Abstract We consider a container of fluid with a rod inserted in the centre. As the rod rotates the surface of the fluid forms a curved surface whose shape correctly balances the forces of gravity, internal stress, atmospheric pressure, and surface tension. The surface of the fluid is depressed in the neighbourhood of the rod in the case of a Newtonian fluid, but the fluid may climb along the rod in the case of non-Newtonian fluids. In recent work by D. D. Joseph and R. S. Fosdick this free surface problem has been treated quantitatively by virtue of a formal perturbation series in which the solution is developed in powers of the angular velocity of the rod. The purpose of the present paper is to give a rigorous proof of convergence in the case of a Newtonian fluid. The method here may possibly be applied to other free surface problems - for example, surface waves of a viscous fluid. The convergence proof provides, to our knowledge, the first rigorous existence theorem for a free surface problem in the theory of viscous fluids. The proof also raises a novel problem in the theory of elliptic systems of partial differential equations. By means of the implicit function theorem, the question of convergence is reduced to that of obtaining a priori estimates for an elliptic boundary value problem. That problem is formulated on a domain with a ridge where the fluid surface meets the rod. In addition, the type of boundary conditions prescribed differ on the free surface and on the rod. In general, the solution to such a mixed boundary value problem is not smooth at the ridge, even if the boundary data is smooth. The solution will be smooth, however, if the boundary data satisfy certain consistency conditions which make it compatible with the given set of partial differential equations. The consistency conditions in question here are a set of linear relations between various derivatives of the boundary and inhomogeneous data. It is shown that if one makes the assumption that the wetting angle of the surface is zero, the consistency conditions are invariant under the full nonlinear equations of the free surface problem. This makes it possible to consider the original problem on a smaller function space - namely the subclass of functions satisfying the appropriate consistency conditions - and in this subclass one can apply the implicit function theorem and obtain the required a priori estimates. The solution thus obtained is regular up to the ridge.
Navier-Stokes equation solutions
Elasticity and Material Modeling
Advanced Numerical Methods in Computational Mathematics
All chapters end with Notes. Preface. 1. The Field of Social Welfare Policy. Institutional Perspectives on the Study of Social Welfare Policy. Evolving Institutions and the Welfare State. Analytic Perspectives on the Study of Social Welfare Policy. Political Perspectives on the Study of Social Welfare Policy. Individualist and Collective Approaches to Planning. Conceptions of the Public Interest. Competing Values: Participation, Leadership, and Expertise. Why Policy Analysis is Relevant to Direct Service Practitioners. Emerging Issues: Feminist Perspectives on Social Welfare. 2. The Modern Welfare State. The Evolving Welfare State. Theories of Welfare Growth. Is America Exceptional? Welfare Goals. Welfare Scope. Welfare Realms. Emerging Issues: Renegotiating the Boundaries. 3. A Framework for Social Welfare Policy Analysis. Benefit Allocations in the Social Market and the Mixed Economy on Welfare. Elements of an Analytic Framework: Dimensions of Choice. An Example: The Transformation of Social Services. Application of the Framework. Distributive Justice in Public Assistance. Individual and Collective Values in Public Assistance. Theories, Assumptions, and Social Choice. Emerging Issues: The Search for Equity. 4. The Basis of Social Allocation. Who Shall Benefit? Universality and Selectivity in Income Maintenance. Child Support and Asset Building. Social Effectiveness and Cost Effectiveness. Another Perspective on Allocation: A Continuum of Choice. Allocative Principles and Institutional-Residual Conceptions of Social Welfare. Operationalizing the Allocative Principles. Eligibility Versus Access. Emerging Issues: Generational Equity. 5. The Nature of Social Provisions. Basic Forms: Cash Versus In-Kind. Alternative Forms: An Extension of Choice. Vouchers: Balancing Social control and Consumer Choice. Substance of the Social Provision. Social Provisions as Reflections of Policy Values. Cash, Kind, and the Cycles of Public Assistance. Emerging Issues: Choice for Whom? 6. The Design of the Delivery System. Privatization and Commercialization in Service Delivery. Promoting Coherence and Accessibility: Service Delivery Strategies. Unsettled Questions. Selecting Strategies. Emerging Issues: Services Rationing and Managed Care. 7. The Mode of Finance: Sources of Funds. Sources of Funds. The Philanthropic Contribution. Contributory Schemes and Fee Charging. Public Financing: Not Entirely a Public Matter. Emerging Issues: Financing Social Security. 8. The Mode of Finance: Systems of Transfer. Centralization, Decentralization, and Their Ideologies. How the Money Flows. How Transfers Are Conditioned. Devolving Public Welfare. AFDC to TANF. Emerging Issues: Immigrants, Social Policy, and the States. 9. Policy Dimensions: International Trends in the 21st Century. Pressures for Change. Directions of Change. Implications of Change.
