On the definition of the ‘Best’ confidence interval

The definition of a confidence interval used in risk and reliability calculations is not the best one because it does not define the shortest confidence interval for skew distributions. In this paper the definition of the cumulative distribution was generalized by using Lebesgue integration. The application of a new definition allows the introduction of the shortest confidence interval (or domain) for all cases.     

On the ISAPS ’11 in Hakone

The Eighth International Symposium on Applied Plasma Science (ISAPS ’11) was held at the Yumoto Fujiya Hotel, in Hakone, Japan on September 26 through 30, 2011. The selected papers presented at ISAPS ’11 were written after the symposium. Those were peer refereed and are compiled in this special issue of Vacuum.     

‘Triad’ or ‘tetrad’? On global changes in a dynamic world

The US-EU race for world leadership in science and technology has become the favourite subject of recent studies. Studies issued by the European Commission reported the increase of the European share in the world’s scientific production and announced world leadership of the EU in scientific output at the end of the last century. In order to be able to monitor those types of global changes, the present study is based on the 15-year period 1991–2005. A set of bibliometric and technometric indicators is used to analyse activity and impact patterns in science and technology output. This set comprises publication output indicators such as (1) the share in the world total, (2) subject-based publication profiles, (3) citation-based indicators like journal-and subject-normalised mean citation rates, (4) international co-publications and their impact as well as (5) patent indicators and publication-patent citation links (both directions). The evolution of national bibliometric profiles, ‘scientific weight’ and science-technology linkage patterns are discussed as well. The authors show, using the mirror of science and technology indicators, that the triad model does no longer hold in the 21^st century. China is challenging the leading sciento-economic powers and the time is approaching when this country will represent the world’s second largest potential in science and technology. China and other emerging scientific nations like South Korea, Taiwan, Brazil and Turkey are already changing the balance of power as measured by scientific production, as they are at least in part responsible for the relative decline of the former triad.     

Response to ‘On negative refraction in classical vacuum’

An analysis [McCall, M.W. J. Mod. Opt. 2007, 54, 119–128] based on the electromagnetic energy-momentum tensor, to explore the prospects for negative-phase-velocity (NPV) propagation in gravitationally affected vacuum, did not consider (i) the total energy-momentum tensor and (ii) the global perspective of curved spacetime. Also, the appearance of NPV was wrongly attributed to a change in signature of the spacetime metric.     

On ‘ sudden death’ testing

Application of basic statistical theory shows that ‘ sudden death testing ’ is an accelerated teat procedure for specimens having a Weibull ‘ life to failure’ distribution only if the shape parameter is less than 1-6. In no case do the non-failed test specimens contribute to estimating efficiency and sudden death testing is in general a more costly procedure, than full tests of equivalent statistical content.     

On symmetries of the Fokker–Planck equation

This paper is devoted to Lie point symmetries of the Fokker–Planck (FP) equation. It describes the relation between symmetries and first integrals of stochastic differential equations (SDEs) and symmetries of the associated FP equations. This relation is illustrated on symmetries of (1 + 1)-dimensional FP equations specified by Lie group classification of the scalar SDE. Further, it is used to find symmetries of (1 + 2)-dimensional FP equations specified by Lie group classification of the system of two SDEs.     

Flexible job-shop scheduling problems with ‘AND’/‘OR’ precedence constraints

The purpose of this research is to solve flexible job-shop scheduling problems with ‘AND’/‘OR’ precedence constraints in the operations. We first formulate the problem as a Mixed-Integer Linear Program (MILP). The MILP can be used to compute optimal solutions for small-sized problems. We also developed a heuristic algorithm that can obtain a good solution for the problem regardless of its size. Moreover, we have developed a representation and schedule builder that always produces a legal and feasible solution for the problem, and developed genetic and tabu search algorithms based on the proposed schedule builder. The results of the computational experiments show that the developed meta-heuristics are very effective.     

Stability analysis of the Fourier–Bessel method for the Cauchy problem of the Helmholtz equation

This paper is concerned with the Cauchy problem connected with the Helmholtz equation in a smooth-bounded domain. The Fourier–Bessel method with Tikhonov regularization is applied to achieve a regularized solution to the problem with noisy data. The convergence and stability are obtained with a suitable choice of the regularization parameter. Numerical experiments are also presented to show the effectiveness of the proposed method.     

A local integral equation formulation to solve coupled nonlinear reaction–diffusion equations by using moving least square approximation

A new procedure is developed for the numerical solution of the nonlinear reaction–diffusion equations responsible for appearance of diffusion driven instabilities. The system of two nonlinear partial differential equations of the parabolic type is proposed to be solved by the local integral equation formulation and one-step time discretization method. The spatial variations are approximated by moving least squares and the nonlinear terms are treated iteratively within each time step. The developed formulation is verified in two numerical test examples with investigating the convergence and accuracy of numerical results.     

