On the computation of hilbert—Poincaré series

We prove a theorem, which provides a formula for the computation of the Poincaré series of a monomial ideal ink[X₁,, X_n], via the computation of the Poincaré series of some monomial ideals ink[X ₁,, X_i,, X_n]. The complexity of our algorithm is optimal for Borel-normed ideals and an implementation in CoCoA strongly confirms its efficiency. An easy extension computes the Poincaré series of graded modules over standard algebras.The paper was partly written while the third author was visiting Queen's University, during the academic year 1989/90. It was partly supported by the Natural Sciences & Engineering Research Council of Canada, Queen's University (Kingston, Canada) and Consiglio Nazionale delle Ricerche     

Viewing angle of liquid-crystal displays: representation on the Poincaré sphere

Using the extended Jones calculus for oblique incidence, we have succeeded in representing light propagation through birefringent media on the Poincaré sphere for arbitrary propagation directions. The situation is far more complicated than for the case of perpendicular transmission. To achieve a simple representation method we had to define appropriate conventions. One can use the method to evaluate the efficiency of existing viewing-angle compensation foils. The Poincaré sphere turns out to be a valid geometrical method for the design of new compensation foils that optimize the contrast ratio. The different parameters of a homogeneous compensation foil that is applied to a liquid-crystal display to improve the viewing-angle properties can be systematically determined.     

Poincaré sphere representation of the fixed-polarizer rotating-retarder optical system

The trajectory of the polarization state of a monochromatic light beam after it passes through a fixed linear polarizer and a rotating linear retarder of arbitrary retardance delta is determined on the Poincaré sphere. The three-dimensional figure-8 contour is shown to be the line of intersection of a right-circular cylinder with the sphere. The cylinder is parallel to the polar (S3) axis, touches the sphere at the equator (at the point that represents the linear polarization transmitted by the fixed polarizer), and has a radius r = sin2(delta/2). Projections of the trajectory in the coordinate planes of the normalized Stokes parameter space (s1, s2, S3) are also determined.     

Analysis of clusters and uniformity of distribution of states of polarization on the Poincaré sphere

An analysis of the clusters and the uniformity of distribution of states of polarization on the surface of a Poincaré sphere generated by rotating wave plates is given. The analysis of clusters of the states of polarization is based on a spherical radial distribution function. For uniform analysis of the distribution, two methods are proposed. The first method is based on calculation of the correlation coefficient; the second method is based on calculation of the angles between pairs of the states of polarization on the Poincaré sphere. For polarization scramblers consisting of eight or more rotating wave plates, nonclustered and near-uniform distribution of states of polarization is obtained.     

Statistical characteristics of Poincaré return times within the local approach under presence of noise

The dependences of the mean time and dispersion of Poincaré return times on the ? vicinity of the initial state have been analyzed in the absence and in the presence of external noise.     

A bibliometric visualization of the economics and sociology of wealth inequality: a world apart?

Scientometrics - Wealth inequality research is fragmented across different social science disciplines. This article explores the potential of interdisciplinary perspectives by investigating the...     

Effect of noise-induced crisis of attractor on characteristics of Poincaré recurrence

The effect of noise on the Poincaré recurrence time has been studied in a one-dimensional map with quasi-attractor. The validity of the Kac theorem in application to noise systems is substantiated. Results of calculations of the distribution of recurrence times in a noisy system are presented.     

The mean Poincaré return time locking: A criterion of chaos induced synchronization

A new method for diagnostics of the induced synchronization of chaotic self-oscillation is proposed, which is based on the local theory of Poincaré recurrences. It is established that, in the region of synchronization, the mean Poincaré return time is locked by an external harmonic signal.     

Multivariate statistical process control charts based on the approximate sequential χ2 test

Similar to the univariate CUSUM chart, a multivariate CUSUM (MCUSUM) chart can be designed to detect a particular size of the mean shift optimally based on the scheme of a sequential likelihood ratio test for the noncentrality parameter. However, in multivariate case, the probability ratio of a sequential test is intractable mathematically and the test statistic based on the ratio does not have a closed form expression which makes it impractical for real application. We drive an approximate log-likelihood ratio and propose a multivariate statistical process control chart based on a sequential χ² test to detect a change in the noncentrality parameter. The statistical properties of the proposed test statistic are explored. The average runs length (ARL) performance of the proposed charts is compared with other MCUSUM charts for process mean monitoring. The experimental results reveal that the proposed charts achieve superior, both zero-state and steady-state, ARL performance over a wide range of mean shifts, especially when the dimension of measurements is large.     

Pull testing of a glass fiber soldered into a ferrule: how long should the test specimen be?

A simple analytical model is developed for the evaluation of the bending stress caused by the misalignment of the ends of a glass fiber specimen soldered into a ferrule and subjected to tension during pull testing. It is shown that this stress can be reduced by use of sufficiently long specimens. It is also shown how the uncertainty in the prediction of the misalignment of the ends can be considered when one is establishing the appropriate specimen length.     

Exploring the phenomenon of company-specific production systems: one-best-way or own-best-way?

This explorative study investigates the phenomenon of the company-specific production system (XPS). It has been a strong and recent trend across many manufacturing industries to develop and deploy such a corporate improvement programme. Five propositions regarding the uniqueness of XPSs are derived from universalistic versus contingent perspectives on improvement programmes. The main XPS principles of 30 renowned multinationals are analysed for similarities and differences. In conclusion, XPSs largely represent variants of the same in content. They represent an own-best-way approach to the one-best-way paradigm. Even though a tight relationship to the Toyota Production System (TPS) and lean production is established, the findings raise a red flag that XPSs might suffer under a too rigid, path-dependent development process from what has become an overly technical understanding of the TPS. This study also questions whether modern manufacturers have sufficiently integrated other essential elements of modern operations such as the use of ERP, automation and real-time response technologies in their XPSs. These findings have direct implications for practitioners and provide interesting opportunities for further research.     