Local Conservative associations have traditionally run their affairs independently and have successfully resisted interference from Central Office. Far from constituting a ‘centralized machine’ (as authors such as McKenzie, Beer and Crossman have maintained) the main feature of Conservative organization has been its decentralized, voluntary character. Nowhere has resistance to control by the party headquarters been more determined than in the major provincial cities. Here, confederations of city constituency associations, financed mainly by local business interests, have virtually excluded the Central Office area agents from participating in constituency organization. Attempts by successive national party chairmen to bring the city associations into the Central Office orbit have regularly been rebuffed. Consequently, Central Office's recent success in integrating the city associations into its area office organization marks the end of an era. It raises the question of whether the Conservative organization is at last becoming as centralized as many commentators have long supposed it to be. This note describes recent developments and assesses their significance.
Today's China, still a developing country with per capita health expenditure of 50 cents to one dollar (U.S.), has established a complex network of health facilities and well-distributed health personnel through the efforts of the existing political structure. The curative health services are decentralized and provide care through a variety of plans which combine capitation prepayment and modified fee-for service. Each plan is striving for the goal of making health care accessible to all at low cost, and hence, efforts of cost containment for self-sufficiency are widely practiced. The responsibility of the preventive health services (such as health education, screening, family planning, food distribution, etc.) are assumed by the central government and they are provided without charge to encourage maximal utilization. Other features of the Chinese system discussed include self-reliance, self-sufficiency, mass orientation, regionalization and innovative utilization of existing facilities, and personnel.
Martin Lang, Frederick Novotny, Mohan Jethwani, Charles Samowitz
The establishment of a centralized sewerage agency in 1963 has enabled the development of a program to upgrade and augment New York City’s sewer system to meet the vital life supporting needs of the 21st century. The previous decentralized structure, with five different design standards and financing assessments, did not lend itself to a rational and sound engineering approach to the drainage problems. The shift of population to the periphery of the city, the elimination of sewer assessment, and the antiquated sewerage mandated launching a crash effort. Citywide planning, new management techniques, infusion of new engineers, and optimal use of in-house staff and consultants have all culminated in sixfold acceleration of the sewer construction program.
SINCE 1954 nearly all vestiges of legal segregation of public schools in the South have been eliminated. But, at the same time, the suburbanization of households in Southern cities has contributed to the de facto resegregation of some schools. Just as the Tiebout hypothesis (1956) suggests that households locate according to their preferences regarding local public goods, there is some evidence to indicate that preferences for segregated schools may have contributed to this resegregation. Glantz and Delaney (1973) found that, by one measure, metropolitan residential segregation increased more during the 1960's in Southern metropolitan areas -where city schools were substantially desegregated than in the Northern metropolitan areas studied. And for some organizations, a primary reason for supporting recently ordered metropolitan desegregation plans which would effectively combine city and suburban school systems is the belief that desegregation of city schools alone merely contributed to white flight from the city.' But, because there are other factors which may also cause suburbanization of whites, such as employment decentralization and the growth of Negro ghettos, it is not clear whether school desegregation has had an independent effect on the demand for housing by households. This paper presents an analysis of housing prices to determine whether desegregation has an independent effect on the price paid by whites for housing. Since the supply of housing is relatively inelastic in the short run, an effect of this kind would support the hypothesis that desegregation affects households' demand for housing. While shifts in demand will result primarily in price