Smith Normal Form of a Multivariate Matrix Associated with Partitions

Consideration of a question of E. R. Berlekamp led Carlitz, Roselle, and Scoville to give a combinatorial interpretation of the entries of certain matrices of determinant~1 in terms of lattice paths. Here we generalize this result by refining the matrix entries to be multivariate polynomials, and by determining not only the determinant but also the Smith normal form of these matrices. A priori the Smith form need not exist but its existence follows from the explicit computation. It will be more convenient for us to state our results in terms of partitions rather than lattice paths.Comment: 12 pages; revised version (minor changes on first version); to appear in J. Algebraic Combinatoric

The Persistence Behaviour of Registered Apprentices: Who Continues, Quits, or Completes Programs?

We utilize a multinomial probit model and the 2007 National Apprenticeship Survey (NAS) to investigate the persistence behaviour of individuals enrolled in apprenticeship programs. These behaviours include continuing, discontinuing (or quitting) and completing programs. The NAS contains detailed demographic data as well as other data regarding respondents’ backgrounds and apprenticeship characteristics. Our results show that program completion is positively related to being married, having fewer children, being non-Aboriginal and not a visible minority, not being disabled and having a higher level of education before the beginning of the program. Completion is negatively related to time in the program (beyond the normal program length) and the number of employers. Type of technical training and having a journeyperson always present enhance the probability of completion. The regional unemployment rate has little effect on completion. There are also large provincial and trade group differences that are generally consistent with the sparse literature on this topic. Males and females have similar completion probabilities when we control for other influences.Apprenticeship Training, Completion Outcomes, Canada

Fiscal decentralization and intergovernmental relations in transition economics : toward a systematic framework of analysis

The decentralization of government in Eastern Europe represents a reaction both from below (to tight central political control) and from above (to privatize the economy and relieve the central government's fiscal stress). In all transitional economies, the developing structure of intergovernmental relations is intimately related to such critical policy issues as privatization, stabilization, and the social safety net. In the fiscal sphere, tax reform, deficit control, and intergovernmental finance are a tripod. Unless each leg is set up properly, the whole structure could collapse. The present strategy of devolving expenditures downward while holding back on revenue flows and transfers to balance the central budget is unlikely to succeed for more than a year or two at best. Net spending reductions at the subnational level may be difficult to achieve. From 10 to 40 percent of outlays go to the subnational sector, and in many countries local governments provide much of the social safety that makes the pain of the economic transition politically tolerable. And, most housing and many enterprises have been shifted to local ownership, with the maintenance and subsidy cost this implies. Since the revenue sources assigned to local governments cannot finance expected levels of local activity, the result of shifting spending downward is likely to be strong demands for increased, rather than decreased, transfers. Alternatively, subnational government may look to coping mechanisms such as holding on to their enterprises (which provide vital social services), developing extrabudgetary revenues, or borrowing. These coping mechanisms threaten privatization, reduce budgetary transparency, and impede stabilization policies. The authors describe the risks to privatization, to macroeconomic stability, and to an adequate social safety net that present policies toward local government may imply. Its themes are that the subnational sector needs to be more realistically factored into national plans - and that subnational expenditures be more clearly assigned and revenue needs more realistically assessed. Such assessments are likely to acknowledge a larger sphere for subnational governments and the need for access to more robust revenue sources. Giving local government a share in the personal income tax is one possible and perhaps desirable approach to meeting these revenues needs. Careful attention needs to be paid to the design and implementation of the intergovernmental fiscal transfers likely to remain prominent features of the intergovernmental landscape for years to come. Caution is also needed on borrowing by subnational government. Consolidating and integrating extrabudgetary funds at the subnational (and national) levels is crucial to enhanced budgetary transparency and macrostability.Banks&Banking Reform,National Governance,Public Sector Economics&Finance,Municipal Financial Management,Urban Economics

