Financing exponential growth at H3

H3 is a fast-food chain that introduced the concept of gourmet hamburgers in the Portuguese market. This case-study illustrates its financing strategy that supported an exponential growth represented by opening 33 restaurants within approximately 3 years of its inception. H3 is now faced with the challenge of structuring its foreign ventures and change its financial approach. The main covered topics are the options an entrepreneur has for financing a new venture and how it evolves along the life cycle and different business approaches, namely franchising. It aims to be used as a learning tool in courses such as entrepreneurial finance.

On a Class of Elliptic Equations for the N-Laplacian in R^n with One-Sided Exponential Growth

2000 Mathematics Subject Classification: 35J40, 49J52, 49J40, 46E30

Singular Solutions with Exponential Growth for the (3+1)-D Wave Equation

Недю И. Попиванов, Тодор П. Попов, Рудолф Шерер - Разглеждат се четиримерни гранични задачи за нехомогенното вълново уравнение. Те са предложени от М. Протер като многомерни аналози на задачата на Дарбу в равнината. Известно е, че единственото обобщено решение може да има силна степенна особеност само в една гранична точка. Тази сингулярност е изолирана във върха на характеристичния конус и не се разпространява по конуса. Друг аспект на проблема е, че задачата не е фредхолмова, тъй като има безкрайномерно коядро. Предишни резултати сочат, че решението може да има най-много експоненциален ръст, но оставят открит въпроса дали наистина съществуват такива решения. Показваме, че отговора на този въпрос е положителен и строим обобщено решение на задачата на Протер с експоноциална особеност.

Siderophore Production by Bacillus megaterium: Effect of Growth Phase and Cultural Conditions

Siderophore production by Bacillus megaterium was detected, in an iron-deficient culture medium, during the exponential growth phase, prior to the sporulation, in the presence of glucose; these results suggested that the onset of siderophore production did not require glucose depletion and was not related with the sporulation. The siderophore production by B. megaterium was affected by the carbon source used. The growth on glycerol promoted the very high siderophore production (1,182 μmol g−1 dry weight biomass); the opposite effect was observed in the presence of mannose (251 μmol g−1 dry weight biomass). The growth in the presence of fructose, galactose, glucose, lactose, maltose or sucrose, originated similar concentrations of siderophore (546–842 μmol g−1 dry weight biomass). Aeration had a positive effect on the production of siderophore. Incubation of B. megaterium under static conditions delayed and reduced the growth and the production of siderophore, compared with the incubation in stirred conditions.

Growth and differentiation on a trypanosome of the subgenus Schizotrypanum from the bat Phyllostomus hastatus

The effects of temperature, pH, osmolarity and aeration on the growth and differentiation of a trypanosome ofthe subgenus Schizotrypanum isolatedfrom the bat Phyllostomus hastatus were studied. In general, the growth characteristics ofthe flagellate were similar to those of Trypanosoma (Schizotrypanum) cruzi. However, the parasite did not growth at 33 or 37C. Increase in the osmolarity and aeration promoted growth at 33C. Significant metacyclogenesis was detected only in the growth condition where maximal growth occured (28C, pH 7.3, 380m0s/kg, in tissue cullure flasks), at the end ofthe exponential growth phase. The begining of the metacyclogenesis process was coincident with most glucose utilization and lowest pH. During metacyclogenesis both culture medium pH and osmolarity increased steadly.

Asynchronous growth and competition in a two-sex age-structured population model

Asynchronous exponential growth has been extensively studied in population dynamics. In this paper we find out the asymptotic behaviour in a non-linear age-dependent model which takes into account sexual reproduction interactions. The main feature of our model is that the non-linear process converges to a linear one as the solution becomes large, so that the population undergoes asynchronous growth. The steady states analysis and the corresponding stability analysis are completely made and are summarized in a bifurcation diagram according to the parameter R0. Furthermore the effect of intraspecific competition is taken into account, leading to complex dynamics around steady states.

Repression of flagellar genes in exponential phase by CsgD and CpxR, two crucial modulators of Escherichia coli biofilm formation.