effects in the short run, quantity changes and locational rearrangement will be most important in the long run. In order to determine if shifts in demand have accompanied desegregation, this paper will examine such price effects. The metropolitan area studied is Atlanta, Georgia, a Southern city which experienced school desegregation and apparent white flight during the 1960's. In 1960, a year before desegregation was begun, 37.2 % of the students in the city school system were Negro. By 1970 this figure was 67.1%. During the decade the proportion of Negro families in the city rose from 34.0% to 47.7%o. These changes reflect a number of different locational trends, one of the most important of which was a rapid growth in the city's Negro population. In order to assess the independent effect of school desegregation on housing demand, it is above all necessary to separate the effect of school racial composition from that of neighborhood racial composition, as well as other supply and demand factors affecting housing prices. The analysis presented in this paper uses data on housing prices and characteristics drawn from 1960 and 1970 census tract reports for Atlanta. The comparatively rapid end to de jure segregation in that city during the decade of the 1960's provides a unique opportunity to separate the effects of neighborhood and school integration. The empirical analysis supports the hypothesis that school desegregation does have a significant effect on housing prices, independent of neighborhood racial change. Section I discusses the use of housing prices in determining the effect of public service characteristics on housing demand. Sections II and III describe the data and the empirical findings. Section IV summarizes the analysis. Received for publication December 3, 1973. Revision acaccepted for publication July 30, 1974. * I am grateful to Professors Martin Feldstein, John Kain, Richard Freeman, and Gregory Ingram, members of the public finance and urban economics seminars at Harvard, and referees for this Review for comments on earlier drafts of this paper. Financial support was provided by the Ford Foundation. 1 See, for example, the testimony of William L. Taylor, Director of the Center for National Policy Review in hearings before the Senate Select Committee on Equal Educational Opportunity, November 30, 1971, p. 10475 or Junie Brown, City School Case: No End in Sight, Atlanta Journal-Constitution, December 31, 1972, pp. IA, 6A.
W HILE debate rages on, it seems only a matter of time before some form of national health insurance becomes a reality. Aside from the central questions regarding coverage, financing, and eligibility, an important issue involves the administration of such an insurance program. A recent analysis of 13 proposed national health insurance bills found that 10 of the bills include the existing industry to one degree or another.' This strategy makes sense because of the expertise and machinery that presently exist within the health insurance industry. If such a strategy is adopted, the fundamental problem of allocating the administrative responsibility remains. There is wide disparity in the average costs of administration among the insuring organizations. Ideally, designation of responsibility for administering any national health insurance program should be based upon efficiency considerations. To the extent that economies of scale are present within the administrative function of existing health insurers, centralization in one or a few hands can be justified. In contrast, if economies of scale are not present, administrative responsibility should be decentralized on efficiency grounds. The purpose of the present paper is to examine the administrative cost experience of the commercial health insurers in an effort to determine whether economies of scale exist.
Linear programming models of specialized financial decision problems such as working capital management [21], short-term financing [22], or capital bug-geting [24] are deficient in that they may lead to decisions which are suboptimal with respect to the firm as a whole. Each model attacks a single decision problem and neglects its interaction with the other activities of the firm. On the other hand, a model which reflects these interdependences and interactions by including the various financing, investment, and operating decisions in a single model tends to become excessively large and inefficient to use. What is needed is a model that incorporates the efficiencies inherent in smaller, more specialized models which can be utilized on a decentralized basis and which can simultaneously lead to decisions that are optimal for the firm as a whole.
