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Concrete Problems (concrete + problem)
Selected AbstractsSignal representation and approximation,fundamental limitsEUROPEAN TRANSACTIONS ON TELECOMMUNICATIONS, Issue 5 2007Holger Boche The expansion of functions in orthonormal bases is an important analytical and practical instrument in many different areas such as in signal processing, in system and information theory and in communications. However, the selection of an optimal basis is a non-trivial task in general and depends strongly on the performance measure of the concrete problem. This paper considers the basis selection problem for three different applications, starting with a problem from system theory, looking on entropy based methods from information theory, and finally it investigates the peak-to-average power ratio problem in communication systems. In particular, it is investigated under which conditions the problems are solvable, that is under which conditions there exists an appropriate basis. Copyright © 2007 John Wiley & Sons, Ltd. [source] Problem solving therapy for the depression-executive dysfunction syndrome of late lifeINTERNATIONAL JOURNAL OF GERIATRIC PSYCHIATRY, Issue 8 2008George S. Alexopoulos Abstract Background The ,depression executive dysfunction syndrome' afflicts a considerable number of depressed elderly patients and may be resistant to conventional pharmacotherapy. Non-pharmacological approaches addressing their behavioral deficits may reduce disability and experienced stress and improve depression. Methods This paper focuses on problem solving therapy (PST) because it targets concrete problems that can be understood by patients with executive dysfunction and trains patients to address them using an easy to comprehend structured approach. Results We suggest that PST is a suitable treatment for patients with the depression-executive dysfunction syndrome because it has been found effective in uncomplicated geriatric major depression and in other psychiatric disorders accompanied by severe executive dysfunction. Furthermore, PST can address specific clinical features of depressed patients with executive dysfunction, especially when modified to address difficulties with affect regulation, initiation and perseveration. Conclusions A preliminary study suggests that appropriately modified PST improves problem solving skills, depression and disability in elderly patients with the depression-executive dysfunction syndrome of late life. If these findings are confirmed, PST may become a therapeutic option for a large group of depressed elderly patients likely to be drug resistant. Copyright © 2008 John Wiley & Sons, Ltd. [source] On Cauchy estimates and growth orders of entire solutions of iterated Dirac and generalized Cauchy,Riemann equationsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 14 2006D. Constales Abstract In this paper, we study the growth behaviour of entire Clifford algebra-valued solutions to iterated Dirac and generalized Cauchy,Riemann equations in higher-dimensional Euclidean space. Solutions to this type of systems of partial differential equations are often called k -monogenic functions or, more generically, polymonogenic functions. In the case dealing with the Dirac operator, the function classes of polyharmonic functions are included as particular subcases. These are important for a number of concrete problems in physics and engineering, such as, for example, in the case of the biharmonic equation for elasticity problems of surfaces and for the description of the stream function in the Stokes flow regime with high viscosity. Furthermore, these equations in turn are closely related to the polywave equation, the poly-heat equation and the poly-Klein,Gordon equation. In the first part we develop sharp Cauchy-type estimates for polymonogenic functions, for equations in the sense of Dirac as well as Cauchy,Riemann. Then we introduce generalizations of growth orders, of the maximum term and of the central index in this framework, which in turn then enable us to perform a quantitative asymptotic growth analysis of this function class. As concrete applications we develop some generalizations of some of Valiron's inequalities in this paper. Copyright © 2006 John Wiley & Sons, Ltd. [source] Further results on the asymptotic growth of entire solutions of iterated Dirac equations in ,nMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 5 2006D. Constales Abstract In this paper, we establish some further results on the asymptotic growth behaviour of entire solutions to iterated Dirac equations in ,n. Solutions to this type of systems of partial differential equations are often called polymonogenic or k -monogenic. In the particular cases where k is even, one deals with polyharmonic functions. These are of central importance for a number of concrete problems arising in engineering and physics, such as for example in the case of the biharmonic equation for the description of the stream function in the Stokes flow regime with low Reynolds numbers and for elasticity problems in plates. The asymptotic study that we are going to perform within the context of these PDE departs from the Taylor series representation of their solutions. Generalizations of the maximum term and the central index serve as basic tools in our analysis. By applying these tools we then establish explicit asymptotic relations between the growth behaviour of polymonogenic functions, the growth behaviour of their iterated radial derivatives and that of functions obtained by applying iterations of the , operator to them. Copyright © 2005 John Wiley & Sons, Ltd. [source] State of the Art: Addressing the INGO ,Legitimacy Deficit'POLITICAL STUDIES REVIEW, Issue 2 2005Vivien Collingwood While the numbers and competencies of international non-governmental organisations (INGOs) have increased dramatically in the past few decades, questions have been raised about the legitimacy of their new activities. A number of scholars have identified significant tensions between INGOs' legitimacy claims and the realities of their working practices. We examine the current state of the debate on INGO legitimacy in two contrasting literatures: normative work on global governance and its implications for the role of INGOs, and policy-oriented work on INGOs' legitimacy. The first shows how INGO involvement in global governance opens the door to a range of alternative conceptions of world order, rooted in notions of universal human rights, democracy, and theories of redistributive justice. The latter set of voices is concerned less with locating INGOs' roles as agents in global normative structures than with analysing concrete problems arising from increased INGO participation in the development process. Future research might take into account key questions concerning the sources and the scope and nature of INGO legitimacy. [source] Kelsen's Development of the Fehlerkalkül -TheoryRATIO JURIS, Issue 1 2005CHRISTOPH KLETZER The issues dealt with feature under various headings,albeit always prominently,in the national schools of legal theory. What distinguishes the Viennese approach is the extraordinary generality and height of abstraction it has reached and that facilitates the unification of most disparate legal phenomena. The intention of the article is threefold: firstly, to bring the important, albeit mostly maltreated theory of the Fehlerkalkül ("error-calculus") into the light of theoretical attention; secondly, to demonstrate Kelsen's method of developing legal philosophy only given concrete problems of the positive law and its theory; finally, to deal with criticism. [source] Empirical Challenges and Concept Formation in the History of HydrodynamicsCENTAURUS, Issue 3 2008Olivier Darrigol Abstract Although the fundamental equations of hydrodynamics were known at an early stage of its history, this theory long remained irrelevant to most of the practical problems of flow. The advent of a more efficient fluid mechanics in the early twentieth century depended on conceptual schemes that could not be read directly from the basic equations. Attention to concrete problems of flow, rather than purely mathematical deduction or purely intuitive guessing, permitted the gradual introduction of relevant substructures and their ultimate combination in powerful approximation schemes. This history is in part singular, owing to the extreme difficulty of dealing with non-linear systems with infinitely many degrees of freedom. But it is also typical as an illustration of the futility of reducing a physico-mathematical theory to its fundamental equations. Any advanced theory of physics must include an evolving modular structure that plays an essential role in melding the formal with the empirical. [source] | ||||||||||