On a mathematical model of tumor growth based on cancer stem cells

We consider a simple mathematical model of tumor growth based on cancer stem cells. The model consists of four hyperbolic equations of first order to describe the evolution of different subpopulations of cells: cancer stem cells, progenitor cells, differentiated cells and dead cells. A fifth equation is introduced to model the evolution of the moving boundary. The system includes non-local terms of integral type in the coefficients. Under some restrictions in the parameters we show that there exists a unique homogeneous steady state which is stable.

Behavior of several two-dimensional fluid equations in singular scenarios

We give conditions that rule out formation of sharp fronts for certain two-dimensional incompressible flows. We show that a necessary condition of having a sharp front is that the flow has to have uncontrolled velocity growth. In the case of the quasi-geostrophic equation and two-dimensional Euler equation, we obtain estimates on the formation of semi-uniform fronts.

How does social security affect economic growth? Evidence from cross-country data

This paper investigates how social security interacts with growth and growth determinants (savings, human capital investment, and fertility). Our empirical investigation finds that the estimated coefficient on social security is significantly negative in the fertility equation, insignificant in the saving equation, and significantly positive in the growth and education equations. By contrast, the estimated coefficient on growth is insignificant in the social security equation. The results suggest that social security may indeed be conducive to growth through tipping the trade-off between the number and quality of children toward the latter.

Prediction of the growth of wear-type rail corrugation

The growth behaviour of the vibrational wear phenomenon known as rail corrugation is investigated analytically and numerically using mathematical models. A simplified feedback model for wear-type rail corrugation that includes a wheel pass time delay is developed with an aim to analytically distil the most critical interaction occurring between the wheel/rail structural dynamics, rolling contact mechanics and rail wear. To this end, a stability analysis on the complete system is performed to determine the growth of wear-type rail corrugations over multiple wheelset passages. This analysis indicates that although the dynamical behaviour of the system is stable for each wheel passage, over multiple wheelset passages, the growth of wear-type corrugations is shown to be the result of instability due to feedback interaction between the three primary components of the model. The corrugations are shown analytically to grow for all realistic railway parameters. From this analysis an analytical expression for the exponential growth rate of corrugations in terms of known parameters is developed. This convenient expression is used to perform a sensitivity analysis to identify critical parameters that most affect corrugation growth. The analytical predictions are shown to compare well with results from a benchmarked time-domain finite element model. (C) 2004 Elsevier B.V. All rights reserved.

The development and stability analysis of a nonlinear growth model for microorganisms

A nonlinear dynamic model of microbial growth is established based on the theories of the diffusion response of thermodynamics and the chemotactic response of biology. Except for the two traditional variables, i.e. the density of bacteria and the concentration of attractant, the pH value, a crucial influencing factor to the microbial growth, is also considered in this model. The pH effect on the microbial growth is taken as a Gaussian function G0e-(f- fc)2/G1, where G0, G1 and fc are constants, f represents the pH value and fc represents the critical pH value that best fits for microbial growth. To study the effects of the reproduction rate of the bacteria and the pH value on the stability of the system, three parameters a, G0 and G1 are studied in detail, where a denotes the reproduction rate of the bacteria, G0 denotes the impacting intensity of the pH value to microbial growth and G1 denotes the bacterial adaptability to the pH value. When the effect of the pH value of the solution which microorganisms live in is ignored in the governing equations of the model, the microbial system is more stable with larger a. When the effect of the bacterial chemotaxis is ignored, the microbial system is more stable with the larger G1 and more unstable with the larger G0 for f0 > fc. However, the stability of the microbial system is almost unaffected by the variation G0 and G1 and it is always stable for f0 < fc under the assumed conditions in this paper. In the whole system model, it is more unstable with larger G1 and more stable with larger G0 for f0 < fc. The system is more stable with larger G1 and more unstable with larger G0 for f0 > fc. However, the system is more unstable with larger a for f0 < fc and the stability of the system is almost unaffected by a for f0 > fc. The results obtained in this study provide a biophysical insight into the understanding of the growth and stability behavior of microorganisms.