A review of optimal control theory for linear systems with quadratic cost functions is presented. Some of the theoretical and practical limitations are discussed with special reference to distributed parameter systems. First a procedure is described for finding the optimal control by constructing a sequence of controllers that converges to the optimal; this method is valid for systems of infinite dimension provided that the operators in the state differential equation satisfy certain conditions. The proof is carried out both for the finite and infinite time interval and the connection is shown with the Riccati equation. The main problem in implementation is that one needs complete knowledge of the state at all times in order to build the optimal controller, this is almost certainly impossible for distributed parameter systems. When the state cannot be measured completely it is proved that an optimal control is realisable for time invariant finite dimensional systems. \n \nThe problems of finding this control are then investigated and computational methods discussed. If the optimal control with complete knowledge of the state cannot be implemented, a method is presented whereby one can find bounds on the possible increase in the value of the cost function arising from the use of some sub-optimal control; several examples are considered. The constrained optimal control depends on the initial state and new optimisation criteria must be put forward to deal with the case in which the initial state is unknown; the most common consist of minimising the cost that can result from the worst initial state. It is then shown how the controllers designed according to these criteria may be improved by using one's limited observation at time zero to place some constraints on the initial state. The Liapunov matrix equation plays an important part in calculating the cost of any control so reducing the computational effort in its solution is useful. It is shown how this can be done and it is of special relevance for distributed parameter systems with their states expressed as an infinite series of eigenfunctions; the results are applied to a diffusion equation example. \n \nFinally, it is shown how optimal control theory may be applied to the design of proportional-integral-derivative controllers. This is done from two standpoints and the resulting controllers are shown to be identical, though the second method of proof is valid for infinite dimensional systems. The results are then applied to a simple example and to a distributed population dynamics system. The practicality of the methods of the thesis are applied to a system with realistic parameters; recommendations are made as to the best approaches. \n
ARE CONCLUSIVE PROOFS IRRELEVANT TO RELIGION? FOR CENTURIES the proofs for God's existence have been debated and their role in religious belie£-systems assessed. There have been those who claim that the proofs are conclusive, those who claim that they are invalid , and those who claim that they are valid but inconclusive . There have been disputes, furthermore, as to whether the logical base for religious belie£ systems should be sought in proofs and evidence rather than in "self-authenticating" religious experiences and acceptance o£ religious authority. But no one, until recently, ever contended that even if the proofs were conclusive it would be irrelevant to religious believers. People have thought that religion must be undergirded by proof, aan be undergirded by proof, and need not be undergirded by proof, but not that proof would be irrelevant. Now o£ course there are many senses in which a proof could be relevant to religious believers. The Vatican Council affirmed that i£ people denied that God could be known with certainty by the natural light of human reason they would be anathema. Thus it could have made quite serious practical differences to a believer whether he accepted the proofs or not. As philosophers we are not concerned with this sort of practical difference but with philosophical ones, and the question to be explored is: Is there something philosophically at stake for believers in this question o£ the proofs for the existence o£ God? I want to contend that Steven M. Cahn is utterly wrongheaded in his claim that religious believers have no real interest in philosophical proofs for the existence of God.1 I am assuming that this 1 Steven M. Cahn, " The Irrelevance to Religion of Philosophic Proofs for the Existence of God," The American Philosophical Quarterly (April, 1969), pp. 170-72. Further citations will be given by page number in the text. Cahn has 727 7~8 FRANK B. DILLEY is not a statistical claim to be settled by polls but rather a philosophical claim. Cahn makes no effort to produce questionnaire results from a proper sample of believers nor shall I. To examine this question, in the context of Cahn's contention , it is fortunately not necessary to resolve the question of the validity of the proofs. In an effort to dismiss them once for all, Cahn is willing to assume that the proofs are valid, for the sake of the argument. " Suppose we assume, contrary to what most philosophers, I among them, believe, that all of these proofs are valid. Let us grant the necessary existence (whatever that might mean) of the most perfect conceivable Being, a Being who is ali-good and is the designer and creator of the universe. What implications can be drawn from this fact which would be of relevance to human life? In other words, what difference would it make in men's lives if God existed?" (p. 170) In support of his surprising thesis that religious believers are right in ignoring the proofs, he gives two chief arguments, that religious believers make their decisions as to what beliefs to hold and what practices to follow on the basis of "self-validating " personal experiences which render the proofs unnecessary , and that the success of the proofs would not enable a newly converted unbeliever to know what beliefs and practices to choose. He therefore contends that the proofs are relevant for neither the believer nor the unbeliever. In examining his contention about the relevancy of proofs I propose to look at what religious belief systems say about this problem, an approach Cahn does not seem to care to use. In this connection it should be noted that his sources are curious, for he cites not one person who would be taken by anyone to be a normal religious believer. He cites Antony Flew, Wallace Matson, C. B. Martin, and Mordecai Kaplan, but not John reprinted this essay in his Philosophy of Religion (Harper & Row, 1970), and it can also be found in Philosophy in the Age of Crisis, ed. Eleanor Kuykendall (Harper & Row, 1970) and God, Man, and Rdigion: Readings in the Philosophy of Rdigion, ed. by Keith Yandell (McGraw-Hill, 1973). ARE CONCLUSIVE PROOFS IRRELEVANT...
