Periodic solutions of integro-differential equations which arise in population dynamics

The problem of the existence and stability of periodic solutions of infinite-lag integra-differential equations is considered. Specifically, the integrals involved are of the convolution type with the dependent variable being integrated over the range (- ∞,t), as occur in models of population growth. It is shown that Hopf bifurcation of periodic solutions from a steady state can occur, when a pair of eigenvalues crosses the imaginary axis. Also considered is the existence of traveling wave solutions of a model population equation allowing spatial diffusion in addition to the usual temporal variation. Lastly, the stability of the periodic solutions resulting from Hopf bifurcation is determined with aid of a Floquet theory.

The first chapter is devoted to linear integro-differential equations with constant coefficients utilizing the method of semi-groups of operators. The second chapter analyzes the Hopf bifurcation providing an existence theorem. Also, the two-timing perturbation procedure is applied to construct the periodic solutions. The third chapter uses two-timing to obtain traveling wave solutions of the diffusive model, as well as providing an existence theorem. The fourth chapter develops a Floquet theory for linear integro-differential equations with periodic coefficients again using the semi-group approach. The fifth chapter gives sufficient conditions for the stability or instability of a periodic solution in terms of the linearization of the equations. These results are then applied to the Hopf bifurcation problem and to a certain population equation modeling periodically fluctuating environments to deduce the stability of the corresponding periodic solutions.

Length-weight relationship and organ indices of pond raised and wild population of C. gariepinus (Burchell 1822) pisces-Claridae

Samples of C. gariepinus collected from the wild and cultured populations in Plateau and Niger States of Nigeria were analyzed for length-weight relationship and organ indices (Gonadosomatic index (GSI), hepatosomatic index (HSI), renalsomatic index (RSI) and somatic fat deposit index (PDI). High correlation and linear relationship between body length and body weight was observed in all sample population (P<0.05). A significant difference was observed between the GSI of males and females of both wild and cultured population and also between females of the wild and cultured population,(P < 0.05).There was no significant difference in HSI, CSI RSI and PDI of all the sample populations (P < 0.05).The importance of length-weight relationship and organ indices in fish production are discussed

Two mechanisms for population inversion via two-colour coherent excitation in three-level systems

We analyse the physical origin of population inversion via continuous wave two-colour coherent excitation in three-level systems by dressing the inverted transition. Two different mechanisms are identified as being responsible for the population inversion. For V-configured systems and cascade (E) configured systems with inversion on the lower transition, the responsible mechanism is the selective trapping of dressed states, and the population inversion approaches the ideal value of 1. For Lambda-configured systems and Xi-configured systems with inversion on the upper transition, population inversion is based on the selective excitation of dressed states, with the population inversion tending towards 0.5. As the essential difference between these two mechanisms, the selective trapping of dressed states occurs in systems with strong decay into dressed states while the selective excitation appears in systems with strong decay out of dressed states.

Coherent population transfer with chirped few-cycle laser pulses in an excited-doublet four-level system

The behavior of population transfer in an excited-doublet four-level system driven by linear polarized few-cycle ultrashort laser pulses is investigated numerically. It is shown that almost complete population transfer can be achieved even when the adiabatic criterion is not fulfilled. Moreover, the robustness of this scheme in terms of the Rabi frequencies and chirp rates of the pulses is explored.

Evaluation of transferred fisheries technology in Kainji Lake basin

Fisheries is important to Nigeria agricultural economy because it provides employment for fisherfolks (men and women fishers, fishmongers (fish traders), fish processors and fish farmers. It also supplies protein to the diet of Nigerians and it is equally a viable source of foreign exchange earning to the government.The estimated Nigeria population of 120 million consumes about 1.2million metric tones of fish and fish products annual. This justified the important role fisheries could play in nigerian diet considering that Nigeria has vast inland waters that cover an estimated total surface area of 199,580km super(2) and equally vast sea area of 25,000km super(2). In these waters the author claimed that there are diverse fish resources that are of economic importance in both inland and seawaters. FDF (2000) also estimated that the current annual yield of both inland and seawater put together is about 418,069,3 metric tones from artisanal fisheries and 23,720 metric tones from aquaculture. The shortage between the annual consumption level of 1.2million metric tones and annual yield of 418,069,3 metric tones is made available through importation. It is therefore of concern that given the level of current fish yield from the various fisheries resources the demand still exceeds supply. One wonders whether the production inadequacy is due to poor management of available fisheries resources or that improved fisheries technology that could aid increased production was not efficiently transferred to fish farmers. To answer these questions one need to examine the past and present extension policy in Nigeria as they affect dissemination of fisheries technologies

Sideband manipulation of population inversion in a three-level Λ atomic system

Sideband manipulation of population inversion in a three-level A atomic configuration is investigated theoretically. Compared with the case of a nearly monochromatic field, a population inversion between an excited state and a ground state has been found in a wide sideband intensity range by increasing the difference in frequency between three components. Furthermore, the population inversion can be controlled by the sum of the relative phases of the sideband components of the trichromatic pump field with respective to the phase of the central component. Changing the sum phase from 0 to pi, the population inversion between the excited state and the ground state can increase within nearly half of the sideband intensity range. At the same time, the sideband intensity range that corresponds to the system exhibiting inversion rho(00) > rho 11 also becomes wider evidently.