Financing local government in Hungary

Hungary has undertaken a bold and far-ranging reform of its system of subnational finances. This paper outlines the changes introduced in the system of local finance as a result of the 1990 Local Self-Government Act, and the 1990 Act on Local Taxes and provides a preliminary assessment of their implications as well as the need for further reform. These Acts, together with the annual Act on the Budget, define the overall scope and authorities of Hungary's approximately 3100 new local self-governments. These Acts: (i) define the new assignment of expenditures between central and local government; (ii) define the new local revenue sources; and (iii) establish the economic foundation, property rights and entrepreneurial functions of the localities. The paper outlines the historical evolution of the system, provides international comparisons, and describes its present-day form. Drawing on this background, it suggests some revised policies that should not only both help avert the potentially undesirable outcomes of the current system but, more positively, help Hungary to achieve its goal of a smaller, more efficient government sector without unduly exacerbating social inequalities. In turn, issues and recommendations are discussed in the following areas: local finance; assignment of expenditures; assignment of taxes; design of the transfer system; role of the localities in property management; capital investment; and other requisites for sound local finance.Banks&Banking Reform,Municipal Financial Management,National Governance,Urban Economics,Public Sector Economics&Finance

Promoting environmentally sustainable enterprises: some policy options

Governments around the world are taking an increasing interest in promoting environmentally-sustainable economic activity. They have developed a variety of policy approaches in an effort to address environmental issues that range from localised pollution incidents to global climate change. This chapter examines the kinds of intervention tools that are being used to improve the environmental performance of SMEs, and to guide entrepreneurial energies towards more environmentally-benign goals. The chapter aims to: (1) outline the main options available to policy-makers; (2) compare specific intervention tools, noting their strengths and limitations; and (3) discuss the case for adopting more holistic approaches to address the pervasive, complex and often deeply-rooted challenges of sustainable development. Key lessons are that policy makers need to select appropriate combinations of tools based on careful reviews of the evidence, and that well-integrated, context-sensitive policies are likely to prove the most effective

European Starlings (Sturnus Vulgaris) : Avian Model and Monitor of Contaminant and Remedial Effects at Crab Orchard National Wildlife Refuge

WMRC Project #94-12

Authentic student inquiry: the mismatch between the intended curriculum and the student-experienced curriculum

As a means of achieving scientific literacy goals in society, the last two decades have witnessed international science curriculum redevelopment that increasingly advocates a 'new look' inquiry-based approach to learning. This paper reports on the nature of the student-experienced curriculum where secondary school students are learning under a national curriculum that is intent on promoting students' knowledge and capabilities in authentic scientific inquiry, that is, inquiry that properly reflects that practiced by members of scientific communities. Using a multiple case study approach, this study found that layers of curriculum interpretation from several 'sites of influence' both outside and inside of the schools have a strong bearing on the curriculum enacted by teachers and actually experienced by the students, and runs counter to the aims of the national curriculum policy. Over-emphasis on fair testing limits students' exposure to the full range of methods that scientists use in practice, and standards-based assessment using planning templates, exemplar assessment schedules and restricted opportunities for full investigations in different contexts tends to reduce student learning about experimental design to an exercise in 'following the rules'. These classroom realities have implications for students' understanding of the nature of authentic scientific inquiry and support claims that school science is still far removed from real science

ACCOUNTING FOR THE IMPORTANCE OF NONFARM INCOME ON FARM FAMILY INCOME INEQUALITY IN NEW YORK

As the proportion of farm family income due to nonfarm sources continues to grow nationally, it is important to understand how farm families in various regions or states are affected. This paper develops a better understanding of the contribution of income from nonfarm sources to the level and distribution of income among farm families in New York. In analyzing income distribution, the Gini ratio is decomposed to determine the effects of marginal changes in income by source to overall inequality. The results are compared with the simulated changes in income inequality due to changes in income by source as measured by an "adjusted" Gini ratio which accounts specifically for negative farm incomes. Differences in the policy implications from both procedures are compared. The relationships among sources of income and policy implications can be brought into sharper focus by examining both measures.Agricultural Finance,