Existence and multiplicity results for quasilinear elliptic equations

The goal of this paper is to study the multiplicity of positive solutions of a class of quasilinear elliptic equations. Based on the mountain pass theorems and sub-and supersolutions argument for p-Laplacian operators, under suitable conditions on nonlinearity f (x, s), we show the following problem: -Delta(p)u = lambda f(x,u) in Omega, u/(partial derivative Omega) = 0, where Omega is a bounded open subset of R-N, N >= 2, with smooth boundary, lambda is a positive parameter and Delta(p) is the p-Laplacian operator with p > 1, possesses at least two positive solutions for large lambda.

Multiplicity results for second-order two-point boundary value problems with nonlinearities across several eigenvalues

We consider the boundary value problems for nonlinear second-order differential equations of the form u '' + a(t)f (u) = 0, 0 < t < 1, u(0) = u (1) = 0. We give conditions on the ratio f (s)/s at infinity and zero that guarantee the existence of solutions with prescribed nodal properties. Then we establish existence and multiplicity results for nodal solutions to the problem. The proofs of our main results are based upon bifurcation techniques. (c) 2004 Elsevier Ltd. All rights reserved.

Multiplicity results for second-order two-point boundary value problems with superlinear or sublinear nonlinearities

We consider boundary value problems for nonlinear second order differential equations of the form u + a(t) f(u) = 0, t epsilon (0, 1), u(0) = u(1) = 0, where a epsilon C([0, 1], (0, infinity)) and f : R --> R is continuous and satisfies f (s)s > 0 for s not equal 0. We establish existence and multiplicity results for nodal solutions to the problems if either f(0) = 0, f(infinity) = infinity or f(0) = infinity, f(0) = 0, where f (s)/s approaches f(0) and f(infinity) as s approaches 0 and infinity, respectively. We use bifurcation techniques to prove our main results. (C) 2004 Elsevier Inc. All rights reserved.

Development of the Minimum Information Specification for in situ Hybridization and Immunohistochemistry Experiments (MISFISHIE)

We describe the creation process of the Minimum Information Specification for In Situ Hybridization and Immunohistochemistry Experiments (MISFISHIE). Modeled after the existing minimum information specification for microarray data, we created a new specification for gene expression localization experiments, initially to facilitate data sharing within a consortium. After successful use within the consortium, the specification was circulated to members of the wider biomedical research community for comment and refinement. After a period of acquiring many new suggested requirements, it was necessary to enter a final phase of excluding those requirements that were deemed inappropriate as a minimum requirement for all experiments. The full specification will soon be published as a version 1.0 proposal to the community, upon which a more full discussion must take place so that the final specification may be achieved with the involvement of the whole community. This paper is part of the special issue of OMICS on data standards.

Prediction of minimum spouting velocity in two-dimensional flat bottom spouted beds

Spouted beds have been used in industry for operations such as drying, catalytic reactions, and granulation. Conventional cylindrical spouted beds suffer from the disadvantage of scaleup. Two-dimensional beds have been proposed by other authors as a solution for this problem. Minimum spouting velocity has been studied for such two-dimensional beds. A force balance model has been developed to predict the minimum spouting velocity and the maximum pressure drop. Effect of porosity on minimum spouting velocity and maximum pressure drop has been studied using the model. The predictions are in good agreement with the experiments as well as with the experimental results of other investigators.

Minimum description length, regularisation and multi-modal data

Relationships between clustering, description length, and regularisation are pointed out, motivating the introduction of a cost function with a description length interpretation and the unusual and useful property of having its minimum approximated by the densest mode of a distribution. A simple inverse kinematics example is used to demonstrate that this property can be used to select and learn one branch of a multi-valued mapping. This property is also used to develop a method for setting regularisation parameters according to the scale on which structure is exhibited in the training data. The regularisation technique is demonstrated on two real data sets, a classification problem and a regression problem.

