Urban Growth

This paper models and examines empirically the evolution of cities in an economy. Twentieth century evolution in the USA is characterized by parallel growth of cities of different types and on-going entry of new cities, together maintaining a stable relative size distribution of cities. Each type of city has a particular industrial composition and good(s) it specializes in and corresponding equilibrium size. This evolution is modeled in an economy with exogenous population growth and endogenous human capital accumulation. Within cities, there are knowledge spillovers as well as scale externalities. Individual city sizes grow with human capital accumulation; and cities grow in number if national population growth is high enough. Different types of cities grow in parallel in size and human capital accumulation. However, per capita income and human capital levels differ across city types by production process and benefits of human investments and spillovers, so there is observed inequality across cities among otherwise identical individuals.

Convolution spline approximations for time domain boundary integral equations

We introduce a new "convolution spline'' temporal approximation of time domain boundary integral equations (TDBIEs). It shares some properties of convolution quadrature (CQ) but, instead of being based on an underlying ODE solver, the approximation is explicitly constructed in terms of compactly supported basis functions. This results in sparse system matrices and makes it computationally more efficient than using the linear multistep version of CQ for TDBIE time-stepping. We use a Volterra integral equation (VIE) to illustrate the derivation of this new approach: at time step t_n = n\dt the VIE solution is approximated in a backwards-in-time manner in terms of basis functions $\phi_j$ by u(t_n-t) \approx \sum_{j=0}^n u_{n-j}\,\phi_j(t/\dt) for $t \in [0,t_n]$. We show that using isogeometric B-splines of degree $m\ge 1$ on $[0,\infty)$ in this framework gives a second order accurate scheme, but cubic splines with the parabolic runout conditions at $t=0$ are fourth order accurate. We establish a methodology for the stability analysis of VIEs and demonstrate that the new methods are stable for non-smooth kernels which are related to convergence analysis for TDBIEs, including the case of a Bessel function kernel oscillating at frequency \oo(1/\dt). Numerical results for VIEs and for TDBIE problems on both open and closed surfaces confirm the theoretical predictions

The Incidence of Income Taxes

For a considerable period it has been held by economists that the incidence of a general income tax is not shifted, and that such a tax has no tendency to raise or otherwise alter the prices of commodities. The most careful formulation of this theory, which, for convenience, I refer to as the older theory, can be found in the writings of Professor Seligman and Mr. Coates, and the same view of the matter was for the most part adopted by the Colwyn Committee on National Debt and Taxation which made its Report in 1927. In December of 1927 however, a very important article by Mr. D.H. Robertson appeared, which made it plain that the arguments on which the economists had relied to show that the incidence of a general income tax is not shifted, were erroneous. The whole matter was seen to require further investigation. The following two Chapters of part I of this book outline the older theory of the incidence of a general income tax and go on to criticise this theory. When it has been made clear that the older theory is no longer tenable, instead of proceeding direct to a. reconstruction of this theory we deal in Part II with the incidence of partial income taxes. This is partly on account of the interest and importance of such taxes in themselves and partly because an insight into the nature of these taxes seems likely to be helpful to an understanding of the incidence of a general income tax. In Part III the problem of the incidence of a general income tax is again taken up: to construct a theory of the incidence of a general income ta,x is the main object of this book. Part IV goes on to supplement Part III and deals with a number of related questions. Parts I, II and III can be read independently of one another; and if the student chooses he may omit reading Part I or Part II; or else,.if his interest be mainly in the incidence of partial income taxes, he may read Part II alone, Part IV should only be read after Part III