Ultrafast transient ring-shaped population grating

We demonstrate an ultrafast transient, ring-shaped population grating induced by an ultrashort hollow Gaussian laser bullet by solving the three-dimensional full-wave Maxwell-Bloch equations. Through adjusting the beam waist and the area of the pulse, we can control the number of lines and the period of the grating. Based on this coherent control scheme, a door to produce gratings with complex transverse structure is opened.

Coherent population accumulations of multiphoton transitions induced by an ultrashort pulse train in polar molecules

Coherent population accumulations of multiphoton transitions induced by an ultrashort pulse train in a two-level polar molecule are investigated theoretically by solving the density-matrix equations without invoking any of the standard approximations. It is shown due to the effects of permanent dipole moments, that the population accumulation of multiphoton transitions can be obtained in the polar molecule. Moreover, the population accumulations depend crucially on the relative phase between two sequential pulses, and the period in which the maximum population accumulation occurs is 2 pi/N in N-photon transitions.

Engineered underdominance as a method of insect population replacement and reproductive isolation

Insect vector-borne diseases, such as malaria and dengue fever (both spread by mosquito vectors), continue to significantly impact health worldwide, despite the efforts put forth to eradicate them. Suppression strategies utilizing genetically modified disease-refractory insects have surfaced as an attractive means of disease control, and progress has been made on engineering disease-resistant insect vectors. However, laboratory-engineered disease refractory genes would probably not spread in the wild, and would most likely need to be linked to a gene drive system in order to proliferate in native insect populations. Underdominant systems like translocations and engineered underdominance have been proposed as potential mechanisms for spreading disease refractory genes. Not only do these threshold-dependent systems have certain advantages over other potential gene drive mechanisms, such as localization of gene drive and removability, extreme engineered underdominance can also be used to bring about reproductive isolation, which may be of interest in controlling the spread of GMO crops. Proof-of-principle establishment of such drive mechanisms in a well-understood and studied insect, such as Drosophila melanogaster, is essential before more applied systems can be developed for the less characterized vector species of interest, such as mosquitoes. This work details the development of several distinct types of engineered underdominance and of translocations in Drosophila, including ones capable of bringing about reproductive isolation and population replacement, as a proof of concept study that can inform efforts to construct such systems in insect disease vectors.

Transient population and polarization gratings induced by (1+1)-dimensional ultrashort dipole soliton

An ultrafast transient population grating induced by a (1+1)-dimensional, ultrashort dipole soliton is demonstrated by solving the full-wave Maxwell-Bloch equations. The number of lines and the period of the grating can be controlled by the beam waist and the area of the pulse. Of interest is that a polarization grating is produced. A coherent control scheme based on these phenomena can be contemplated as ultrafast transient grating techniques.

Cheese consumption and prevalence of overweight and obesity in a Basque adult population: a crosssectional study

[EN] Studies have reported a negative association between dairy product consumption and weight status. However, not as much research has focused on cheese; therefore, the aim of this study was to study the association between cheese intake and overweight and obesity in a representative Basque adult population. A food frequency questionnaire (FFQ) was obtained from a random sample of 1081 adults (530 males and 551 females, 17–96 years old). Cheese consumption data were expressed as g/1000 kcal/day. The prevalence of overweight/obesity was higher in men (55.1%) than in women (35.4%) (p50.001). Participants with low or moderate intake of fresh and processed cheese demonstrated a higher prevalence of excess weight, compared with those with higher consumption. The confounding variables selected in multivariate analysis were occupational status and age in both genders; and place of residence in men. In conclusion, negative associations were found between consumption of some types of cheese and overweight and obesity in this population.

Morphological variation with interspecific implications in a population of Sigara dorsalis (Leach) (Hemiptera Heteroptera: Corixidae), and a request for British specimens

Sigara dorsalis belongs to a very closely related group of six species forming the sub-genus Sigara sensu strictu. Each of the six species has a distinct allopatric geographical distribution in Europe. Studies were started on a series of populations in the north west Midlands of England. All the populations examined, except one, contained only males with the typical diagnostic features of S. dorsalis, albeit with considerable variation. One pond near Congleton, Cheshire situated in a permanent-ley pasture and apparently free from pollution contained typical S. dorsalis males but, in addition, many atypical individuals. From one sample of forty-six males, all possessed left parameres with the slight point on the dorsal surface characteristic of S. dorsalis. However, almost half possessed additional morphological features intermediate between S. dorsalis and S. striata.