Escherichia coli adapts its lifestyle to the variations of environmental growth conditions, swapping between swimming motility or biofilm formation. The stationary-phase sigma factor RpoS is an important regulator of this switch, since it stimulates adhesion and represses flagellar biosynthesis. By measuring the dynamics of gene expression, we show that RpoS inhibits the transcription of the flagellar sigma factor, FliA, in exponential growth phase. RpoS also partially controls the expression of CsgD and CpxR, two transcription factors important for bacterial adhesion. We demonstrate that these two regulators repress the transcription of fliA, flgM, and tar and that this regulation is dependent on the growth medium. CsgD binds to the flgM and fliA promoters around their -10 promoter element, strongly suggesting direct repression. We show that CsgD and CpxR also affect the expression of other known modulators of cell motility. We propose an updated structure of the regulatory network controlling the choice between adhesion and motility.

Atomic Force Microscopy Stiffness Tomography on Living Arabidopsis thaliana Cells Reveals the Mechanical Properties of Surface and Deep Cell-Wall Layers during Growth.

Cell-wall mechanical properties play a key role in the growth and the protection of plants. However, little is known about genuine wall mechanical properties and their growth-related dynamics at subcellular resolution and in living cells. Here, we used atomic force microscopy (AFM) stiffness tomography to explore stiffness distribution in the cell wall of suspension-cultured Arabidopsis thaliana as a model of primary, growing cell wall. For the first time that we know of, this new imaging technique was performed on living single cells of a higher plant, permitting monitoring of the stiffness distribution in cell-wall layers as a function of the depth and its evolution during the different growth phases. The mechanical measurements were correlated with changes in the composition of the cell wall, which were revealed by Fourier-transform infrared (FTIR) spectroscopy. In the beginning and end of cell growth, the average stiffness of the cell wall was low and the wall was mechanically homogenous, whereas in the exponential growth phase, the average wall stiffness increased, with increasing heterogeneity. In this phase, the difference between the superficial and deep wall stiffness was highest. FTIR spectra revealed a relative increase in the polysaccharide/lignin content.

Demographic Modelling of Human Population Growth

This work presents models and methods that have been used in producing forecasts of population growth. The work is intended to emphasize the reliability bounds of the model forecasts. Leslie model and various versions of logistic population models are presented. References to literature and several studies are given. A lot of relevant methodology has been developed in biological sciences. The Leslie modelling approach involves the use of current trends in mortality,fertility, migration and emigration. The model treats population divided in age groups and the model is given as a recursive system. Other group of models is based on straightforward extrapolation of census data. Trajectories of simple exponential growth function and logistic models are used to produce the forecast. The work presents the basics of Leslie type modelling and the logistic models, including multi- parameter logistic functions. The latter model is also analysed from model reliability point of view. Bayesian approach and MCMC method are used to create error bounds of the model predictions.

Exploring TERRA (TElomeric Repeat-containing RNA) Expression and Regulation During Cell Growth in Saccharomyces cerevisiae

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Estimation of population growth or decline in genetically monitored populations

This article introduces a new general method for genealogical inference that samples independent genealogical histories using importance sampling (IS) and then samples other parameters with Markov chain Monte Carlo (MCMC). It is then possible to more easily utilize the advantages of importance sampling in a fully Bayesian framework. The method is applied to the problem of estimating recent changes in effective population size from temporally spaced gene frequency data. The method gives the posterior distribution of effective population size at the time of the oldest sample and at the time of the most recent sample, assuming a model of exponential growth or decline during the interval. The effect of changes in number of alleles, number of loci, and sample size on the accuracy of the method is described using test simulations, and it is concluded that these have an approximately equivalent effect. The method is used on three example data sets and problems in interpreting the posterior densities are highlighted and discussed.

