On a Stable and Consistent Finite Difference Scheme for a Time-Dependent Schrodinger Wave Equation in a Finitely Low Potential Well

In this paper, a stable and consistent criterion to an explicit finite difference scheme for a time-dependent Schrodinger wave equation (TDSWE) was presented. This paper is a departure from the well-established time independent Schrodinger Wave Equation (SWE). To develop the stability criterion for the scheme, the Fourier series method of von Newmann was adopted, while in establishing the consistency property, the concise definition of the consistent scheme was applied. This research is carried out for a particular case of a finitely low potential well.Keywords: Time-Dependent Schrodinger Wave Equation, Stability, Consistency, Finite Potential Well, Finite Difference

Economic, nutritional and medicinal values of African walnut (Tetracarpidium conophorum) in Nigeria (Hutch. & Dalziel): a review

The Nigeria Walnut (Tetracarpidium conophorum) is a climber crop species that help in poverty reduction through improvement of the purchasing power of families and their standard of living. African walnut has proven evidence that leads to general acceptability to its protective effects against certain diseases majorly the cardiovascular disease (CDV). It has many other medicinal values such as treatment of Diabetic, maintenance of healthy bone, Anti-malarial, diseases prevention, pregnancy protection and sperm improvement, weight management and so on. The consumption of this fruit is not only effective for the health of man but contributes to other lifestyles characteristics backed up by evidence from certain scientific investigations. However, the challenges facing its year round availability have not been fully documented and data related to its contributions to livelihoods of rural farmers and it nutritional value is not readily available to the populace, thereby places the plant in danger of genetic extinction and disappearance which have the potential to restrict its development options. Therefore, this paper reviewed the monetary contribution of African Walnut, its potential roles in poverty reduction, commitment to national advancement and value added exports from Nigeria, hence the investigation is expected to bridge some of this gap, giving an overview of the present information encompassing the economic commitment of Walnut, it nutritional and medicinal values in Nigeria. Key words: Economics, Nutrition, Medicinal Benefits, Chemical composition, Walnu

A Station-Based Southern Annular Mode Index from 1884 to 2005

Atmospheric pressure observations from the Southern Hemisphere are used to estimate monthly and annually averaged indexes of the southern annular mode (SAM) back to 1884. This analysis groups all relevant observations in the following four regions: one for Antarctica and three in the subtropical zone. Continuous surface pressure observations are available at a number of locations in the subtropical regions since the end of the nineteenth century. However, year-round observations in the subpolar region near the Antarctic continent began only during the 1940-60 period. The shorter Antarctic records seriously compromise the length of a traditionally estimated SAM index. To improve the situation "proxy'' estimates of Antarctic sea level pressure anomalies are provided based on the concept of atmospheric mass conservation poleward of 208S. This allows deriving a longer SAM index back to 1884. Several aspects of the new record, its statistical properties, seasonal trends, and the regional pressure anomaly correlations, are presented

Geometrical tests of cosmological models. II. Calibration of rotational widths and disc scaling relations

This series of papers is dedicated to a new technique to select galaxies that can act as standard rods and standard candles in order to perform geometrical tests on large samples of high redshift galaxies to constrain different cosmological parameters. The goals of this paper are (1) to compare different rotation indicators in order to understand the relation between rotation velocities extracted from observations of the Halpha line and the [OII]3727 line, and (2) determine the scaling relations between physical size, surface brightness and magnitude of galaxies and their rotation velocity using the SFI++, a large catalog of nearby galaxies observed at I-band. A good correlation is observed between the rotation curve-derived velocities of the Halpha and [OII] observations, as well as between those calculated from velocity histograms, justifying the direct comparison of velocities measured from Halpha rotation curves in nearby galaxies and from [OII] line widths at higher redshifts. To provide calibration for the geometrical tests, we give expressions for the different scaling relations between properties of galaxies (size, surface brightness, magnitude) and their rotation speeds. Apart from the Tully-Fisher relation, we derive the size-rotation velocity and surface brightness-rotation velocity relations with unprecedentedly small scatters. We show how the best size-rotation velocity relation is derived when size is estimated not from disc scale lengths but from the isophotal diameter r23.5, once these have been corrected for inclination and extinction effects.Comment: 14 pages and 10 figures. A&A submitte

