Approximation of the perturbation equations of a quasi-linear hyperbolic system in the neighborhood of a bicharacteristic

In 1956 Whitham gave a nonlinear theory for computing the intensity of an acoustic pulse of an arbitrary shape. The theory has been used very successfully in computing the intensity of the sonic bang produced by a supersonic plane. [4.] derived an approximate quasi-linear equation for the propagation of a short wave in a compressible medium. These two methods are essentially nonlinear approximations of the perturbation equations of the system of gas-dynamic equations in the neighborhood of a bicharacteristic curve (or rays) for weak unsteady disturbances superimposed on a given steady solution. In this paper we have derived an approximate quasi-linear equation which is an approximation of perturbation equations in the neighborhood of a bicharacteristic curve for a weak pulse governed by a general system of first order quasi-linear partial differential equations in m + 1 independent variables (t, x1,…, xm) and derived Gubkin's result as a particular case when the system of equations consists of the equations of an unsteady motion of a compressible gas. We have also discussed the form of the approximate equation describing the waves propagating upsteam in an arbitrary multidimensional transonic flow.

Analytical method for solving a set of inhomogeneous infinite simultaneous equations

It is shown that a method based on the principle of analytic continuation can be used to solve a set of inhomogeneous infinite simultaneous equations encountered in the analysis of surface acoustic wave propagation along the periodically perturbed surface of a piezoelectric medium.

Essays on Illegal Activities, Institutions and Economic Growth

In public economics, two extremist views on the functions of a government compete: one emphasizes government working for the public interest to provide value for the citizens, while another regards government mainly as a workhorse for private interests. Moreover, as the sole legitimate authority, the government has the right to define the rules and laws as well as to enforce them. With respect to regulation, two extremes arise: from too little regulation to too much of it. If the government does not function or ceases to exist, the state falls into anarchy or chaos (Somalia). If it regulates too much, it will completely suffocate private activities, which might be considered extralegal (the former Soviet Union). In this thesis I scrutinize the government s interventionist policies and evaluate the question of how to best promote economic well-being. The first two essays assume that the government s policies promote illegal activity. The first paper evaluates the interaction between the government and the mafia, and pays attention to the law enforcement of underground production. We show that the revenue-maximizing government will always monitor the shadow economy, as monitoring contributes to the government s revenue. In general, both legal and illegal firms are hurt by the entry of the mafia. It is, however, plausible that legal firms might benefit by the entry of the mafia if it competes with the government. The second paper tackles the issue of the measurement of the size of the shadow economy. To formulate policies it is essential to know what drives illegal economic activity; is it the tax burden, excess regulation, corruption or a weak legal environment? In this paper we propose an additional explanation for tax evasion and shadow production, namely cultural factors as manifested by religion as determinants of tax morality. According to our findings, Catholic and Protestant countries do not differ in their tax morale. The third paper contributes to the literature discussing the role of the government in promoting economic and productivity growth. Our main result is that, given the complex relationship between economic growth and economic freedom, marketization has not necessarily been beneficial in terms of growth. The last paper builds on traditional growth literature and revisits the debate on convergence clubs arising from demographic transition. We provide new evidence against the idea that countries within a club would converge over time. Instead, we propose that since the demographic transition is a dynamic process, one can expect countries to enter the last regime of stable, modern growth in stages.

An appendix to the paper "approximation of the perturbation equations of a quasi-linear hyperbolic system in the neighborhood of a bicharacteristic"

The theory of Varley and Cumberbatch [l] giving the intensity of discontinuities in the normal derivatives of the dependent variables at a wave front can be deduced from the more general results of Prasad which give the complete history of a disturbance not only at the wave front but also within a short distance behind the wave front. In what follows we omit the index M in Eq. (2.25) of Prasad [2].

Essays on macroeconomic effects of fiscal policy rules

Economic and Monetary Union can be characterised as a complicated set of legislation and institutions governing monetary and fiscal responsibilities. The measures of fiscal responsibility are to be guided by the Stability and Growth Pact, which sets rules for fiscal policy and makes a discretionary fiscal policy virtually impossible. To analyse the effects of the fiscal and monetary policy mix, we modified the New Keynesian framework to allow for supply effects of fiscal policy. We show that defining a supply-side channel for fiscal policy using an endogenous output gap changes the stabilising properties of monetary policy rules. The stability conditions are affected by fiscal policy, so that the dichotomy between active (passive) monetary policy and passive (active) fiscal policy as stabilising regimes does not hold, and it is possible to have an active monetary - active fiscal policy regime consistent with dynamical stability of the economy. We show that, if we take supply-side effects into ac-count, we get more persistent inflation and output reactions. We also show that the dichotomy does not hold for a variety of different fiscal policy rules based on government debt and budget deficit, using the tax smoothing hypothesis and formulating the tax rules as difference equations. The debt rule with active monetary policy results in indeterminacy, while the deficit rule produces a determinate solution with active monetary policy, even with active fiscal policy. The combination of fiscal requirements in a rule results in cyclical responses to shocks. The amplitude of the cycle is larger with more weight on debt than on deficit. Combining optimised monetary policy with fiscal policy rules means that, under a discretionary monetary policy, the fiscal policy regime affects the size of the inflation bias. We also show that commitment to an optimal monetary policy not only corrects the inflation bias but also increases the persistence of output reactions. With fiscal policy rules based on the deficit we can retain the tax smoothing hypothesis also in a sticky price model.