Essays on investment, growth and income distribution

In this dissertation, I examine both theoretically and empirically the relationship between stock prices and income distribution using an endogenous growth model with social status impatience.^ The theoretical part looks into how status impatience and current economic status jointly determine time preference, savings, future economic status, stock prices, growth and wealth distribution in the steady state. This work builds on Burgstaller and Karayalcin (1996).^ More specifically, I look at (i) the effects of the distribution of status impatience levels on the distribution of steady state assets, incomes and consumption and (ii) the effects of changes in relative levels of status impatience on stock prices. Therefore, from (i) and (ii), I derive the correlation between stock prices, incomes and asset distribution. Also, the analysis of the stack market is undertaken in the presence of adjustment costs to investments.^ The empirical chapter looks at (i) the correlation between income inequality and long run economic growth on the one hand and (ii) the correlation between stock market prices and income inequality on the other. The role of stock prices and social status is examined to better understand the forces that enable a country to grow overtime and to determine why output per capita varies across countries. The data are from Summers and Heston (1988), Barro and Wolf (1989), Alesina and Rodrik (1994), Global financial Database (1997) and the World Bank. Data for social status are collected through a primary sample survey on the internet. Twenty-five developed and developing countries are included in the sample.^ The model developed in this study was specified as a system of simultaneous equations, in which per capita growth rate and income inequality were endogenous variables. Additionally, stock price index and social status measures were also incorporated. The results indicate that income inequality is inversely related to economic growth. In addition, increase in income inequality arising from higher stock prices constrains growth. Moreover, where social status is determined by income levels, it influences long run growth. Therefore, these results support findings of Persson and Tabellini (1994) and Alesina and Rodrik (1994). ^

The Causal Links between FDI and Economic Growth in Developing Countries: A Case Study of the Republic of Rwanda

The study examines the short-run and long-run causality running from real economic growth to real foreign direct investment inflows (RFDI). Other variables such as education (involving combination of primary, secondary and tertiary enrolment as a proxy to education), real development finance, unskilled labour, to real RFDI inflows are included in the study. The time series data covering the period of 1983 -2013 are examined. First, I applied Augmented Dicky-Fuller (ADF) technique to test for unit root in variables. Findings shows all variables integrated of order one [I(1)]. Thereafter, Johansen Co-integration Test (JCT) was conducted to establish the relationship among variables. Both trace and maximum Eigen value at 5% level of significance indicate 3 co-integrated equations. Vector error correction method (VECM) was applied to capture short and long-run causality running from education, economic growth, real development finance, and unskilled labour to real foreign direct investment inflows in the Republic of Rwanda. Findings shows no short-run causality running from education, real development finance, real GDP and unskilled labour to real FDI inflows, however there were existence of long-run causality. This can be interpreted that, in the short-run; education, development finance, finance and economic growth does not influence inflows of foreign direct investment in Rwanda; but it does in long-run. From the policy perspective, the Republic of Rwanda should focus more on long term goal of investing in education to improve human capital, undertake policy reforms that promotes economic growth, in addition to promoting good governance to attract development finance – especially from Nordics countries (particularly Norway and Denmark).

The Becker-Döring equations with exponentially size-dependent rate coefficients

This paper is concerned with an analysis of the Becker-Döring equations which lie at the heart of a number of descriptions of non-equilibrium phase transitions and related complex dynamical processes. The Becker-Döring theory describes growth and fragmentation in terms of stepwise addition or removal of single particles to or from clusters of similar particles and has been applied to a wide range of problems of physicochemical and biological interest within recent years. Here we consider the case where the aggregation and fragmentation rates depend exponentially on cluster size. These choices of rate coefficients at least qualitatively correspond to physically realistic molecular clustering scenarios such as occur in, for example, simulations of simple fluids. New similarity solutions for the constant monomer Becker-Döring system are identified, and shown to be generic in the case of aggregation and fragmentation rates that depend exponentially on cluster size.