Many policies use two categories of instruments: a financial incentive (most often a tax) for polluters, and direct undertakings or financing of some restorations or maintenances or improvements of environmental qualities. The financial consequences of such policies, when optimum, are important for considerations of public finance, decentralization (financial autonomy), and equity (must polluters pay?). They turn out essentially to depend upon the mathematical structure of, first, the environment function, i.e., the way in which qualities depend upon both deteriorating and improving activities, and, second, the various constraints of the problem. Constraints which can be expressed by functions homogeneous of any degree are shown to have no direct financial effect. Apart from the constraints' effects, budgetary equilibrium, surplus or deficit are respectively given by functions which present constant, decreasing, or increasing qualitative returns to scale, i.e., weighted homogeneity of degree zero, positive or negative. The opposite polar cases of cleaning and dilution types of improvement technology are presented, with some other mixed simple cases and a few examples of application of the results.
A series of recent judicial decisions has focused public attention on the issue of local choice in the provision of public education. In Serrano vs. Priest, Rodriguez vs. San Antonio (1971), and similar cases in other states, the lower courts confirmed that education is a responsibility of the state government and held that local expenditures on education may not be a function of the taxable wealth of the local community.1 Although the United States Supreme Court has overturned these decisions in the appeal of Rodriguez vs. San Antonio (1973), the pressure to change the current system remains strong. The Supreme Court majority indicated that its decision reflected the limits of the federal constitutional authority and was not an approval of the status quo in educational finance. Litigation is now likely to shift to challenging the current methods as unconstitutional under state constitutions which, unlike the federal constitution, do deal specifically with education.2 Moreover, fundamental changes in the financing of local education may not require further pressure from the courts; state legislatures may seek to neutralize the effects of local wealth differences even if the current systems are not held to be unconstitutional. These judicial decisions and the ensuing legislative proposals run counter to the general economic view of local government finance. The basic presumption of economic analysis is that, because local governments can select different levels of service and because individuals can choose their area of residence, decentralized finance by local governments allows the provision of public services to reflect the variety of individual preferences for public services.3 Although the level of local spending may be nonoptimal because of intercommunity externalities and because of the method of local budget determination, fiscal decentralization still remains the only alternative to the insuperable problem of determining the optimal level of expenditure on a public service provided by a central government. In effect, autonomous decentralized financing of education provides a quasi market in which households can exercise their diverse preferences by their location decisions. This paper considers the problem of * Professor of economics, Harvard University. I am grateful to Charles Clotfelter for assistance with the statistical analysis, to Stephen Weiss for providing unpublished data on school expenditures, and to the Ford Foundation and National Science Foundation for financial support. I have benefited from discussions of an earlier version in seminars at Harvard, M.I.T., and Berkeley, and from comments by Noel Edelson, Eric Toder, and David Stern. An earlier and more complete discussion of this study was distributed as Harvard Institute of Economic Research paper no. 293, May 1973 (revised July 1973). 1 In Serrano vs. Priest, the landmark case in this area, the plaintiff and the courts were very much influenced by the line of argument and suggested remedies develope(l in John Coons et al. For a further discussion of the legal precedents, see Arthur Wise. 2 Almost immediately after the United States Supreme Court decision in Rodriguez vs. San Antonio, the New Jersey Supreme Court held that the current system of local finance violated the New Jersey state constitution. See Wise for a summary of the provisions of other state constitutions. I Charles Tiebout presented a formal analysis of the full efficiency of local government provision of public services under quite special conditions. See Wallace Oates and James Buchanan and Charles Goetz for a further discussion of these issues.
