Abstract:
Groundnut is the most important legume in Ghana. The crop is grown in all the agroecologies in the country; from the dry savannah regions to the moist forest areas. Several food preparations incorporate groundnut to improve the protein level, taste and flavour. Despite the importance of the crop, the chemical compositions of the varieties grown by farmers have not been analyzed according to their nutritional quality. Oil, fatty acids, protein, oleic/linoleic (O/L) acid ratio, iodine value and free soluble sugars were studied in 20 groundnut varieties grown in Ghana to determine their nutritional quality and to inform endusers which variety to choose for maximum benefit. Results indicated a significant difference (p<0.05) in oil content among the varieties. Oil content ranged from 33.60 to 54.95%. Mean oil content of the subspecies hypogaea (49.7%) was higher than in subspecies fastigiata (47.3%). The major fatty acids were oleic and linoleic which accounted for 77.89% of the total fatty acids. The subspecies hypogaea had significantly higher (p<0.01) content of oleic acid (55.9%) than the subspecies fastigiata (43.3%). The sum of three fatty acids oleic, linoleic and palmitic acid constitute 89.35% of the total fatty acids of the seeds. The mean O/L ratio ranged from 1.14 to 3.66; the mean for subspecies hypogaea was 2.59 as compared to 1.28 for subspecies fastigiata. There was high correlation between oleic and O/L acid ratio (r2=0.983) and negative correlation between oleic acid and linoleic acid (r2=-0.996). The iodine value ranged from 85.77 to 98.43% and total soluble sugars from 9.20 to 13.30%. Protein of defatted portion ranged from 39.65 to 53.45%. Subspecies fastigiata had higher mean protein content than subspecies hypogaea. Generally, there were significant variations in the parameters measured in the groundnut varieties. Five varieties with O/L ratio more than 2.0 were identified and their oils would be further tested for their stability.

Abstract:
Groundnut production and utilization in Ghana has tripled in the last decade due to its high nutritive value and the number of uses it can be put into. The chemical quality of seeds of Ghanaian groundnut are different from those of other countries, however, no previous studies has been done. This study was initiated to examine the nutritional quality of 20 groundnut varieties grown in Ghana. Dry samples were examined for oil content, crude protein, total carbohydrate, calcium, potassium, magnesium, sodium, zinc, copper, iron and manganese. Results from these analyses showed significant variation between the parameters measured. Virginia cultivars which belong to subspecies hypogaea had higher oil content (49.7%) than the Spanish and Valencia market types, which belong to subspecies fastigiata (47.3%). The mean protein content of subspecies fastigiata was however higher (25.69%) than subspecies hypogaea (22.78%). The mineral elements examined were substantial in reducing malnutrition especially in young and growing children. Broni fufuo, a Spanish market type had the highest crude protein content (30.53%) and the least oil content (33.60%) and is idea for products which require more protein and less oil. Substantial genetic variability exists for chemical composition and nutritional traits which could be utilised for various food preparations and selection for breeding purpose.

Abstract:
The velocity of perihelion rotation of Mercury's orbit relatively motionless space is computed. It is prove that it coincides with that calculated by the Newtonian interaction of the planets and of the compound model of the Sun’s rotation.

Abstract:
Ion beam deceleration properties of a newly developed low-energy ion beam implantation system were studied. The objective of this system was to produce general purpose low-energy (5 to 15 keV) implantations with high current beam of hundreds of μA level, providing the most wide implantation area possible and allowing continuously magnetic scanning of the beam over the sample(s). This paper describes the developed system installed in the high-current ion implanter at the Laboratory of Accelerators and Radiation Technologies of the Nuclear and Technological Cam-pus, Sacavém, Portugal (CTN).

Abstract:
If the augmented density of a spherical anisotropic system is assumed to be multiplicatively separable to functions of the potential and the radius, the radial function, which can be completely specified by the behavior of the anisotropy parameter alone, also fixes the anisotropic ratios of every higher-order velocity moment. It is inferred from this that the non-negativity of the distribution function necessarily limits the allowed behaviors of the radial function. This restriction is translated into the constraints on the behavior of the anisotropy parameter. We find that not all radial variations of the anisotropy parameter satisfy these constraints and thus that there exist anisotropy profiles that cannot be consistent with any separable augmented density.