Assessment of Extension Officers Contribution to Cocoa Production in Nigeria

This study was carried out to evaluate the extension officer contribution to cocoa production in Nigeria. Multistage sampling technique was used, where two hundred and sixteen questionnaires were distributed in Osun and Ondo state , the information gathered were analyzed using descriptive statistic such as; frequency and percentage, while chi-square analysis was used to analyze the data obtained. From the results, married (77.6%), male (84.0%), secondary school holders (52.0%), between 40-49 (34.4%) years old farmers were seen as the highest cocoa producers. Extension training(64.0%), commercial agents(64.0%), fellowship(52.8%), self observation(76.0%) were the best source of information on extension service of cocoa farming , most respondents (65.0%); get extension training programme at regular basis, identified Constraints facing cocoa production in the study area includes deficient credit facilities, high cost of labour, bad road, poor marketing/storage facilities, lack of technical knowledge / assess to technical tools and so on. in view of afore mentioned result it is therefore recommended that the government should make loan available to the cocoa famers at very low interest rate and urge cocoa farmers to form cooperative society, strengthen their agricultural extension agents so that they will be able to rain cocoa farmers on the basic things they should know about primary processing such as fermentation and drying of cocoa beans in improving the quality in Nigeria to meet international market

Limits on dust emission from z~5 LBGs and their local environments

We present 1.2mm MAMBO-2 observations of a field which is over-dense in Lyman Break Galaxies (LBGs) at z~5. The field includes seven spectroscopically-confirmed LBGs contained within a narrow (z=4.95+/-0.08) redshift range and an eighth at z=5.2. We do not detect any individual source to a limit of 1.6 mJy/beam (2*rms). When stacking the flux from the positions of all eight galaxies, we obtain a limit to the average 1.2 mm flux of these sources of 0.6mJy/beam. This limit is consistent with FIR imaging in other fields which are over-dense in UV-bright galaxies at z~5. Independently and combined, these limits constrain the FIR luminosity (8-1000 micron) to a typical z~5 LBG of LFIR<~3x10^11 Lsun, implying a dust mass of Mdust<~10^8 Msun (both assuming a grey body at 30K). This LFIR limit is an order of magnitude fainter than the LFIR of lower redshift sub-mm sources (z~1-3). We see no emission from any other sources within the field at the above level. While this is not unexpected given millimetre source counts, the clustered LBGs trace significantly over-dense large scale structure in the field at z = 4.95. The lack of any such detection in either this or the previous work, implies that massive, obscured star-forming galaxies may not always trace the same structures as over-densities of LBGs, at least on the length scale probed here. We briefly discuss the implications of these results for future observations with ALMA.Comment: 10 pages, 6 figures, MNRAS Accepte

The stellar mass function of the most massive galaxies at 3<=z<5 in the UKIDSS Ultra Deep Survey

We have analysed a sample of 1292 4.5 micron-selected galaxies at z>=3, over 0.6 square degrees of the UKIRT Infrared Deep Survey (UKIDSS) Ultra Deep Survey (UDS). Using photometry from the U band through 4.5 microns, we have obtained photometric redshifts and derived stellar masses for our sources. Only two of our galaxies potentially lie at z>5. We have studied the galaxy stellar mass function at 3<=z<5, based on the 1213 galaxies in our catalogue with [4.5]<= 24.0. We find that: i) the number density of M > 10^11 Msun galaxies increased by a factor > 10 between z=5 and 3, indicating that the assembly rate of these galaxies proceeded > 20 times faster at these redshifts than at 0<z<2; ii) the Schechter function slope alpha is significantly steeper than that displayed by the local stellar mass function, which is both a consequence of the steeper faint end and the absence of a pure exponential decline at the high-mass end; iii) the evolution of the comoving stellar mass density from z=0 to 5 can be modelled as log10 (rho_M) =-(0.05 +/- 0.09) z^2 - (0.22 -/+ 0.32) z + 8.69. At 3 10^11 Msun galaxies would be missed by optical surveys with R<27 or z<26. Thus, our study demonstrates the importance of deep mid-IR surveys over large areas to perform a complete census of massive galaxies at high z and trace the early stages of massive galaxy assembly.Comment: 16 pages, 15 figures, 2 tables. Accepted for publication in MNRA

