1999), and submitted to PR

Controllability on infinite-dimensional manifolds

Following the unified approach of A. Kriegl and P.W. Michor (1997) for a treatment of global analysis on a class of locally convex spaces known as convenient, we give a generalization of Rashevsky-Chow's theorem for control systems in regular connected manifolds modelled on convenient (infinite-dimensional) locally convex spaces which are not necessarily normable.Comment: 19 pages, 1 figur

Geometric Approach to Pontryagin's Maximum Principle

Since the second half of the 20th century, Pontryagin's Maximum Principle has been widely discussed and used as a method to solve optimal control problems in medicine, robotics, finance, engineering, astronomy. Here, we focus on the proof and on the understanding of this Principle, using as much geometric ideas and geometric tools as possible. This approach provides a better and clearer understanding of the Principle and, in particular, of the role of the abnormal extremals. These extremals are interesting because they do not depend on the cost function, but only on the control system. Moreover, they were discarded as solutions until the nineties, when examples of strict abnormal optimal curves were found. In order to give a detailed exposition of the proof, the paper is mostly self\textendash{}contained, which forces us to consider different areas in mathematics such as algebra, analysis, geometry.Comment: Final version. Minors changes have been made. 56 page