Finite-dimensional non-associative algebras and codimension growth

Let A be a (non-necessarily associative) finite-dimensional algebra over a field of characteristic zero. A quantitative estimate of the polynomial identities satisfied by A is achieved through the study of the asymptotics of the sequence of codimensions of A. It is well known that for such an algebra this sequence is exponentially bounded. Here we capture the exponential rate of growth of the sequence of codimensions for several classes of algebras including simple algebras with a special non-degenerate form, finite-dimensional Jordan or alternative algebras and many more. In all cases such rate of growth is integer and is explicitly related to the dimension of a subalgebra of A. One of the main tools of independent interest is the construction in the free non-associative algebra of multialternating polynomials satisfying special properties. (C) 2010 Elsevier Inc. All rights reserved.

Effects of Initial Fat Thickness, Hip Height, and Concentration of Dietary Energy on Growth of Area of the Longissimus dorsi Muscle and Subcutaneous Fat of Yearling Steers

Steers were sorted into four groups based on hip height and fat cover at the start of the finishing period. Each group of sorted steers was fed diets containing 0.59 or 0.64 Mcal NEg per lb. of diet dry matter. Steers with less initial fat cover (0.08 in.) compared with those with more (0.17) had less carcass fat cover 103 days later. The steers with less fat cover accumulated fat at a faster rate, but this was not apparent prior to 80 days. Accretion of fat was best predicted by an exponential growth equation, and was not affected by the two concentrations of energy fed in this study. Steers with greater initial height accumulated fat cover at a slower rate than shorter steers. This difference was interpreted to mean that large-frame steers accumulate subcutaneous fat at a slower rate than medium-frame steers. Increase in area of the ribeye was best described by a linear equation. Initial fat cover, hip height, and concentrations of energy in the diet did not affect rate of growth of this muscle. Predicting carcass fat cover from the initial ultrasound measurement of fat thickness found 46 of the 51 carcasses with less than 0.4 in. of fat cover. Twelve carcasses predicted to have less than 0.4 in. of fat cover had more than 0.4 in. Five carcasses predicted to have more than 0.4 in. actually had less than that. Accurate initial measurements of initial fat thickness with ultrasound might be a useful measurement to sort cattle for specific marketing grids.

The effects of growth phase and salinity on the hydrogen isotopic composition of alkenones produced by coastal haptophyte algae

The isotopic fractionation of hydrogen during the biosynthesis of alkenones produced by marine haptophyte algae has been shown to depend on salinity and, as such, the hydrogen isotopic composition of alkenones is emerging as a palaeosalinity proxy. The relationship between fractionation and salinity has previously only been determined during exponential growth, whilst it is not yet known in which growth phases natural haptophyte populations predominantly exist. We have therefore determined the relationship between the fractionation factor, alpha alkenones-water, and salinity for C37 alkenones produced in different growth phases of batch cultures of the major alkenone-producing coastal haptophytes Isochrysis galbana (strain CCMP 1323) and Chrysotila lamellosa (strain CCMP 1307) over a range in salinity from ca. 10 to ca. 35. alpha alkenones-water was similar in both species, ranging over 0.841-0.900 for I. galbana and 0.838-0.865 for C. lamellosa. A strong (0.85 <= R**2 <= 0.97; p < 0.0001) relationship between salinity and fractionation factor was observed in both species at all growth phases investigated. This suggests that alkenone dD has the potential to be used as a salinity proxy in coastal areas where haptophyte communities are dominated by these coastal species. However, there was a marked difference in the sensitivity of alpha alkenones-water to salinity between different growth phases: in the exponential growth phase of I. galbana, alpha alkenones-water increased by 0.0019 per salinity unit (S 1), but was less sensitive at 0.0010 S 1 and 0.0008 S 1 during the stationary and decline phases, respectively. Similarly, in C. lamellosa alpha alkenones-water increased by 0.0010 S 1 in the early stationary phase and by 0.0008 S 1 during the late stationary phase. Assuming the shift in sensitivity of alpha alkenones-water to salinity observed at the end of exponential growth in I. galbana is similar in other alkenone-producing species, the predominant growth phase of natural populations of haptophytes will affect the sensitivity of the alkenone salinity proxy. The proxy is likely to be most sensitive to salinity when alkenones are produced in a state similar to exponential growth.