Machines and mechanisms realize processes, from the shaping process of a milling machine and the motion process of an automotive system to the trajectory realization of a robot. The dynamics of a machine generated by a properly chosen set of constraints in combination with an appropriate drive system is designed to meet the prescribed requirements of the process, which is done by projecting the machine equations of motion on the process dynamics. We get a set of nonlinear relations, which represent the machine motion in terms of the required process motion. A well-known example is the projection of arbitrary many robot degrees of freedom (DOFs) on a given path resulting in a set of nonlinear equations with one DOF only, the path coordinate s. Application of this idea can be used to construct a mobility space $(\ddot{s}, \dot{s}, s)$ for any combination of coordinates and constraints. The paper presents a corresponding approach for n-link robots by applying multibody system theory. Method might be interesting for layout of machines and mechanisms. Practical aspects are discussed, and an example is given.

Several authors have pointed out that in the next few decades dementia will affect a considerably increasing number of the elderly. To our knowledge there exist no calculations of the number of demented persons for the whole European region. We made calculations on the number of dementia cases for the period 2000–2050 based on the population projections of the United Nations. For this purpose, we used the results of several meta-analyses of epidemiological studies. The number of prevalent dementia cases in the year 2000 was 7.1 million. Within the next 50 years, this number will rise to about 16.2 million dementia sufferers. The number of new dementia cases per year will increase from about 1.9 million in the year 2000 to about 4.1 million in the year 2050. Contrarily, the working-age population will considerably decrease during the next 50 years. In the year 2000, 7.1 million dementia cases faced 493 million persons in working-age. This equals a ratio of 69.4 persons in working-age per one demented person. Until the year 2050, this ratio will decrease to only 21.1. Thus, the financial and emotional burden placed by dementia on the working-age population will markedly rise.

This paper analyses the implications that demographic and economic projections have on public pension spending in the European Union (EU). Using some stylised facts, we study the aging trends of the population, as well as labour force and employment projections. Indices of both demographic and economic dependence are built. All of this is used to determine the impact on public pension spending in the EU. Although we detect substantial heterogeneity of circumstances, we show that the states in which aging of the population weights more in explaining public pension expenditure growth as a percentage of gross domestic product (GDP) are generally the ones that make greater efforts to control this spending. Given the limited capacity of policies to increase active population or employment to offset the effects of aging, measures aimed at diminishing the generosity of the public pension system and at promoting private schemes have gained relevance.

If $f,\,g:\,{{\mathbb{R}}^{n}}\,\to \,{{\mathbb{R}}_{\ge 0}}$ are non-negative measurable functions, then the Prékopa–Leindler inequality asserts that the integral of the Asplund sum (provided that it is measurable) is greater than or equal to the 0-mean of the integrals of $f$ and $g$. In this paper we prove that under the sole assumption that $f$ and $g$ have a common projection onto a hyperplane, the Prékopa–Leindler inequality admits a linear refinement. Moreover, the same inequality can be obtained when assuming that both projections (not necessarily equal as functions) have the same integral. An analogous approach may be also carried out for the so-called Borell-Brascamp-Lieb inequality.

The supertree construction problem is about combining several phylogenetic trees with possibly conflicting information into a single tree that has all the leaves of the source trees as its leaves and the relationships between the leaves are as consistent with the source trees as possible. This leads to an optimization problem that is computationally challenging and typically heuristic methods, such as matrix representation with parsimony (MRP), are used. In this paper we consider the use of answer set programming to solve the supertree construction problem in terms of two alternative encodings. The first is based on an existing encoding of trees using substructures known as quartets, while the other novel encoding captures the relationships present in trees through direct projections. We use these encodings to compute a genus-level supertree for the family of cats (Felidae). Furthermore, we compare our results to recent supertrees obtained by the MRP method.

The forest and agriculture sectors are linked by having a portion of their land bases suitable for use in either sector. A substantial part of the southern land base is suitable for either forestry or agriculture use, with most of forestation on U.S. agriculture land in the South. We examine how land exchanges between forestry and agriculture are influenced by specific federal conservation and farm support policies, including changes in the Conservation Reserve Program. Reallocation of land is a significant part of the sectors' responses to the policies, along with intensification of timber management on existing southern forests.