A prognosis of patent activity development — II. Verification of the statistical theory for estimating the rate of development of a technical field

This article is a continuation of a previous article in World Patent Information, Vol. 8 No. 2, pp. 122–142, which described the basis of a statistical theory of the development of a technical field. It presents a detailed verification of the possibility of failure of the theory through not describing the development of patent activity with sufficient accuracy. The analysis is based on the simplest model of the theory and discusses in detail:

• 1.1. Analysis of activity in the field of coil dialyzers.
• 2.2. Analysis of Edison's patents.
• 3.3. Application of the theory to several examples published in World Patent Information.
• 4.4. Analysis of citations.

The main conclusions are that the simple model of the theory is relatively accurate for fields of small extent but for large fields, or those comprising several sub- fields, the simple model is not satisfactory. For extensive files the simplest model can be used to provide a rough estimate of trend of development.     

What’s in a name? Exploring the conceptual structure of emerging organizations

Scientometrics - This study describes the conceptual structure of emerging organisations on the basis of research over the past 26 years. During this period, terms and theoretical...     

Visualization and calculation of polarized light. I. The polarization ellipse, the Poincaré sphere and the hybrid polarization sphere

We describe the historical and mathematical development of the polarization ellipse and the Poincaré sphere. We point out the limitations of the Poincaré sphere in its present use. To overcome these limitations we describe a new polarization sphere that we call the hybrid polarization sphere. This name is used because phase shifting and rotation of polarization components are described by small circles. Furthermore, longitudinal and latitudinal great circles are introduced so that the coordinates of a point on the sphere can be read. The hybrid polarization sphere is described and applied to polarizers, wave plates, and rotators. As a result, the hybrid polarization sphere can be used for both visualization and calculation and enables the difficulties associated with the Poincaré sphere to be overcome.     

Using a statistical model for the analysis of the influence of the type of matrix carbon–epoxy composites on the fatigue delamination under modes I and II of fracture

This paper analyzes delamination processes under modes I and II fracture and fatigue loading for two types of composite materials. The studied materials were manufactured with the same unidirectional carbon reinforcement though with two types of epoxy matrix. Experimental data were treated with a probabilistic model based on a Weibull distribution allowing the identification of relevant aspects of the fatigue behavior of the materials, such as the estimation of the fatigue strength for periods greater than the tested values and the analysis of the reliability of the results.This study suggests a variable behavior depending on the type of fracture loading: modes I and II, and the type of matrix used.     

An overview of the inequality in China’s carbon intensity 1997–2016: a Theil index decomposition analysis

Clean Technologies and Environmental Policy - Although China has experienced an overall decline in CO2 emissions intensity from 2009 to 2016, the intensity from one province to another varies...     

Fantasies of the street: Emigré photography in interwar Paris

A vibrant centre of cultural and artistic production, interwar Paris attracted many photographers from central Europe. Bringing with them inherited traditions and visual lexicons from their countries of origin, this heterogeneous group of photographers, which included Ilse Bing, André Kertész and Germaine Krull, put their acquired skills and habits to use in new contexts, drawing inspiration from each other, from their engagement with the vibrant culture of France, and most of all from a widespread fascination with Paris as photographic topos. Responding to nostalgia for images of a ‘popular Paris’ in the illustrated press, these photographers accomplished an alchemical transformation of Paris into a city in which past and present were poignantly reconciled. At the same time, many of their photographs, shot through with themes of exile and homelessness, reveal the fragility of the myth of a ‘popular Paris’, particularly after the advent of economic and social crises in the 1930s.     

Constraints on the applicability range of Hill’s criterion: strong orthotropy or transverse isotropy

Commonly used orthotropic Hill’s criterion of plastic flow initiation (Hill in Proc R Soc Lond A 193:281–297, 1948) suffers from some constraints and inconsistencies, which are of two different origins. Firstly, in case of high orthotropy degree, the quadratic form corresponding to Hill’s criterion may change type from convex and closed elliptic to concave and open hyperbolic in the deviatoric stress space (Ottosen and Ristinmaa in the mechanics of constitutive modeling, Elsevier, Amsterdam, 2005). Secondly, application of classical Hill’s criterion to transversely isotropic materials shows a discrepancy between Hill’s limit curves in the transverse isotropy plane and the Huber-von Mises prediction for isotropic materials (Huber 1904; von Mises 1913). The basic result of the present paper is to propose the new transversely isotropic von Mises–Hu–Marin’s-type criterion of hexagonal symmetry that is free from both constraints. The new enhanced Hu–Marin’s-type limit surface represents an elliptic cylinder, the axis of which is proportional to stress/strength, in contrast to Hill’s-type limit surface possessing the hydrostatic axis. Hence, this condition does not exhibit the deviatoricity property, which is a price for coincidence with the Huber–von Mises condition in the transverse isotropy plane, but with cylindricity ensured for an arbitrarily high orthotropy degree. The hybrid-type transversely isotropic Hu–Marin’s criterion of mixed symmetry based on additional biaxial bulge test, capable of fitting experimental findings for some complex composites, is also proposed. Application of this criterion has been verified for a unidirectional SiC/Ti composite examined by Herakovich (Thermal stresses V, Lastran Corp. Publ. Division, pp 1–142, 1999).