Growth of the mangrove crab Ucides cordatus (Brachyura, Ocypodidae)

During monthly samplings between September 1998 and August 2000. 3,660 specimens of Ucides cordatus (Linnaeus, 1763) (2054 males and 1606 females) were obtained and examined for size (CW carapace width) to determine growth-age equations for each sex. This species showed a slower growth, with a marked seasonal oscillation, in females as compared to males, suggesting application of the seasonal and nonseasonal von Bertalanffy growth model, respectively. CW&PROP; and k constant were closely similar for the two sexes (CW&PROP; (male) = 90.3 mm: CW&PROP; (female) = 88.6 mm; k(male) = 0.28; k(female) = 0.26). The age at sexual maturity was estimated to be around 3 years, while the age at legal size (CW = 60 mm) was 3.8 and 4.7 years for males and females, respectively. In the laboratory, juvenile stages did not show differences in growth rates under the same temperature and photoperiod conditions.

Growth of the speckled swimming crab, Arenaeus cribrarius (Lamarck, 1818) (Crustacea, Brachyura, Portunidae), in Ubatuba (SP), Brazil

A total of 2629 individuals of Arenaeus cribrarius (1293 males and 1336 females) were captured in Ubatuba (SP), from August 1996 to July 1997. Individuals were distributed in 5 mm size class carapace width (CW), to verify sex-specific growth-age equations. The Von Bertalanffy model was chosen to determine the growth rate and expressed by CW=120.52[1-e(-1.80t)] for males and CW=100.81[1-e(-1.60t)] for females. The age estimated for the first juvenile stage (t(o)) was 6.1 and 8.3 days for males and females, respectively. The maximum age determined was 1.8 years for males and 2 years for females, which correspond to a maximum size of 115.8 and 96.7 mm, respectively. The maximum size (CWmax) estimated using 95% of asymptotic size was 114.5 mm for males and 95.8 mm for females. Males have a precocious sexual maturity (5 months) when compared to females (6.8 months). The growth rate and size of A. cribrarius are higher than other portunid species, with great interest for aquaculture.

Growth and body nutrient deposition of two broiler commercial genetic lines

The objective of this work was to study growth and body nutrient deposition profiles of male and female Cobb and Ross broilers using Gompertz equations. A total number of 1,920 one- to 56-day-old broilers were used. A randomized experimental design in a factorial arrangement (2 strains x 2 sex), with 4 replicates of 120 birds each, was applied. Diets were formulated to supply the nutrient requirements recommended by the genetic companies. A sample of birds was weekly weighed and sacrificed after 24 hours fasting. Carcasses were de-feathered and weighed again. The parameters of the Gompertz equation for body weight and its components (water, ashes, protein, and fat) were estimated. An interaction (p<0.05) between sex and breed was observed for mature weight (Wm) (kg), growth rate (b) (daily) and time at maximum growth rate (t*) (day) of body weight, and body water and ash. Cobb was presented earlier growth and body protein and ash deposition. Ross strain was superior in body water deposition.

Sufficient conditions for the existence of heteroclinic solutions for Phi-Laplacian differential equations

In this paper we consider the second order discontinuous equation in the real line, (a(t)φ(u′(t)))′ = f(t,u(t),u′(t)), a.e.t∈R, u(-∞) = ν⁻, u(+∞)=ν⁺, with φ an increasing homeomorphism such that φ(0)=0 and φ(R)=R, a∈C(R,R\{0})∩C¹(R,R) with a(t)>0, or a(t)<0, for t∈R, f:R³→R a L¹-Carathéodory function and ν⁻,ν⁺∈R such that ν⁻<ν⁺. We point out that the existence of heteroclinic solutions is obtained without asymptotic or growth assumptions on the nonlinearities φ and f. Moreover, as far as we know, this result is even new when φ(y)=y, that is, for equation (a(t)u′(t))′=f(t,u(t),u′(t)), a.e.t∈R.