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
to promote the circulation of scientific research by offering an ideal research
publication platform with due consideration of internationally accepted
standards on publication ethics. The Editorial Board would like to extend its
sincere apologies for any inconvenience this retraction may have caused.

Editor guiding this retraction: Prof. Hari
M. Srivastava (EiC of AJCM)

The full
retraction notice in PDF is
preceding the original paper, which is marked \"RETRACTED\".

Abstract:
The least massive fermion generation is attributed to an analogue of Weyl curvature which occurs when a closed, spin-string sweeps out a closed world tube: , where S represents string length. A second order tube and consequent second order fermion mass are associated with a closed tube which circulates and itself sweeps out a closed tube: . Finally a K^{th} order tube and kth order fermion generation are associated with the general expression . By hypothesis six world tube orders establish an SU(3) symmetry and each closed tube interacts with a SUGRA connection of spin-. Such connections can either be photon-fermion composites or composites that consist strictly of fermions. Interactions that involve no photons are, by hypothesis unobserved and are therefore associated with closed world tubes that are classified as dark mass-energy. It is demonstrated that interactions involving ordinary mass-energy are identities (e.g. interactions that are incapable of generating the proposed SU(3) symmetry). It is therefore concluded that dark mass-energy is a necessary condition for the SU(3) symmetry that by hypothesis characterizes the proposed model. Since 95% of the mass-energy in the universe is regarded as dark, the total mass-energy that constitutes the proposed SU(3) symmetry can be calculated as , where Q_{L} is a left-handed quark, where Ψ_{L} is a left-handed spin particle and where is a right-handed anti-lepton. Thus the mass-energy that is associated with the wave is about 10^{67} GeV/c^{2} (the approximate mass of a typical galaxy). This wave is regarded by hypothesis as a single galactic unit and as the ground state of a large-scale quantization; i.e. as the ground state of a series of abstract waves which mimic de Broglie waves in the sense that the ground state is a wave of one anti-node which oscillates about