A new technique to derive the Green’s type integral formula in thermoelasticity

New closed-form influence functions of a unit point heat source on elastic displacements and new Green’s type integral formula for a boundary-value problem (BVP) for a thermoelastic half-space are presented. The main difficulties in obtaining such results are observed in deriving the influence functions of a concentrated unit force onto elastic volume expansion and, also, in Green’s functions in heat conduction. For canonical Cartesian domains, these functions have been derived successfully for hundreds of BVPs and were published in a handbook. So, this paper shows the way to derive not only thermoelastic influence functions and Green’s type integral formulas for the half-space, but also for many new BVPs in thermoelasticity in other Cartesian canonical domains. Moreover, the technique proposed here may be applied in any orthogonal canonical domain provided by the lists of Green’s functions in heat conduction and influence functions for elastic volume expansion that are known.     

A Burton–Miller formulation of the boundary element method for baffle problems in acoustics and the BEM/FEM coupling

Baffle problems, i.e. radiation problems from objects mounted behind a hole of an infinite hard reflecting wall, can be simulated as a multi domain problem consisting of a finite interior domain around the object, and two infinite half spaces in front and behind the baffle plane. A formulation of such problems is presented in the context of the Burton–Miller boundary element method. Additionally, the coupling of the acoustic boundary element method and the structural finite element method in the context of the Burton–Miller-formulation of the baffle problem is discussed.     

Dickens and ‘photography’ in ‘household words’

Abstract

The January 1981 issue of History of Photography (Vol. 5, No. 1 , p. 51), Lindsay Lambert writes: ‘The following article [‘Photography, 1853’] appeared in Household Words (19th March 1853). The journal was edited by Charles Dickens, and since the article carries no other by-line, it may well have been written by the editor himself’.     

A numerical method based on the boundary integral equation and dual reciprocity methods for one-dimensional Cahn–Hilliard equation

This paper describes a numerical method based on the boundary integral equation and dual reciprocity methods for solving the one-dimensional Cahn–Hilliard (C–H) equation. The idea behind this approach comes from the dual reciprocity boundary element method that introduced for higher order dimensional problems. A time-stepping method and a predictor–corrector scheme are employed to deal with the time derivative and the nonlinearity respectively. Numerical results are presented for some examples to demonstrate the usefulness and accuracy of this approach. For these problems the energy functional dissipation and the mass conservation properties are investigated.     

A methodology to evaluate the usability of digital socialization in ‘‘virtual’’ engineering design

We develop a methodology to evaluate the usability of prototypes for supporting digital socialization within geographically dispersed, or “virtual”, engineering design teams. Socialization converts individual into group tacit knowledge to enhance collaborative work. Extant theory in computer-supported collaborative work (CSCW) underpins IDRAK, a proof-of-concept prototype of a rich Internet application to promote socialization. Our methodology employs an engineering design exercise (Delta design, as in Bucciarelli (Delta design game, MIT, Cambridge, 1994) to simulate, in a computer lab, a virtual team undertaking a project feasibility stage. We apply this methodology to evaluate the usability of IDRAK to support “virtual” four-people teams (architect, project manager, thermal and structural engineers). Our findings yield few statistically significant differences between the performance of virtual and co-located teams. The experiments suggest that IDRAK encourages individuals to work collaboratively. It allows for a leveling of status and eases communication since individuals’ accents are not an issue. However, IDRAK makes it difficult for the project manager to exercise authority and it cannot capture nuances in speech such as tone and expression. The experiments suggest that more research is needed to explore the ways to enhance the performance of virtual teams by: first, alternating between voice/video and text-based chat; second, documenting chat-based conversations; and third, enforcing communication and design process protocols.

On blow-up phenomena for the weakly dissipative Camassa–Holm equation

We study the Cauchy problem for the weakly dissipative Camassa?CHolm equation: $$u_{t}-u_{txx}+3uu_{x}+\lambda \left( u-u_{xx} \right)=2u_{x}u_{xx}+uu_{xxx}, \quad t >0 ,x\in \mathbb{R}$$ . A new blow-up result for positive strong solutions of the equation with certain profiles is presented. In particular, we use a condition where the initial data u ₀ and its derivative u _0x are not simultaneously involved and the parameter ?? is not bounded from above.     

Comment on ‘Wigner equation of motion for time-dependent potentials’

Abstract

A correction is pointed out to a statement made by Galleani and Cohen (2002, J. mod. Optics, 49, 561) regarding the impossibility of deriving an equation of evolution for the Wigner function corresponding to the Schrödinger equation with a time-dependent potential.