Spatial Clustering of High Redshift Lyman Break Galaxies

We present a physically motivated semi-analytic model to understand the clustering of high redshift LBGs. We show that the model parameters constrained by the observed luminosity function, can be used to predict large scale (\theta > 80 arcsec) bias and angular correlation function of galaxies. These predictions are shown to reproduce the observations remarkably well. We then adopt these model parameters to calculate the halo occupation distribution (HOD) using the conditional mass function. The halo model using this HOD is shown to provide a reasonably good fit to the observed clustering of LBGs at both large (\theta>80") and small (\theta < 10") angular scales for z=3-5 and several limiting magnitudes. However, our models underpredict the clustering amplitude at intermediate angular scales, where quasi-linear effects are important. The average mass of halos contributing to the observed clustering is found to be 6.2 x 10^{11} M_\odot and the characteristic mass of a parent halo hosting satellite galaxies is 1.2 \times 10^{12} M_\odot for a limiting absolute magnitude of -20.5 at z=4. For a given threshold luminosity these masses decrease with increasing z and at any given z these are found to increase with increasing value of threshold luminosity. We find that approximately 40 % of the halos above a minimum mass M_{min}, can host detectable central galaxies and about 5-10 % of these halos are likely to also host a detectable satellite. The satellites form typically a dynamical timescale prior to the formation of the parent halo. The small angular scale clustering is due to central-satellite pairs and is quite sensitive to changes in the duration of star formation in a halo. The present data favor star formation in a halo lasting typically for a few dynamical time-scales. Our models also reproduce different known trends between parameters related to star formation.Comment: Accepted for publication in MNRA

Geometrical tests of cosmological models. III. The cosmology-evolution diagram at z=1

The rotational velocity of distant galaxies, when interpreted as a size (luminosity) indicator, may be used as a tool to select high redshift standard rods (candles) and probe world models and galaxy evolution via the classical angular diameter-redshift or Hubble diagram tests. We implement the proposed testing strategy using a sample of 30 rotators spanning the redshift range 0.2<z<1 with high resolution spectra and images obtained by the VIMOS/VLT Deep Redshift Survey (VVDS) and the Great Observatories Origins Deep Survey (GOODs). We show that by applying at the same time the angular diameter-redshift and Hubble diagrams to the same sample of objects (i.e. velocity selected galactic discs) one can derive a characteristic chart, the cosmology-evolution diagram, mapping the relation between global cosmological parameters and local structural parameters of discs such as size and luminosity. This chart allows to put constraints on cosmological parameters when general prior information about discs evolution is available. In particular, by assuming that equally rotating large discs cannot be less luminous at z=1 than at present (M(z=1) < M(0)), we find that a flat matter dominated cosmology (Omega_m=1) is excluded at a confidence level of 2sigma and an open cosmology with low mass density (Omega_m = 0.3) and no dark energy contribution is excluded at a confidence level greater than 1 sigma. Inversely, by assuming prior knowledge about the cosmological model, the cosmology-evolution diagram can be used to gain useful insights about the redshift evolution of the structural parameters of baryonic discs hosted in dark matter halos of nearly equal masses.Comment: 14 pages and 11 figures. A&A in pres

The Rising Star-Formation Histories of Distant Galaxies and Implications for Gas Accretion with Time

Distant galaxies show correlations between their current star-formation rates (SFRs) and stellar masses, implying that their star-formation histories (SFHs) are highly similar. Moreover, observations show that the UV luminosities and stellar masses grow from z=8 to 3, implying that the SFRs increase with time. We compare the cosmologically averaged evolution in galaxies at 3 < z < 8 at constant comoving number density, n = 2 x 10^-4 Mpc^-3. This allows us to study the evolution of stellar mass and star formation in the galaxy predecessors and descendants in ways not possible using galaxies selected at constant stellar mass or SFR, quantities that evolve strongly in time. We show that the average SFH of these galaxies increase smoothly from z=8 to 3 as SFR ~ t^alpha with alpha = 1.7 +/- 0.2. This conflicts with assumptions that the SFR is either constant or declines exponentially in time. We show that the stellar mass growth in these galaxies is consistent with this derived SFH. This provides evidence that the slope of the high-mass end of the IMF is approximately Salpeter unless the duty cycle of star formation is much less than unity. We argue that these relations follow from gas accretion (either through accretion or delivered by mergers) coupled with galaxy disk growth under the assumption that the SFR depends on the local gas surface density. This predicts that gas fractions decrease from z=8 to 3 on average as f_gas ~ (1+z)^0.9 for galaxies with this number density. The implied galaxy gas accretion rates at z > 4 are as fast and may even exceed the SFR: this is the "gas accretion epoch". At z < 4 the SFR overtakes the implied gas accretion rate, indicating a period where galaxies consume gas faster than it is acquired. At z < 3, galaxies with this number density depart from these relations implying that star formation and gas accretion are slowed at later times.Comment: Accepted for publication in MNRAS. 13 pages, 7 figures. Comments welcome. Updated with MNRAS-accepted versio