Essays on Finnish Economic Growth and Productivity, 1860-2005

This study examines Finnish economic growth. The key driver of economic growth was productivity. And the major engine of productivity growth was technology, especially the general purpose technologies (GPTs) electricity and ICT. A new GPT builds on previous knowledge, yet often in an uncertain, punctuated, fashion. Economic history, as well as the Finnish data analyzed in this study, teaches that growth is not a smooth process but is subject to episodes of sharp acceleration and deceleration which are associated with the arrival, diffusion and exhaustion of new general purpose technologies. These are technologies that affect the whole economy by transforming both household life and the ways in which firms conduct business. The findings of previous research, that Finnish economic growth exhibited late industrialisation and significant structural changes were corroborated by this study. Yet, it was not solely a story of manufacturing and structural change was more the effect of than the cause for economic growth. We offered an empirical resolution to the Artto-Pohjola paradox as we showed that a high rate of return on capital was combined with low capital productivity growth. This result is important in understanding Finnish economic growth 1975-90. The main contribution of this thesis was the growth accounting results on the impact of ICT on growth and productivity, as well as the comparison of electricity and ICT. It was shown that ICT s contribution to GDP growth was almost twice as large as electricity s contribution over comparable periods of time. Finland has thus been far more successful as an ICT producer than a producer of electricity. Unfortunately in the use of ICT the results were still more modest than for electricity. During the end of the period considered in this thesis, Finland switched from resource-based to ICT-based growth. However, given the large dependency on the ICT-producing sector, the ongoing outsourcing of ICT production to low wage countries provides a threat to productivity performance in the future. For a developed country only change is constant and history teaches us that it is likely that Finland is obliged to reorganize its economy once again in the digital era.

Food intake, growth and social interactions of signal crayfish, Pacifastacus leniusculus (Dana)

The knowledge about the optimal rearing conditions, such as water temperature and quality, photoperiod and density, with the understanding of animal nutritional requirements forms the basis of economically stable aquaculture for freshwater crayfish. However, the shift from a natural environment to effective culture conditions induces several changes, not only at the population level, but also at the individual level. The social contacts between conspecifics increase with increasing animal density. The competition for limited resources (e.g. food, shelter, mates) is more severe with the presence of agonistic behaviour and may lead to unequal distribution of these. The objectives of this study were to: 1) study the distribution of a common food resource between communally reared signal crayfish (Pacifastacus leniusculus) and to assign potential feeding hierarchy on the basis of individual food intake measurements, 2) explore the possibilities of size distribution manipulations to affect population dynamics and food intake to improve growth and survival in culture and 3) study the effect of food ration and spatial distribution on food intake and to explore the effect of temperature and food ration on growth and body composition of freshwater crayfish. The feeding ranks between animals were assigned with a new method for individual food intake measurement of communally reared crayfish. This technique has a high feasibility and a great potential to be applied in crayfish aquaculture studies. In this study, signal crayfish showed high size-related variability in food consumption both among individuals within a group (inter-individual) and within individual day-to-day variation (intra-individual). Increased competition for food led to an unequal distribution of this resource and this may be a reason for large growth differences between animals. The consumption was significantly higher when reared individually in comparison with communal housing. These results suggest that communally housed crayfish form a feeding hierarchy and that the animal size is the major factor controlling the position in this hierarchy. The optimisation of the social environment ( social conditions ) was evaluated in this study as a new approach to crayfish aquaculture. The results showed that the absence of conspecifics (individual rearing vs. communal housing) affects growth rate, food intake and the proportion of injured animals, whereas size variation between animals influences the number and duration of agonistic encounters. In addition, animal size had a strong influence on the fighting success of signal crayfish reared in a social milieu with a wide size variation of conspecifics. Larger individuals initiated and won most of the competitions, which suggests size-based social hierarchy of P. leniusculus. This is further supported by the fact that the length and weight gain of smaller animals increased after size grading, maybe because of a better access to the food resource due to diminished social pressure. However, the high dominance index was not based on size under conditions of limited size variation, e.g. those characteristic of restocked natural populations and aquaculture, indicating the important role of behaviour on social hierarchy.