Minimum description length, regularisation and multi-modal data

Conventional feed forward Neural Networks have used the sum-of-squares cost function for training. A new cost function is presented here with a description length interpretation based on Rissanen's Minimum Description Length principle. It is a heuristic that has a rough interpretation as the number of data points fit by the model. Not concerned with finding optimal descriptions, the cost function prefers to form minimum descriptions in a naive way for computational convenience. The cost function is called the Naive Description Length cost function. Finding minimum description models will be shown to be closely related to the identification of clusters in the data. As a consequence the minimum of this cost function approximates the most probable mode of the data rather than the sum-of-squares cost function that approximates the mean. The new cost function is shown to provide information about the structure of the data. This is done by inspecting the dependence of the error to the amount of regularisation. This structure provides a method of selecting regularisation parameters as an alternative or supplement to Bayesian methods. The new cost function is tested on a number of multi-valued problems such as a simple inverse kinematics problem. It is also tested on a number of classification and regression problems. The mode-seeking property of this cost function is shown to improve prediction in time series problems. Description length principles are used in a similar fashion to derive a regulariser to control network complexity.

A comparison of the vocational training system of Britain and West Germany as experienced by minimum-age school leavers.

The sectoral and occupational structure of Britain and West Germany has increasingly changed over the last fifty years from a manual manufacturing based to a non-manual service sector based one. There has been a trend towards more managerial and less menial type occupations. Britain employs a higher proportion of its population in the service sector than in manufacturing compared to West Germany, except in retailing, where West Germany employs twice as many people as Britain. This is a stable sector of the economy in terms of employment, but the requirements of the workforce have changed in line with changes in the industry in both countries. School leavers in the two countries, faced with the same options (FE, training schemes or employment) have opted for the various options in different proportions: young Germans are staying longer in education before embarking on training and young Britons are now less likely to go straight into employment than ten years ago. Training is becoming more accepted as the normal route into employment with government policy leading the way, but public opinion still slow to respond. This study investigates how vocational training has adapted to the changing requirements of industry, often determined by technological advancements. In some areas e.g. manufacturing industry the changes have been radical, in others such as retailing they have not, but skill requirements, not necessarily influenced by technology have changed. Social-communicative skills, frequently not even considered skills and therefore not included in training are coming to the forefront. Vocational training has adapted differently in the two countries: in West Germany on the basis of an established over-defined system and in Britain on the basis of an out-dated ill-defined and almost non-existent system. In retailing German school leavers opt for two or three year apprenticeships whereas British school leavers are offered employment with or without formalised training. The publicly held view of the occupation of sales assistant is one of low-level skill, low intellectual demands and a job anyone can do. The traditional skills - product knowledge, selling and social-communicative skills have steadily been eroded. In the last five years retailers have recognised that a return to customer service, utilising the traditional skills was going to be needed of their staff to remain competitive. This requires training. The German retail training system responded by adapting its training regulations in a long consultative process, whereas the British experimented with YTS, a formalised training scheme nationwide being a new departure. The thesis evaluates the changes in these regulations. The case studies in four retail outlets demonstrate that it is indeed product knowledge and selling and social-communicative skills which are fundamental to being a successful and content sales assistant in either country. When the skills are recognised and taught well and systematically the foundations for career development in retailing are laid in a labour market which is continually looking for better qualified workers. Training, when planned and conducted professionally is appreciated by staff and customers and of benefit to the company. In retailing not enough systematic training, to recognisable standards is carried out in Britain, whereas in West Germany the training system is nevertheless better prepared to show innovative potential as a structure and is in place on which to build. In Britain the reputation of the individual company has a greater role to play, not ensuring a national provision of good training in retailing.

Optical link design for minimum power consumption and maximum capacity

Using a well-established analytic nonlinear signal-to-noise ratio noise model we show that there are very simple, fibre independent, amplifier gains which minimize the total energy requirement for amplified systems. Power savings of over 50% are shown to be possible by choosing appropriate amplifier gain and output power.

Minimum Mean Square Error Approach in Images Processing for Full-field Displacements and Deformation Measurements

A vision system is applied to full-field displacements and deformation measurements in solid mechanics. A speckle like pattern is preliminary formed on the surface under investigation. To determine displacements field of one speckle image with respect to a reference speckle image, sub-images, referred to Zones Of Interest (ZOI) are considered. The field is obtained by matching a ZOI in the reference image with the respective ZOI in the moved image. Two image processing techniques are used for implementing the matching procedure: – cross correlation function and minimum mean square error (MMSE) of the ZOI intensity distribution. The two algorithms are compared and the influence of the ZOI size on the accuracy of measurements is studied.