We study the reflexivity and transitivity of a double triangle lattice of subspaces in a Hilbert space. We show that the double triangle lattice is neither reflexive nor transitive when some invertibility condition is satisfied (by the restriction of a projection under another). In this case, we show that the reflexive lattice determined by the double triangle lattice contains infinitely many projections, which partially answers a problem of Halmos on small lattices of subspaces in Hilbert spaces.

A key feature of population ageing in Europe and other more economically developed countries is the projected unprecedented rise in need for long-term care in the next two decades. There is, however, considerable uncertainty over the future supply of unpaid care for older people by their adult children. The future of family care is particularly important in countries planning to reform their long-term care systems, as is the case in England. This article makes new projections of the supply of intense unpaid care for parents aged 65 and over in England to 2032, and compares these projections with existing projections of demand for unpaid care by older people with disabilities from their children. The results show that the supply of unpaid care to older people with disabilities by their adult children in England is unlikely to keep pace with demand in future. By 2032, there is projected to be a shortfall of 160,000 care-givers in England. Demand for unpaid care will begin to exceed supply by 2017 and the unpaid ‘care gap’ will grow rapidly from then onwards. The article concludes by examining how far this unpaid ‘care gap’ is likely to be met by other sources of unpaid care or by developments in new technology and examines the implications of the findings for long-term care policy.

We review recent stability and separation results in volume comparison problems and usethem to prove several hyperplane inequalities for intersection and projection bodies.

This paper addresses the process of estimating loss reserves for a company or syndicate writing in the London Market. Particular emphasis is placed on insurers maximising the value of the process, and ensuring that the process is not simply a series of mathematical calculations. The use of sophisticated mathematical techniques should not distract from the importance of understanding the business and ensuring that data are correct. Sophisticated mathematical techniques can give rise to misleading impressions of confidence and accuracy to estimates, which are often subject to considerable uncertainty. The principles (rather than the detailed techniques) are illustrated by a case study based on a hypothetical London Market writer. Many of these principles are relevant to other markets.

Canada's demographic situation in the future will differ substantially from what we have known in the past. Unless there is an early return to high fertility the average age of both the population and the labour force will increase substantially, while the overall dependency ratio will be low by historical standards. Our analysis suggests that up to about 2010 population change will have less of an impact on the real (i.e., constant—price) level of aggregate government expenditures than on the size of the real gross national product However, we can anticipate compositional changes in government expenditures as a result of population change: very large increases in the real social security costs, lesser (but still large) increases in health costs, and a reduction in education costs. Finally, a relatively large portion of the aggregate expenditure increases will be at the federal government level.

Micro-data from a 1984 survey of adult education in Canada are used in the study. The data for persons 65 years of age and over are analysed using probit techniques. Prior level of education is found to be of considerable importance in determining the probabilities that elderly people will make use of adult education facilities. It is argued that future elderly population cohorts will have higher average education levels than present ones and that their members will therefore be more likely to take courses. Projections of increases in course enrolment by persons 65 and over are made for the next quarter century, based on the results of the probit analysis and projections of the population.

Background: This study explores how the views of a panel of experts on dementia would affect projected long-term care expenditure for older people with dementia in England in the year 2031.

Methods: A Delphi-style approach was used to gather the views of experts. The projections were carried out using a macro-simulation model of future demand and associated expenditure for long-term care by older people with dementia.

Results: The panel chose statements that suggested a small reduction in the prevalence of dementia over the next fifty years, a freeze in the numbers of people in care homes, and an increase in the qualifications and pay of care assistants who look after older people with dementia. Projections of expenditure on long-term care that seek to capture the views of the panel suggest that future expenditure on long-term care for this group will rise from 0.6% of GDP in 2002 to between 0.82% and 0.96% of GDP in 2031. This range is lower than the projected expenditure of 0.99% of GDP in 2031 obtained under a range of base case assumptions.

Conclusions: This paper attempts to bridge the gap between qualitative forecasting methods and quantitative future expenditure modelling and has raised a number of important methodological issues. Incorporating the panel's views into projections of future expenditure in long-term care for people with dementia would result in projected expenditure growing more slowly than it would otherwise.