Finite field computation technique for exact solution of systems of linear equations and interval linear programming problems

An error-free computational approach is employed for finding the integer solution to a system of linear equations, using finite-field arithmetic. This approach is also extended to find the optimum solution for linear inequalities such as those arising in interval linear programming probloms.

Analytical method for solving a set of infinite simultaneous equations

It is shown that a method based on the principle of analytic continuation can be used to solve a set of infinite simultaneous equations encountered in solving for the electric field of a periodic electrode structure.

Rate of ribonucleic acid chain growth in Mycobacterium tuberculosis H37Rv.

Two methods were employed to measure the rate of ribonucleic acid (RNA) chain growth in vivo in Mycobacterium tuberculosis H37Rv cultures growing in Sauton medium at 37 degrees C, with a generation time of 10 h. In the first, the bacteria were allowed to assimilate [3H]uracil or [3H]guanine into their RNA for short time periods. The RNA was then extracted and hydrolyzed with alkali, and the radioactivity in the resulting nucleotides and nucleosides was measured. The data obtained by this method allowed the calculation of the individual nucleotide step times during the growth of RNA chains, from which the average rate of RNA chain elongation was estimated to be about 4 nucleotides per s. The second method employed the antibiotic rifampin, which specifically inhibits the initiation of RNA synthesis without interfering with the elongation and completion of nascent RNA chains. Usint this method, the transcription time of the 16S, 23S, and 5S ribosomal RNA genes was estimated to be 7.6 min, which corresponds to a ribosomal RNA chain growth rate of 10 nucleotides per s.

N-syndecan and HB-GAM in neural migration and differentiation : Modulation of growth factor activity in brain

The juvenile sea squirt wanders through the sea searching for a suitable rock or hunk of coral to cling to and make its home for life. For this task it has a rudimentary nervous system. When it finds its spot and takes root, it doesn't need its brain any more so it eats it. It's rather like getting tenure. Daniel C. Dennett (from Consciousness Explained, 1991) The little sea squirt needs its brain for a task that is very simple and short. When the task is completed, the sea squirt starts a new life in a vegetative state, after having a nourishing meal. The little brain is more tightly structured than our massive primate brains. The number of neurons is exact, no leeway in neural proliferation is tolerated. Each neuroblast migrates exactly to the correct position, and only a certain number of connections with the right companions is allowed. In comparison, growth of a mammalian brain is a merry mess. The reason is obvious: Squirt brain needs to perform only a few, predictable functions, before becoming waste. The more mobile and complex mammals engage their brains in tasks requiring quick adaptation and plasticity in a constantly changing environment. Although the regulation of nervous system development varies between species, many regulatory elements remain the same. For example, all multicellular animals possess a collection of proteoglycans (PG); proteins with attached, complex sugar chains called glycosaminoglycans (GAG). In development, PGs participate in the organization of the animal body, like in the construction of parts of the nervous system. The PGs capture water with their GAG chains, forming a biochemically active gel at the surface of the cell, and in the extracellular matrix (ECM). In the nervous system, this gel traps inside it different molecules: growth factors and ECM-associated proteins. They regulate the proliferation of neural stem cells (NSC), guide the migration of neurons, and coordinate the formation of neuronal connections. In this work I have followed the role of two molecules contributing to the complexity of mammalian brain development. N-syndecan is a transmembrane heparan sulfate proteoglycan (HSPG) with cell signaling functions. Heparin-binding growth-associated molecule (HB-GAM) is an ECM-associated protein with high expression in the perinatal nervous system, and high affinity to HS and heparin. N-syndecan is a receptor for several growth factors and for HB-GAM. HB-GAM induces specific signaling via N-syndecan, activating c-Src, calcium/calmodulin-dependent serine protein kinase (CASK) and cortactin. By studying the gene knockouts of HB-GAM and N-syndecan in mice, I have found that HB-GAM and N-syndecan are involved as a receptor-ligand-pair in neural migration and differentiation. HB-GAM competes with the growth factors fibriblast growth factor (FGF)-2 and heparin-binding epidermal growth factor (HB-EGF) in HS-binding, causing NSCs to stop proliferation and to differentiate, and affects HB-EGF-induced EGF receptor (EGFR) signaling in neural cells during migration. N-syndecan signaling affects the motility of young neurons, by boosting EGFR-mediated cell migration. In addition, these two receptors form a complex at the surface of the neurons, probably creating a motility-regulating structure.