Impediments to Social Development in Pakistan

The development of infrastructure and the provision of basic services in Pakistan lie in the public domain. The quality of the built infrastructure and the service offered reflect successive governments’ capability as a channel for public sector funds, their role in overall financial and macro-economic planning and management, and their administrative efficiency in implementation, operations and management—in essence the extent to which they are able to adhere to the principles of good and humane governance. Good governance is generally conceived of as the judicious exercise of economic, political and administrative authority in the public and private spheres to manage a country’s affairs at all levels to improve the quality of life of the people. It is a continuing process where divergent opinions and desires are satisfied through compromise and tolerance in a spirit of cooperative action for the mutual benefit of the larger whole. It has three dimensions: one, the political regime; two, the systems and procedures for exercising authority; and three, the capacity of governments [World Bank (1994); UNDP (1997); OECD (1995); Commission on Global Governance (1995)]. When Pakistan gained political freedom in August 1947, it inherited an economic and social infrastructure unable to meet the demands of the large influx of refugees from India. Five decades later, policies emphasising public investment, subsidised credit and regulated private sector development have generated strong economic growth, but failed to implement successful social development. Over the last 50 years and more Pakistan’s economy, measured through its GDP, has grown by more than 10 times, an average annual growth rate of 5.1 percent. Rapid population growth, estimated to have averaged just under 3 percent annually, has resulted in real per capita increases of only 2.1 percent per year.

Spectral Analysis of Certain Schr\"odinger Operators

The $J$-matrix method is extended to difference and $q$-difference operators and is applied to several explicit differential, difference, $q$-difference and second order Askey-Wilson type operators. The spectrum and the spectral measures are discussed in each case and the corresponding eigenfunction expansion is written down explicitly in most cases. In some cases we encounter new orthogonal polynomials with explicit three term recurrence relations where nothing is known about their explicit representations or orthogonality measures. Each model we analyze is a discrete quantum mechanical model in the sense of Odake and Sasaki [J. Phys. A: Math. Theor. 44 (2011), 353001, 47 pages]

Generalized Burchnall-Type Identities for Orthogonal Polynomials and Expansions

Burchnall's method to invert the Feldheim-Watson linearization formula for the Hermite polynomials is extended to all polynomial families in the Askey-scheme and its $q$-analogue. The resulting expansion formulas are made explicit for several families corresponding to measures with infinite support, including the Wilson and Askey-Wilson polynomials. An integrated version gives the possibility to give alternate expression for orthogonal polynomials with respect to a modified weight. This gives expansions for polynomials, such as Hermite, Laguerre, Meixner, Charlier, Meixner-Pollaczek and big $q$-Jacobi polynomials and big $q$-Laguerre polynomials. We show that one can find expansions for the orthogonal polynomials corresponding to the Toda-modification of the weight for the classical polynomials that correspond to known explicit solutions for the Toda lattice, i.e., for Hermite, Laguerre, Charlier, Meixner, Meixner-Pollaczek and Krawtchouk polynomials

Gender Differentials in the Cost of Primary Education: A Study of Pakistan

The paper examines the differences in the cost of primary education by gender and by province. It shows that the growth in enrolment outstrips the growth in the relevant population cohort, except in Sindh, and that this is faster in the case of girls than boys; that the school construction programme for girls in Sindh, unlike other provinces, outstrips the growth in female teacher employment. This is also seen in the boys’ school in Pakistan. Cost of providing education are a function of the availability of teachers and schools, opportunity cost of employment, urbanisation and female literacy. The growth in both recurring and capital outlays and in output costs per student are higher for girls and boys except in Balochistan. Using a pooled time series and analysis the paper concludes that there is an optimal level for the availability of schools per 1000 population [6.02 and 5.67 respectively for girls and boys in the Punjab and 3.88 for boys in NWFP and Balochistan] and for the number of teachers per 1000 students [7.69 for girls and 3.36 for boys]. It suggests the policy prescription to reallocate resources to employing more teachers for boys for greater cost effectiveness.