Abstract:
This paper presents a set of new conditions on the augmented density of a spherical anisotropic system that is necessary for the underlying two-integral phase-space distribution function to be non-negative. In particular, it is shown that the partial derivatives of the Abel transformations of the augmented density must be non-negative. Applied for the separable augmented densities, this recovers the result of van Hese et al. (2011).

Abstract:
Under the separability assumption on the augmented density, a distribution function can be always constructed for a spherical population with the specified density and anisotropy profile. Then, a question arises, under what conditions the distribution constructed as such is non-negative everywhere in the entire accessible subvolume of the phase-space. We rediscover necessary conditions on the augmented density expressed with fractional calculus. The condition on the radius part R(r^2) -- whose logarithmic derivative is the anisotropy parameter -- is equivalent to R(1/w)/w being a completely monotonic function whereas the condition on the potential part is stated as its derivative up to the order not greater than 3/2-b being non-negative (where b is the central limiting value for the anisotropy parameter). We also derive the set of sufficient conditions on the separable augmented density for the non-negativity of the distribution, which generalizes the condition derived for the generalized Cuddeford system by Ciotti & Morganti to arbitrary separable systems. This is applied for the case when the anisotropy is parameterized by a monotonic function of the radius of Baes & Van Hese. The resulting criteria are found based on the complete monotonicity of generalized Mittag-Leffler functions.

Abstract:
An axially symmetric potential psi(R,z)=psi(r,theta) is completely separable if the ratio s:k is constant. Here r*s=d^2(r^2*psi)/dr/d(theta) and k=d^2(psi)/dR/dz. If beta=s/k, then the potential admits an integral of the form of I=(L^2+beta*v_z^2)/2+xi where xi is some function of positions determined by the potential psi. More generally, an axially symmetric potential respects the third axisymmetric integral of motion -- in addition to the classical integrals of the Hamiltonian and the axial component of the angular momentum -- if there exist three real constants a,b,c (not all simultaneously zero, a^2+b^2+c^2>0) such that a*s+b*h+c*k=0 where r*h=d^2(r*psi)/d(sigma)/d(tau) and (sigma,tau) is the parabolic coordinate in the meridional plane such that sigma^2=r+z and tau^2=r-z.

Abstract:
The lipid hypothesis of coronary heart disease proposes that a high total cholesterol level has a causative role in coronary heart disease (CHD), specifically in the development of atherosclerosis. It forms the basis for formulating target levels of serum cholesterol and hence the widespread use of statins for lowering cholesterol. An extension of the lipid hypothesis is the diet/heart hypothesis of coronary heart disease. This theory combines two ideas—that saturated fat raises cholesterol levels, and that a reduced saturated fat intake will lower cholesterol levels, thereby inhibiting the development of atherosclerosis and manifestations of CHD. Those who make diet recommendations or prescribe medication to reduce cholesterol may be unaware of the underpinning science. The original research behind these recommendations has given us “healthy heart” guidelines and preventive measures we assume to be true. While the lipid and diet/heart hypotheses are often presented as fact, they remain inadequately proven theories that have little agreement from experts. Historical perspectives can help us understand the basis of current-day beliefs. In the lipid hypothesis case, research from the 1950s and 60s was instrumental in its formation. This early work should not be considered irrelevant, outdated or obsolete because current recommendations from national heart associations in many countries continue to be shaped by these studies. This paper examines evidence used to formulate the lipid hypothesis and, subsequently, the diet/ heart hypothesis. By critically evaluating steps in the formation of the theory, inconsistencies, mistakes and alternate explanations become apparent and cast doubt on its validity.

The paper does not meet the standards of
\"American Journal of Computational Mathematics\".

This article has been retracted to
straighten the academic record. In making this decision the Editorial Board
follows COPE's Retraction Guidelines. The aim is
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Editor guiding this retraction: Prof. Hari
M. Srivastava (EiC of AJCM)

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