Aspects of purine and pyrimidine metabolism

In Chapter 1 a review of the literature concerning aspects of erythrocyte membrane transport and metabolism, and purine and pyrimidine metabolism is presented. The effects of pH, pO₂ and inorganic phosphate (Pi) on the uptake and metabolism of hypoxanthine by erythrocytes has been studied in Chapter 2. Uptake of hypoxanthine and accumulation of inosine 5'-monophosphate (IMP) were markedly increased at acid pH, high external phosphate concentrations, and low pO₂. Release of accumulated IMP as hypoxanthine occurred at alkaline pH values and low external phosphate concentrations. Conditions favouring IMP accumulation gave rise, in the absence of hypoxanthine, to a corresponding increase in 5'-phosphoribosyl-1-pyrophosphate (PRPP). Intracellular phosphate concentrations were markedly pH dependent and a model is presented whereby hypoxanthine uptake and release are controlled by intracellular concentrations of inorganic phosphate and 2,3- bisphosphoglycerate (2,3-DPG). These allosteric effectors influence, in opposing ways, two enzymes governing IMP accumulation, namely PRPP synthetase and 5'-nucleotidase. These metabolic properties suggest that the erythrocyte could play a role in the removal of hypoxanthine from anoxic tissue. In Chapter 3 the kinetics and mechanism of transport of orotate across the human erythrocyte membrane and the effect of pH and inorganic phosphate on its metabolism (in the erythrocyte) have been studied. It has been shown that orotate enters erythrocytes with non-saturable kinetics and with a capacity of 190 μmoles/1 packed cells/min at a concentration of 4-6 mmolar. The presence of competition for transport by a number of anions and the lack of competition by uridine is indicative of transport by a general anion transporter, with the ability for concentrative uptake in the absence of other external anions being compatible with transport via a ping-pong mechanism. Inhibition of transport by the specific band 3 inhibitors DIDS and CHCA confirm that transport is via the band 3 anion transporter. This explains the lack of significant uptake of orotate by most differentiated tissues which lack the intact band 3 protein. However, the demonstration of band 3 in rat hepatocytes (Cheng and Levy, 1980) provides a mechanism for the orotate transport which has been observed in liver (Handschumacher and Coleridge, 1979). Changes in pH and inorganic phosphate (Pi) concentrations have been shown to have marked effects on the relative quantities of metabolic products produced by the erythrocyte from orotate. There was an increase in orotate metabolised with increasing Pi, an effect augmented by lowering the pH, and most easily explained by the allosteric activation of PRPP synthetase by Pi. The increase in UTP levels with decreasing pH may be the consequence of both increased PRPP availability for the formation of uridine nucleotide from orotate, and decreased conversion of UMP to uridine by pyrimidine 5'-nucleotidase, which is known to be inhibited by phosphate. The accumulation of UDP sugars is optimal at a phosphate concentration of 10 mmolar, which is unexplained but would be compatible with an inhibitory effect of Pi on CTP synthetase. A PRPP wasting cycle at alkaline pH values is proposed to explain the apparent paradox where no PRPP was observed to accumulate in erythrocytes (Chapter 2) at pH values of 7.6 and above in the presence of 10 mmolar phosphate and no added hypoxanthine, yet the metabolism of orotate, which is a PRPP utilising reaction, at alkaline pH values was readily demonstrable here. This (apparent paradox) can be resolved if one assumes that even in the absence of added hypoxanthine and demonstrable intracellular IMP there are sufficient quantities of hypoxanthine and/or IMP to maintain a PRPP wasting cycle at alkaline pH values. The cycle is interrupted at acidic pH values as phosphate levels rise and inhibit 5'-nucleotidase, an effect augmented by the decreasing levels of 2,3-DPG which accompany decreasing pH. This wasting cycle has recently been confirmed by P. Berman (unpublished). The kinetics of orotate uptake by erythrocytes and its eventual release as uridine provides a role for the erythrocyte in the transport and distribution of pyrimidines to peripheral tissues. A model is proposed and involves the de novo production of orotate in the liver. In the next step erythrocytes take up the orotate secreted by the liver into the circulation, convert it into an intermediate buffer store of uridine nucleotides, whose distribution is a function of pH and phosphate concentration, and eventually release it as uridine, which is a readily available form of pyrimidine for utilisation by peripheral nucleated cells. The enhancement of uptake of labelled orotate into nucleic acids of cultured cells is demonstrated here. The degradative half of the cycle proposes that uracil and palanine are the predominant degradative forms of pyrimidines produced by peripheral cells, and their ultimate metabolic fate is complete catabolism in the liver to CO₂ and water. In the final chapter the possible role of the human erythrocyte in the prevention of reperfusion injury has been investigated. The development of a model of renal ischaemia in the rat is described. The ability of human erythrocytes, "primed" by preincubating in acid medium of high Pi concentration and low pO₂, to take up hypoxanthine in a concentrative manner when perfused through ischaemic rat kidney is demonstrated. Attempts to demonstrate improved survival and renal function in rats with "primed" human erythrocytes prior to reperfusion were, however, unsuccessful. It is further demonstrated that "unprimed" human erythrocytes, resident in ischaemic rat kidney for 3 hours, take up hypoxanthine and convert it to IMP. that erythrocytes could play a physiological prevention of reperfusion injury

Studies on limb blood flow in normal and abnormal pregnancy

Abstract Not Provided

A non-autonomous stochastic discrete time system with uniform disturbances

The main objective of this article is to present Bayesian optimal control over a class of non-autonomous linear stochastic discrete time systems with disturbances belonging to a family of the one parameter uniform distributions. It is proved that the Bayes control for the Pareto priors is the solution of a linear system of algebraic equations. For the case that this linear system is singular, we apply optimization techniques to gain the Bayesian optimal control. These results are extended to generalized linear stochastic systems of difference equations and provide the Bayesian optimal control for the case where the coefficients of these type of systems are non-square matrices. The paper extends the results of the authors developed for system with disturbances belonging to the exponential family