The synchronization task between loosely coupled cyclic sequential processes (as can be distinguished in, for instance, operating systems) can be viewed as keeping the relation “the system is in a legitimate state” invariant. As a result, each individual process step that could possibly cause violation of that relation has to be preceded by a test deciding whether the process in question is allowed to proceed or has to be delayed. The resulting design is readily—and quite systematically—implemented if the different processes can be granted mutually exclusive access to a common store in which “the current system state” is recorded.
IGR and the New Federalism are synonymous. Former President Nixon summarized the New Federalism as "A cooperative venture among governments at all levels ... in which power, funds, and authority are channeled increas ingly to those governments which are closest to the people." IGR is essentially an art and primarily an exercise in the be havioral field. The thread which binds government officials intergovernmentally is the financing and administration of federal grants-in-aid and other forms of federal financial assis tance. Concern in the executive branch for IGR developed in the last 20 years; thus its roots in American governance are not yet very deep. The views and support of public interest groups as well as the sympathetic attention of Congress are essential to the pursuit of IGR goals and objectives in the executive branch. In relations between levels of government, partnership rather than paternalism must prevail. The rise of stronger chief executives and decentralization of power from Washington are noted. Confidence of Americans in their own government is essential to achieving a federal system working in all parts, well-managed and equitably financed.
Before geographers commit themselves to public policy, they need to pose two questions: what kind of geography and what kind of public policy. The evolution of the discipline, in terms both of its aims and its professional organization, must be seen as an adaptation to external conditions, particularly to the development of the corporate state with its emphasis on the 'national interest'. The corporate state forces education to be seen purely as investment in manpower and academic research becomes subservient to the state and is used to preserve and strengthen the status quo. There is here a potential conflict with the academic's sense of moral obligation, but in practice the conflict is resolved by the parochialism and elitism of the humanistic tradition. To help to move away from the corporate state and towards the 'incorporated state' in which men can control the social conditions of their own existence, geographers need to address their efforts towards understanding the tension between the humanistic tradition and the pervasive needs of the corporate state and thereby to learn how to exploit the contradictions within the corporate state itself. CAN geographers contribute successfully, meaningfully and effectively to the formation of public policy ? General Pinochet is a geographer by training, and by all accounts he is successfully putting geography into public policy. As President of the military Junta that overthrew the elected government of Salvador Allende in Chile on I September I973, General Pinochet does not approve of 'subversive' academic disciplines such as sociology, politics and even philosophy. He has asked that 'lessons in patriotism' be taught in all Chilean schools and universities and he is known to look with great favour upon the teaching of geography-such a subject is, he says, ideally suited to instruct the Chilean people in the virtues of patriotism and to convey to the people a sense of their true historic destiny. Since the military have taken full command of the universities and frequently supervise instruction in the schools, it appears that geography will become a very significant discipline in the Chilean educational system. General Pinochet is also actively changing the human geography of Chile. An example is here in order. The health care system of Chile has, for some time, comprised three distinct components: the rich paid for services on a 'free-market' basis; the middle classes made use of hospital-based medicine financed by private insurance schemes; while the lower classes and poor (some 60 per cent of the population) received free medical care in community-based health centres paid for out of a National Health Service.1 Under Allende, resources were switched from the first two sectors into the community health services which had previously been poorly financed and largely ignored. The geography of the health care system began to be transformed from a centralized, provider-controlled, hospital-centred system catering exclusively to the middle and upper classes, to a decentralized, community-controlled, free health care system primarily catering to the needs of the lower classes and the poor. This transformation did not occur without resistance-the providers of hospital-based medicine organized strikes to preserve the old social geography of health care against the emergence of the new. But during the Allende years the community health centres grew and flourished. Also, community control through the creation of Community Health Councils had a profound political impact and many aspects of life began to be organized around the community health centres. The emphasis also shifted from curative medicine (with all of its glamour and expensive paraphernalia) to preventive medicine which sought to treat medical care as something integral to a wide range of environmental issues (water supply, sewage disposal, and the like). The human geography of social contact, political power and distribution changed as hitherto never before, as the lower classes and poor people began to realize the potential for controlling the social conditions of their own existence.